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Lighthouse Math Practice book level D • ISBN 978-1-955773-17-1
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Review 1
In Review 1, we will review
In Review 1, we will review
Addition, Subtraction, Multiplication, Division
Addition, Subtraction, Multiplication, Division
Students will review number sense skills related to the four operations and practice facts to gain fluency.
• Round and estimate
Students will review number sense skills related to the four operations and practice facts to gain fluency.
• Relate addition and subtraction
• Round and estimate
• Addition and subtraction with regrouping
• Relate addition and subtraction
• Represent and solve multiplication and division facts
• Addition and subtraction with regrouping
• Relate multiplication and division
• Represent and solve multiplication and division facts
• Relate multiplication and division
We can round numbers to estimate sums and differences.
We can round numbers to estimate sums and differences.
We can use properties of operations to find missing addends or factors.
We can add and subtract using regrouping.
We can use multiple strategies to multiply and divide.
We can use properties of operations to find missing addends or factors.
We can add and subtract using regrouping. We can use multiple strategies to multiply and divide.
Round numbers to the correct place value and add or subtract.
Round to the nearest ten.
Round each number to the highest place value and add.
Remember: 5 and higher rounds up 4 and lower rounds down
Round to the nearest hundred.
Round each number to the highest place value and then add or subtract.
192 to the nearest ten: 178 to the nearest hundred:
Round each number to the highest place value and then add or subtract.
This week, 4,675 students had hot lunches, and 2,388 students brought their own lunches. About how many students are there in all? Estimate to the nearest hundred before solving.
On Tuesday, 231 students chose the pizza option, and 119 students chose the peanut butter and jelly option for lunch. About how many more students chose pizza than peanut butter and jelly? Round to the nearest ten before solving.
Next week, the cafeteria expects to serve 4,590 breakfasts and 7,103 lunches. About how many more lunches than breakfasts do they expect to serve? Round to the nearest hundred before solving.
896 students have lunch at 11:30 am, and 746 students have lunch at 12:00 pm. How many students have lunch in all? Round to the nearest ten before solving.
Find the missing addend using subtraction.
Find the missing addend: 4 + n = 10
Subtraction: 10 - 4 = 6
Missing addend = 6
Identify the property used in each example. 3 + 4 = 4 + 3 3 + 0 = 3
� 5 = 0 5 + 5 = 10 10 5 = 5
+ (8 + 1) = (4 + 8) + 1
+ (3 + 2) = (6 + 3) + 2
Write the subtraction problem that solves for the missing addend.
+ n = 7
Solve for the missing addend.
1. Walter and Tyler tracked how much fruit they ate this week. How much did they eat on Monday, Tuesday, and Wednesday?
3. How much did they eat in all?
2.
How much did they eat on Wednesday, Thursday, and Friday? 4.
The boys go to school Monday to Friday. How many pieces of fruit did they eat on school days?
At school, Carl spent 285 minutes on math this week and 225 minutes on history. How much time did he spend on both subjects?
There are 136 pages in Bill’s reading book and 256 pages in his math book. How many pages are in both books together?
There are 50 pieces of paper in the paper tray. Timothy is the paper passer and hands out 27 pieces to his classmates. How many pieces of paper are left in the paper tray?
Gary wants to plant a garden. He goes to the store and buys plants and seeds for $34. If he gives the cashier $42, how much change will he get?
Today, the librarian checked out 832 books in the morning and 477 in the afternoon. How many more did the librarian check out in the morning?
The librarian the put 395 books away in the children’s section and 176 in the adult’s section. How many books did the librarian put away in all?
There was a special program at the library in the evening. 1,173 people came for the first hour of the program, and 604 came for the second hour of the program. How many more people came during the first hour?
Before leaving for the night, the librarian checked the number of people with library cards. Right now, 4,503 adults had library cards and 2,625 children had a library card. How many more adults had library cards than children?
Solve multiplication problems. Remember: 6 × 3 can be written 6 + 6 + 6 or 3 + 3 + 3 + 3 + 3 + 3
Use your multiplication strategies to find the products.
+ 6 + 6 + 6 + 6
Solve the equations by writing the missing factors or products.
× 3 = 8 × = 32
× 6 = × 6 = 24
× = 18
× 8 = × 7 = 14 × 4 = 40
Christopher is unpacking tools at the hardware store. He unpacks 3 boxes that each have 6 hammers. Write a number sentence to represent the total number of hammers he unpacked.
Christopher is unpacking tools at the hardware store. He unpacks 5 boxes of screwdrivers and finds that there are 20 total. How many screwdrivers were in each box?
Christopher unpacks 7 boxes of nails on Monday, 7 boxes on Tuesday, 7 boxes on Wednesday, and 7 boxes on Thursday. Write a number sentence to represent the total number of boxes he unpacked.
Christopher puts 8 gallons of paint on each shelf. There are 3 shelves. How many gallons of paint are there?
Mr. Jackson is getting tables ready for art classes. He places a cup of 6 pairs of scissors on each of the 6 student work tables. How many scissors did he put out?
Mr. Jackson is getting tables ready for art classes. He sets up 4 watercolor stations. Each station has 8 different tubes of watercolors. How many watercolor tubes are there in all?
Mr. Jackson is getting tables ready for art classes. He puts a pile of paper next to each of the 4 watercolor stations. There are 5 pieces of paper in each pile. How much paper does he put out?
Mr. Jackson is getting tables ready for art classes. He puts 5 pencils at each of the 6 student worktables. How many pencils does he set out in all?
28 kids played chess. Two kids were at each chess board. How many chess boards were needed?
There are 32 pieces on each chess board, which are divided among the two players. How many pieces does each player get?
Four friends are playing cards. There are 52 cards in the deck. If they divide the cards up evenly, how many does each player get?
A game has 48 playing pieces. If six friends are playing the game and divide the pieces evenly, how many pieces would each friend get?
Complete each fact family.
Write each group of numbers as multiplication and division problems.
Noah placed 6 chairs around 9 tables. How many chairs were there in all?
If the 27 students were divided into 3 teams, how many were on each team?
Jonathan placed 8 cupcakes on each plate. If he made 32 cupcakes, how many plates did he fill?
Eric ran 6 laps around the school each day. How many laps did he run in 6 days?
Review 2
In Review 2, we will review
In Review 2, we will review
Word Problems and Fractions
Word Problems and Fractions
Students will gain fluency in solving word problems and deepen their understanding of fractions. This will prepare them for more advanced problem solving and decimal work in level D.
Students will gain fluency in solving word problems and deepen their understanding of fractions. This will prepare them for more advanced problem solving and decimal work in level D.
• Divide with single-digit divisors
• Problem solve
• Divide with single-digit divisors
• Find perimeter and area
• Problem solve
• Write and model fractions
• Find perimeter and area
• Find equivalent fractions
• Write and model fractions
• Compare and order fractions
• Find equivalent fractions
• Compare and order fractions
We can use arrays to show division and multiplication to check our work.
We can use arrays to show division and multiplication to check our work.
We can solve one-step word problems with all four operations.
We can solve one-step word problems with all four operations.
We can find the perimeter of any shape and the area of a rectangle.
We can visualize and write fractions.
We can find the perimeter of any shape and the area of a rectangle.
We can find equivalent fractions with a model and multiplication or division.
We can visualize and write fractions.
We can find equivalent fractions with a model and multiplication or division.
We can compare and order fractions using number lines and models.
We can compare and order fractions using number lines and models.
Use multiplication facts to solve division problems.
Remember: Division problems can be written two ways.
Since 6 × 4 = 24, the answer is 4.
Draw an array and write the multiplication fact that relates to each division problem.
Edward has 24 treats he wants to share evenly with his 4 cats. How many treats should he give each cat?
Jack places 3 fish in a fish bowl. He has 21 fish. How many fish bowls can he fill?
Bruce spent ten minutes practicing the piano every day. How many days will it take him to practice the piano 120 minutes?
Louis has 54 special rocks that he wants to display in 9 different boxes, with the same number in each box. How many rocks should he put in each box?
Solve one-step word problems.
A green box has 6 coins. A red box has 4 coins. How many coins are there in total?
6 + 4 = 10
10 coins
Hint: “In total” means use addition to solve.
Draw a line from the keyword to the operation that it represents.
Combined
a. Division Product b. Subtraction Difference
c. Addition Split Apart d. Multiplication
Solve the following problem using the CUBES strategy.
5. Moses has read 27 books, and Jamie has read 3 fewer. How many books has Jamie read?
Circle the numbers in the problem above.
6. Rebecca is making cupcakes for the bake sale. If her baking pans hold 8 cupcakes and she has 4 pans, how many cupcakes can she bake altogether?
Circle the numbers in the problem above.
7. Eitan is hoping to reach 100 hours of reading. If he read 24 hours last month and 31 hours this month, how many hours has he read in total?
Circle the numbers in the problem above.
Underline the question. Underline the question. Underline the question. Box the key words and write the operation below.
Eliminate what you don’t need.
Box the key words and write the operation below.
Box the key words and write the operation below.
Eliminate what you don’t need. Eliminate what you don’t need.
Solve. Solve. Solve.
Does your answer make sense?
Does your answer make sense? Does your answer make sense?
Richard picks 92 apples from his apple tree in the morning. His little brother picks 56 apples from the tree that afternoon. How many more apples did Richard pick than his brother?
William is growing flowers. He has 7 flower bulbs in each pot. He plants 8 pots of flowers. How many flowers will he have altogether if all the bulbs bloom?
Rick has 24 stamps in his collection, and his sister Deborah has 57 stamps in her collection. How many stamps do they have combined?
There are 45 balloons at a party. If there are 9 guests and each gets the same number of balloons, how many balloons will each guest receive?
Identify each polygon and write its name on the line below.
Add down each column. Then, check each column by adding up.
Find the perimeter for each shape below.
Kane is building a new fence for his garden. His current garden is too small. He wants to build a garden that is 30 meters wide and 45 meters long. How much fencing will he need to build the garden?
Ben wants to put twinkle lights around the ceiling of his room. If his room is a perfect square, with each side measuring 12 feet, how long of a string of twinkle lights does he need to buy to go all the way around his room?
Solomon is making a picture frame for his school picture. If his picture measures 8 inches wide by 10 inches high, what length of wood will he need to buy to create a simple picture frame?
Tom is building a horse corral for his new horse. The corral will be shaped like a perfect octagon. Each side will measure 12 yards. How much fencing will Tom need to build the corral?
Find areas of rectangles using repeated addition or multiplication.
Find the areas of the shapes below.
Length: Width: Area Equation (Add): Area:
Length: 5 units Width: 5 units
Area Equation (Add): Area: Length: Width: Area Equation (Multiply): Area:
Length = 3
With = 2
Length: Width: Area Equation (Multiply): Area:
Solve the repeated addition equations.
Use the grids below to draw rectangles with the target areas. Use the given lengths to find the correct widths. 6 + 6 + 6 + 6 = Area: 10 sq. units Length: 5 units Width:
Richard is planting grass in his yard. His yard is 12 meters by 5 meters. What is the area of Richard’s yard that he needs to plant?
The Becker Family is looking for a new carpet for their living room. The room is 10 feet by 8 feet. What is the area of the carpet they need to cover their living room floor?
Justin designed a flag that is 9 inches wide and 5 inches high. What is the area of Justin’s flag?
Joseph is painting a wall. He has painted 40 square feet of the wall. If one side of the wall is 8 feet, what is the length of the other side?
Represent fractions as words and pictures.
Write the following as a fraction and draw a picture: three fourths
Shade in each picture to show the fraction given.
Complete the chart to represent each fraction.
There are 12 muffins in the oven. If 4 of them burn, what fraction of the muffins are burnt?
There are 12 muffins in the oven. If 4 of them burn, what fraction of the muffins are not burnt?
Jack puts 5 muffins on the table. He later eats 2 for snack. What fraction of the muffins on the table did he eat?
Jack is now thirsty and drinks half of the milk that was left. What fraction represents the amount of milk he drank?
Represent fractions using pictures as part of a whole and using unit fractions. Represent 3 5 as a set, as a whole, and using unit fractions.
Shade in the correct amount to represent each fraction as a set and as a whole.
Circle the pictures with the same fractions. Write out the unit fraction
Justin’s mom made him cupcakes when he arrived home from school. Based on the set below, what is the fraction to represent the amount of cookies that Justin ate?
David ate 3 7 of his pizza. What fraction does he have left? Draw a picture to support your answer.
Charlie is drawing a part of a set to represent 1 8 . Look at his representation below. Is he correct? If not, what mistake did he make?
Lisa and her little sister Kayla were working to meet the fundraising goal for the local library. Lisa has met 4 5 of her fundraising goal. Kayla has met 2 3 of her fundraising goal. Who is closer to reaching their goal? Use the fraction bars to help you compare.
Lisa Kayla
Color the bars to show equivalent fractions, then write the equivalent fraction.
Complete the equivalent fractions.
Gabriel and Douglas made identical pizzas but cut them into different size pieces. They want to eat the same amount. If Gabriel cut his pizza into 7 pieces and ate 3, would that be the same amount as if Douglas cut his into 14 pieces and ate 5?
Gabriel and Douglas made identical pizzas but cut them into different size pieces. They want to eat the same amount. If Gabriel cut his pizza into 8 pieces and ate 5, would that be the same amount as if Douglas cut his into 16 pieces and ate 10?
Gabriel and Douglas made identical pizzas but cut them into different size pieces. They want to eat the same amount. Gabriel cut his pizza into 3 large slices and ate 1. If Douglas cut his into 6 slices, how many should he eat?
Gabriel and Douglas made identical pizzas but cut them into different size pieces. They want to eat the same amount. Gabriel cut his pizza into 4 slices and ate 3. If Douglas cut his into 8 slices, how many should he eat?
Denominators are the same. The fraction with the larger numerator is larger.
Place the fractions on the number line.
Compare the following fractions using <, >, or =.
Numerators are the same. The fraction with the smaller denominator is larger.
Put each group of fractions in order from least to greatest.
are
Randy and Nathan are watering plants. Randy gave a tomato plant 1 2 gallon of water, and Nathan gave a pepper plant 2 5 of a gallon of water. Which plant received more water?
Randy and Nathan are watering plants. Randy gave a pumpkin plant 2 3 gallon of water, and Nathan gave a watermelon plant 3 6 of a gallon of water. Which plant received more water?
Randy’s tomato plant grew 7 8 of an inch this week, and Nathan’s pepper plant grew 3 4 of an inch. Which plant grew more?
Randy spent 1 3 of an hour weeding his garden today, and Nathan spent 2 9 of an hour. Which boy spent less time weeding today?
Chapter 1
In Chapter 1, we review and learn about
Place Value, Rounding, Patterns with Rules
In Chapter 1, we review and learn about
Place Value, Rounding, Patterns
with Rules
Place Value Skills are important for understanding how to compose and decompose numbers, round, compare numbers, and do operations with numbers.
Place Value Skills are important for understanding how to compose and decompose numbers, round, compare numbers, and do operations with numbers.
• Place value to the millions
• Place value to the millions
• Place value with expanded form
• Patterns in place value
• Place value with expanded form
• Patterns in place value
• Comparing and ordering whole numbers
• Rounding whole numbers
• Comparing and ordering whole numbers
• Number patterns
• Rounding whole numbers
• Number patterns
We can name place values up to the millions.
We can write numbers in different forms.
We can name place values up to the millions.
We can write numbers in different forms.
We can use place value to help us compare and order numbers.
We can round numbers to the indicated place value.
We can use place value to help us compare and order numbers.
We can analyze patterns.
We can round numbers to the indicated place value.
We can analyze patterns.
Use place value to the millions place.
Write the place value of the underlined digit.
Write these numbers in standard form.
five million, seven hundred twenty-three thousand, eighty-two
one million, nine hundred thousand, six hundred forty-two
two million, seventy-four thousand, one hundred sixty
Write the value of each number.
five hundred thirty-eight thousand, two hundred forty-three 169,452
What is the value of the number 4?
What is the value of the number 1?
Read as: nine million, eight hundred twenty-six thousand, six hundred seventy-two
What is the value of the number 8?
What is the value of the number 6? 1,708,234
What is the value of the number 1? What is the value of the number 3?
Jason is learning about the blue whale. He found out that the largest blue whale weighed 418,878 pounds. What is the place value of the 1 in this number?
Jason is learning about the blue whale. He found out that the largest blue whale weighed 418,878 pounds. What is the value of the 4 in this number?
Jason found out that blue whales eat about 15,360,000 ounces of food a year. What is the place value of the 1 in this number?
Jason found out that blue whales eat about 15,360,000 pounds of food a year. What is the value of the 5 in this number?
Use standard and expanded form of numbers. Use zeros to fill in the place values after the number down to the ones place.
Write the value of each digit in each number.
Write these numbers in standard form.
300,000 + 20,000 + 3,000 + 400 + 80 + 6
1,000,000 + 30,000 + 8,000 + 500 + 20 + 7
5,000,000 + 600,000 + 2,000 + 400 + 30 + 1 5,138 5 1 3 8 362,518 = 300,000 + 60,000 + 2,000 + 500 + 10 + 8 47,612 4 7 6 1 2 315,692 3 1 5 6 9 2
Write these numbers in expanded form.
100,452 1,708,200
5,130,068
Last year, Ethan drank 2,920 ounces of milk. What is this number written in expanded form?
Last year, Ethan drank 2,920 ounces of milk. How is the value of the 2 on the left different from the value of the 2 on the right?
Jonesville has 53,619 residents. Write this number in expanded form.
Jonesville has 700+40+9 dogs. Write this number in standard form.
Use multiplication patterns in place value.
Write the number and the word.
Example: 30 × 10 = 300, three hundred
5 × 10 = ,
40 × 10 = ,
200 × 10 = , 30 × 10 = 300 three hundred 4,000 × 10 = 40,000 forty thousand
80 × 10 = , 500 × 10 = , 1,000 × 10 = ,
Write the equation that matches the underlined number.
Example: 1,4 32,687 40,000 × 10 = 400,000
Write the place value of the 3.
Example: 1,432,687 ten thousands
Write these numbers in written form.
Example: 5,300,245 five million, three hundred thousand, two hundred forty-five
5,295,436 4,083,127 201,084 3,726,298 6,834,741 8,967,321 1,708,200 5,130,068 6,104,208 1,473,169 5,328,714 4,567,231 807,104 3,450,610 1,000,829
George lives near the big city, which has 5,601,944 residents. Write this number in written form.
George lives near the big city, which has 5,601,944 residents. What is the place the 6 is in? What is the value?
Plates cost $10 each. The principal is thinking about buying some for the school cafeteria. How much would 4 plates cost? How much would 40 plates cost? How much would 400 plates cost?
If there are 300 pencils in each classroom and 10 classrooms in the building, how many pencils are in the building?
Compare numbers. Which number is larger?
Compare place values starting with the largest.
Compare the following numbers using <, >, or =.
Order the following groups of numbers from greatest to least.
68; 86; 89 ; ; 6,129; 9,126; 6,921; 6,291 ; ; ; 460,125; 406,125; 604,125 ; ; 423; 432; 234; 324 ; ; ; 460,125; 406,125; 604,125 ; ; 273,540; 273,045; 273,450
At the fruit orchard, there are 273 apple trees and 237 pear trees. Which type of tree does the orchard have more of?
On Monday, David picks 791 apples. On Tuesday, he picks 778 apples. On which day did he pick more?
The world’s largest pizza was made from 9,920 pounds of flour, 3,960 pounds of cheese, 1,762 pounds of mushrooms, and 1,984 pounds of tomato puree. Put these in order from the least to greatest weight.
Douglas took five tests and received the following grades: 73, 88, 92, 85, 96. Put these in order from greatest to least.
Round numbers to the given place value.
Round to the nearest ten thousand. 367,899 6 is in the ten thousands place. Look one place right. 7 is bigger than 5, so round up. 370,899.
Round to the nearest millions. 8,672,100 6,423,299 4,199,567 3,916,888
Round to the nearest hundred thousands. 6,827,145 4,493,822 1,910,423 3,516,285 5. 6.
Remember: 5 and above, round up 4 and below, round down
Round to the nearest ten thousands.
to the nearest thousands.
There are 48,678,219 miles between Earth and the planet Mars. Round this number to the nearest millions place.
There are 48,678,219 miles between Earth and the planet Mars. Round this number to the nearest ten thousands place.
There are 56,974,146 miles between Earth and the planet Mercury. Round this number to the nearest hundred thousands place.
There are 56,974,146 miles between Earth and the planet Mercury. Round this number to the nearest thousands place.
Identify numbers based on place value descriptions.
Write a number with a 4 in the tens place, 1 less ones than tens, the same amount of hundreds as tens, and twice as many thousands as hundreds:
Circle the numbers with a 3 in the tens place, and put a rectangle around the numbers with a 3 in the thousands place.
A. 3 ten-thousands, 3 times as many thousands as ten-thousands, one more hundred than ten-thousands, 2 less tens than hundreds, and one less one than tens
B. 7 more thousands as hundreds, one less hundreds and tens as ones, and 3 ones
C. One more thousands than tens, 5 more hundreds than tens, 4 tens and one more ones than tens
D. 3 thousands, 2 more hundreds than thousands, twice as many tens as thousands, and 2 more ones as tens
E. 1 hundred-thousands, one more tens than hundredthousands, one more hundreds than tens, three times the amount of one thousands and ones than hundreds
F. 1 less ten-thousands than thousands, 2 thousands, the same amount of hundreds and tens as ten-thousands, and nine times as many ones as hundreds
What four-digit number has a 9 in the thousands place, 5 less in the hundreds place, one less in the tens than hundreds, and 2 less in the ones than tens?
What five-digit number has three times as many ten-thousands as thousands, 6 thousands, 2 fewer hundreds than thousands, and twice as many tens as hundreds?
Write a problem using place value clues to find the mystery number 2,459.
Write a problem using place value clues to find the mystery number 109,345.
Identify number patterns.
Identify the rule and determine the next number:
40, 20
Rule: Divide by 2 Next number: 10
Count the number of dots in each step, find the pattern, and then find the number of dots in the fifth step. Write the rule. Complete each table using the rule.
Add 9 3, 6, 12, 24, 48, 96
85, 70, 55, 40, 25
51, 58, 65, 72, 79
Mr. Stark was setting up chairs for the school assembly. He realized that there were 4 chairs in the first row, 6 chairs in the second row, 8 chairs in the third row, and 10 chairs in the fourth row. If the pattern continues, how many chairs will be in the sixth row?
Frank loves to read. He is trying to double the amount of time he reads each month. In January, he read 15 minutes. How many minutes will he read in June? Write the number pattern and solve.
Mike loves growing beans in his garden. He started with 42 plants and adds 8 more bean plants each year. How many bean plants will he have in his garden after 5 years?
The school was getting ready for an open house. They were setting up chairs in the library. There were 12 chairs in the first row, 15 chairs in the second row, 18 chairs in the third row, and 21 chairs in the fourth row. If the pattern continues, how many chairs will be in the eighth row?
Write the place value of the underlined digit.
6,542,321
Millions place
Compare the following numbers using <, >, or =.
Line up place values
9,424 ← greater 9,242
< - less than > - greater than = - equal to
Order the following groups of numbers from least to greatest.
437; 473; 347 ; ; 18,418; 18,481; 18,841; 18,814 ; ; ; 11. 12.
Round to the highest place value.
Round up when the digit to the right is 5 or more.
9,824 → 10,000
Round down when the digit to the right is 4 or less.
9,424 → 9,000 2,865,724
On Thursday, Danny ate 1,794 calories, and his brother Brian ate 1,907 calories. Which boy ate more calories?
Bruce weighed five cows and found that they were 1,306, 1,760, 1,396, 1,540, and 1,670 pounds. Put the weights in order from least to greatest.
A farmer farms 473,985 acres. What is the place value of the 7?
This year, the farmer grows 3,776,910 bushels of wheat. Round this number to the largest place value.
Chapter 2
Chapter 2
In Chapter 2, we will expand on
In Chapter 2, we will expand on
Addition and Subtraction with Large Numbers
Addition and Subtraction with Large Numbers
We will apply our knowledge of addition and subtraction and work with larger numbers.
• Estimate sums and differences
We will apply our knowledge of addition and subtraction and work with larger numbers.
• Addition and subtraction to the millions place
• Estimate sums and differences
• Input and output tables with addition and subtraction
• Addition and subtraction to the millions place
• Finding missing digits
• Input and output tables with addition and subtraction
• Solving word problems
• Finding missing digits
• Solving word problems
We can quickly estimate sums and differences by rounding to any place value.
We can quickly estimate sums and differences by rounding to any place value.
We can add and subtract large numbers, including subtracting across zeros.
We can add and subtract large numbers, including subtracting across zeros.
We can write rules and find missing values in input and output tables.
We can write rules and find missing values in input and output tables.
We can use the relationship between addition and subtraction to find missing digits in addition and subtraction problems.
We can use the relationship between addition and subtraction to find missing digits in addition and subtraction problems.
We can write equations and solve addition and subtraction word problems.
We can write equations and solve addition and subtraction word problems.
Estimate to solve addition and subtraction problems.
Estimate the sum by rounding to the nearest hundred. Remember: 5 and above, round up 4 and below, round down
Estimate the sum or difference by rounding to the nearest hundred.
Estimate the sum or difference by rounding to the nearest thousand.
1,553 + 9,825
Estimate the sum or difference by rounding to the nearest ten thousand. 329 + 467
+ 95,632
+ 4,588
− 4,965
+ 162,485
Bus #19 carried 1,280 people today. Bus #2 carried 1,029 people today. About how many people did they carry together? Round to the nearest hundred and solve.
Christopher has 265 newspapers to deliver. He has delivered 189 so far. About how many more newspapers does he need to deliver? Round to the nearest hundred and solve.
Mount Everest is 29,029 feet tall. Mount Elbrus is 18,510 feet tall. About how tall are they together? Round to the nearest thousand and solve.
The deepest part of the ocean is 35,814 feet deep. The deepest lake is 5,387 feet deep. How much deeper is the ocean? Round to the nearest thousand and solve.
12,781 + 68,023
Add, regrouping if necessary.
Regroup the 13: Put the 3 in the ones place and the 1 above the tens place. Regroup the 11: Put the 1 in the tens place and another 1 above the hundreds place. 1 1 237 + 376 613
+ 207 394,258 + 5,975 63,209 24,222 + 5,816 492,213 + 2,568 6,782 + 574 497,315 152,352 + 49,241 2,828 + 795 682,152 + 41,774 875,134 633,321 + 78,111
Set up the addition problems, then add.
625 + 64 = 927 + 193 =
9,587 + 781 = 23,548 + 5,817 =
+ 322,711 = 55,320 + 9,545 598,346 + 34,945
33,678 + 29,422 + 8,124 =
In 2010, a city had 757,890 citizens. In 2020, the city had 203,145 more citizens. How many citizens did it have in 2020?
There were 145,965 gallons of water in the sting ray tank and 87,597 gallons in the penguin exhibit. How many gallons of water were in both exhibits?
A large zoo had 734,590 visitors last year and 602,184 visitors this year. How many visitors came in all?
The Lopez family has two cars. The older car has driven 213,785 miles. The newer car has driven 16,450 miles. How many miles have the two cars driven together?
Subtract with regrouping and check using addition.
Solve each subtraction problem.
Regroup by taking one from the tens place to make 10 in the ones place and by taking one from the hundreds place to make 10 in the tens place.
Rewrite and subtract. Check your answers using addition.
There are 1,000 tickets for a show. If 726 tickets have already been sold, how many are left?
There are 300 seats in the auditorium. Right now, 186 seats are taken. How many seats are still empty?
The school is hoping to raise $2,000 with this play. If they have made $997 so far, how much more do they need to make?
1,200 programs were printed for the show. If 894 have been given out, how many programs are left?
Subtract large numbers using regrouping and check with addition.
Subtract and check with addition.
1. Subtract. Check. 7,846 289
5. Subtract. Check.
Set up the subtraction problems and solve.
2. Subtract. Check.
7,534 4. Subtract. Check.
= 3. Subtract. Check.
6. Subtract. Check.
456 51 = 9. 149,230 79,485 = 11. 5,382,277 387,249 =
507 282 =
In one state, 970,845 acres of corn were planted. Because it was so dry, only 889,024 acres of corn grew. How many acres of corn did not grow?
An airport had 429,355 visitors this year. Last year, it had 49,380 less visitors. How many visitors did it have last year?
A school district had 4,768 students. 810 students were in high school. How many students were not in high school?
A farmer has prepared 175,900 pounds of food for his animals this winter. If he has used 108,288 pounds so far, how much food does he have left?
Find the rule for input and output tables and use it to fill in the missing numbers.
Write the rule, then fill in the missing numbers.
Write the rule, then fill in the missing numbers.
3 + 3 = 6
5 + 3 = 8
Rule = Add 3
Missing numbers: 9 + 3 = 12 20 + 3 = 23
in the missing numbers.
Find missing digits in addition problems.
5 + 8 = 13, so the first missing digit is 5. 1 + 7 + 1 = 9, so the second missing digit is 9.
Eugene finally saved up enough money to buy a bike! He went to the store and got a bike and a helmet. The helmet cost $35, and the total was $167. How much did the bike cost?
Eugene rode his new bike for 187 minutes this week and plans to ride it 264 minutes next week. How long will he ride it in all?
Eugene is supposed to replace his tires every 290 miles. If he has ridden 86 miles so far, how many more miles until he needs to replace the tires?
Eugene traveled 1,568 meters going uphill and then 1,725 meters going downhill. How far did he travel in all?
Write equations to solve word problems.
A store has 29 bags of apples and 12 bags of oranges. How many more bags of apples are there than bags of oranges?
29 - 12 = 17
There are 17 more bags of apples.
Choose the correct equation that matches the story problem and solve. Explain your answer.
There are 63 toys in a bucket. Of these toys, 46 are for outside. The rest are for inside. How many toys are to be used inside?
63 + 46 = t 63 − 46 = t
There are 60 small animals at a pet store. Out of these animals, 28 are either rabbits or hamsters. The rest are guinea pigs. How many guinea pigs are there at the pet store?
60 + 28 = g 60 − 28 = g
There are 120 students in a classroom. Out of these students, 78 have brown or black hair. The rest of the students have blond hair. How many students in the classroom have blond hair?
120 − 78 = b 120 + 78 = b
Hannah has a collection of stamps. She starts with 150 stamps in her album. She then buys a set of 45 stamps from a collector. How many stamps does she have?
150 + 45 = s 150 − 45 = s
Write an equation using a variable that matches the story problem and solve.
The City Art Museum currently exhibits a collection of 28,946 artworks. In a recent initiative, the museum received a donation of 1,874 additional pieces from a local artist. How many artworks will be showcased at the City Art Museum after this generous donation?
A bakery had a stock of 980 cupcakes for a special event. During the event, 365 cupcakes were sold to customers. How many cupcakes are left in the bakery’s inventory after the event?
A farmer harvested a field of wheat, which covered an area of 87,500 square meters. After selling a portion of the harvest, the farmer now has 63,825 square meters of wheat remaining. How much wheat was sold?
Tom has a collection of toy cars. He started with 150 toy cars in his collection. Over time, he decided to give away 64 toy cars to his younger cousin. How many toy cars does Tom have left in his collection?
Sara has been saving money to buy a new bicycle. She started with $120 and received $50 as a gift from her grandparents. Later, she earned $30 for helping her neighbor. How much money does Sarah have for her new bicycle?
Emma is planning a road trip. The distance from her home to the destination is 325 miles. Along the way, she travels an additional 187 miles to visit a friend. How many miles will she have traveled?
Rewrite vertically and solve for the sums or differences.
A farmer harvested four fields of crops. The first field yielded 5,720 pounds of corn, the second field yielded 3,498 pounds of wheat, the third field yielded 6,215 pounds of soybeans, and the fourth field yielded 4,837 pounds of barley. How many pounds of crops did the farmer harvest in total?
A toy store has received four shipments of toys. The first shipment contains 1,250 action figures, the second shipment contains 980 dolls, the third shipment contains 3,560 building blocks, and the fourth shipment contains 2,145 stuffed animals. How many toys in total has the toy store received across all shipments?
A library had a collection of books on a shelf. There were 5,200 books in total. Over time, 2,350 books were borrowed by readers. How many books are still on the library shelf?
A farmer harvested apples from two orchards. The first orchard yielded 8,500 apples, and the second orchard yielded 4,200 apples. The farmer sold 3,750 apples from the combined harvest. How many apples does the farmer have left after selling some?
Chapter 3
Chapter 3
In Chapter 3, we will learn about
In Chapter 3, we will learn about
Multiples, Factors, and Multiplying by a Single Digit
Multiples, Factors, and Multiplying by a Single Digit
The concepts in this chapter build foundational skills that are used for multi-digit multiplication, estimation, and long division.
The concepts in this chapter build foundational skills that are used for multi-digit multiplication, estimation, and long division.
• Find multiples and factors
• Identify prime and composite numbers
• Find multiples and factors
• Multiply by multiples of 10
• Identify prime and composite numbers
• Multiply a multi-digit number by a single digit
• Multiply by multiples of 10
• Multiply a multi-digit number by a single digit
We can use skip counting, repeated addition, or multiplication to find multiples of a number.
We can use skip counting, repeated addition, or multiplication to find multiples of a number.
We can list the factors of a number and determine if it is prime or composite.
We can list the factors of a number and determine if it is prime or composite.
We can multiply a number by a multiple of 10 or multiply two multiples of 10.
We can multiply a number by a multiple of 10 or multiply two multiples of 10.
We can use models, partial products, and/or the standard algorithm to multiply a multi-digit number by a single digit.
We can use models, partial products, and/or the standard algorithm to multiply a multi-digit number by a single digit.
Use repeated addition or multiplication facts to find multiples.
Write the next five multiples of 8. 8: 16, 24, 32, 40, 48.
Remember: You can use repeated addition or multiplication facts to find multiples.
Write the next five multiples for each number.
Skip count by the indicated number to complete the number sequence.
Bryan is buying packs of water bottles. There are 6 in each pack, and he counts the multiples as he places 7 packs in his shopping cart. What numbers does Bryan say?
Arthur is counting the value of his nickels to find out how much they are worth. If he counts out 4 nickels, what numbers does he say?
Jerry knows that gallons of milk weigh about 8 pounds. As he carries in 4 gallons of milk from the car, he counts by 8s to find the total weight. What numbers does he say?
Mr. Larson has paired up students into 6 groups of 3. He wants to know how many students there are in total, so he counts by threes to find the answer. What numbers does he say?
Find factors of a number.
Write the factors of 40: 1, 2, 4, 5, 8, 10, 20, 40
Remember to include 1 and the number itself when writing factors.
Circle the digits that are factors of the target number.
Circle the numbers that are factors of both 8 and 20. 20 8 14 1 2 4 5 7 8 9 10 15 20 1, 2, 3, 4, 5, 6, 9, 10, 20 1, 2, 3, 4, 5, 6, 7, 8
2, 3, 4, 5, 6, 7, 8, 10, 14
Write the factors of each number.
4. 4 and 8 Factors: 4: , , 8: , , ,
GCF: 5. 8 and 12 Factors: 8: , , , 12: , , , , , GCF:
6. 16 and 20 Factors: 16: , , , , 20: , , , , , GCF:
Bruce wrote that the factors of 16 were 1, 2, 8, 16. Which factor did he miss?
Michael wrote that the factors of 10 were 10, 20, 30, 40. Why was Michael wrong?
Guess the number. I am a factor of 72 and a multiple of 6.
Guess the number. I am a factor of 48 and a multiple of 8.
List the factors and determine if a number is prime or composite.
Is the number prime or composite?
13: prime (factors are 1, 13)
12: composite (factors are 1, 2, 3, 4, 6, 12)
Remember: Prime numbers only have 1 and the number itself as factors.
List all the factors of each number. On the hundreds chart, color the number yellow if it’s prime and blue if it’s composite.
George completed a math problem incorrectly. Solve the problem correctly using arrays and words to explain your answer.
Factors of 24: 1, 2, 3, 4, 6, 8, 12, 24
Multiples of 24: 24, 48, 72…
Arrays that make 24:
1 × 24, 2 × 12, 3 × 8, 4 × 6
Prime or composite: prime
Factors of 24:
Multiples of 24:
Arrays that make 24:
Prime or composite:
Henry completed a math problem incorrectly. Solve the problem correctly using arrays and words to explain your answer.
Factors of 12: 1, 2, 3, 4, 6, 12
Multiples of 12: 4, 8, 12, 16, 20, 24
Arrays that make 12: 2 × 6, 3 × 4
Prime or composite: composite
Factors of 12:
Multiples of 12:
Arrays that make 12:
Prime or composite:
I am a two-digit prime number less than 30 made up of two prime numbers with a digit sum of 5.
I am a two-digit prime number less than 30 made up of two prime numbers with a digit sum of 8.
I am a two-digit prime number less than 50 made up of two numbers with a digit sum of 7.
I am a two-digit prime number less than 20 made up of two prime numbers with a digit sum of 4.
Use patterns to multiply by factors of 10.
40 × 300 = Think: 4 × 3 = 12 There are three zeros.
40 × 300 = 12,000
Complete the pattern for multiplying by powers of 10.
Use the patterns of multiplication to solve each problem.
Robert studies 40 minutes a day. If a month has 30 days, how long does he study?
Peter practices running for 20 minutes a day. If he runs 300 days this year, how long does he run in all?
Jordan’s dad drives 60 miles a day for work. If his dad works 20 days this month, how many miles does he drive?
Kevin calls his grandparents each week. If he talks to them for 50 minutes a week and calls 50 weeks this year, how long will he talk to his grandparents on the phone this year?
Multiply two-digit by one-digit numbers without regrouping.
Draw base 10 blocks to represent the multiplication equations and solve for the products.
Multiply.
At Adam’s school, each fourth-grade class has 23 students. How many students would be in all 3 fourth-grade classrooms?
Adam brings cookies for his class. Each of the 23 students gets 2 cookies. How many cookies does Adam give out?
Carl is buying candy. Each piece of candy costs 12 cents. How much would 4 pieces of candy cost?
There are 92 students on the playground. If the same number of students were at lunch, how many students are there in all?
Multiply using partial products.
2 × 4 = 8
Solve the following problems using the partial products strategy.
Partial Products Steps
1) Multiply the ones place.
2) Multiply the tens place.
3) Add your products for a total.
Multiply.
A farmer has 8 fields. He picks 690 cucumbers from each field. How many cucumbers did he pick in all?
There are 197 blueberries in a pound. How many would be in 5 pounds?
Jeremy sleeps for 540 minutes a day. How many minutes does he sleep in a week?
A box of screws says that there are 244 in one pound. How many are in 3 pounds?
Multiply.
Multiply by one-digit numbers with and without regrouping.
Rewrite and multiply. 258 × 4 491 × 8 = 327 × 9 =
7 × 3 = 21
7 × 3 = 21 21 + 1 = 22 1 2
Regroup to add 2 to the tens.
5 × 3 = 15
15 + 2 = 17
Regroup to add 1 to the hundreds.
× 6 =
× 7 =
A building has 328 apartments. Each apartment has 6 windows. How many windows does the building have?
There are 457 students at school. If each student plants 2 flowers, how many flowers are planted?
Vincent is in a running group. He runs for 25 minutes a day. How long will he run in 9 days?
A sheep weighs 205 pounds. How much would 7 sheep weigh?
Find the factors or multiples.
Factors of 6: 1, 2, 3, 6
Multiples of 6: 6, 12, 18…60
Write the next six multiples of 8.
Skip count by 7.
List the factors of 45 and circle the factors that are prime. Factors of 30: 8, 7,
Complete the patterns for multiplying by powers of 10.
3 × 2 = 6
30 × 2 = 60 30 ×
Complete the following problems using a strategy of your choice.
397 students visited the school library this week. If each student checked out 2 books, how many books were checked out?
The art teacher needs 88 pieces of paper for each class. If there are 6 art classes today, how many pieces of paper will the art teacher need?
The cafeteria serves 627 meals a day. How many meals will it serve in 5 days?
There are 6 flamingos at the zoo. If each flamingo eats 45 fish a day, how many fish will be needed each day for all of the flamingos?
Chapter 4
In Chapter 4, we will extend our multiplication skills to
Multiplying Two-Digit Numbers
In Chapter 4, we will extend our multiplication skills to
Multiplying Two-Digit Numbers
These skills are important to expand our skills in multiplication and problem solving.
These skills are important to expand our skills in multiplication and problem solving.
• Multiply two-digit numbers by two-digit numbers
• Estimate products
• Multiply two-digit numbers by two-digit numbers
• Problem solve
• Estimate products
• Identify patterns that follow rules
• Problem solve
• Identify patterns that follow rules
We can understand three different strategies for solving double-digit multiplication problems.
We can accurately and efficiently multiply double-digit numbers.
We can understand three different strategies for solving double-digit multiplication problems.
We can estimate products of double-digit numbers.
We can accurately and efficiently multiply double-digit numbers.
We can identify and solve word problems that require multiplication.
We can estimate products of double-digit numbers.
We can identify and solve word problems that require multiplication.
We can find patterns within and between two sequences.
We can find patterns within and between two sequences.
A grocery store receives shipments of apples in boxes. Each box contains 30 pounds of apples, and the store just received 25 boxes. How many pounds of apples did the store receive in total?
An office supply store is selling school supply packs for classrooms. Each pack contains 25 notebooks, and the store just received an order for 15 packs. If each student in the class receives one notebook, how many notebooks will be distributed in total?
A construction site is receiving shipments of bricks. Each pallet contains 50 bricks, and the construction company just received 20 pallets. How many bricks did the construction company receive in total?
A library is arranging new bookshelves. Each bookshelf can hold 30 books, and there are 12 bookshelves. How many books can the library store on these new bookshelves?
Complete multi-digit multiplication problems.
Remember: 5 and above, round up. 4 and below, round down.
Round the numbers to the nearest tens place and then multiply.
Round the numbers to the highest place and then multiply.
Eugene read for 23 minutes a day. About how long did he read in 31 days?
Gabriel bikes 14 miles to get to and from school each day. About how many miles does he bike in 18 days?
There are 24 pencils in a box. Mr. Thomas buys 29 boxes for his class. About how many pencils does Mr. Thomas buy?
At the read-a-thon, Michael reads 67 pages an hour for 13 hours. About how many pages does he read in all?
Use the area models to solve the equations. Solve the equations.
Michael swam 84 laps a week. How many laps would he swim in 52 weeks?
There are 28 students in Larry’s class. Each student was given 37 blocks to build a tower. How many blocks were there in all?
Each bus holds 67 students. How many students can 19 buses hold?
A candy bar costs 72 cents. How much would 15 candy bars cost?
Multiply using partial products. 34 × 14 476
Think: 4 × 4 = 16 30 × 4 = 120 4 × 10 = 40 30 × 10 = 300 16 + 120 + 40 + 300 = 476
Use the partial products method to solve these equations.
2. 25 × 37 42 × 16 (7 × 5) (7 × 20) (30 × 5) (30 × 20) (6 × ) (6 × ) (10 × ) (10 × )
6. 64 × 83 19 × 55
A farmer places 12 eggs in a carton. He fills 58 cartons. How many eggs did he have in all? Use partial products to solve.
The farmer has planted 26 rows of corn. There are 91 plants in a row. How many plants are there in all? Use partial products to solve.
The farmer has 65 strawberry plants. If each plant produces 13 strawberries, how many strawberries would the farmer have in all? Use partial products to solve.
The sunflowers need 18 quarts of water a week. How much would they need in 16 weeks? Use partial products to solve.
Complete the following problems using the strategy of your choice.
A gardener is planting rows of flowers in her garden. She has 17 rows, and each row contains 28 flowers. How many flowers will there be in the entire garden when all the rows are planted?
A bakery is baking muffins for a special event. They have 18 trays, and each tray can hold 12 muffins. How many muffins will the bakery bake in total?
A farmer has 68 baskets of apples, and each basket contains 52 apples. How many apples are there in total?
A bookstore has 45 shelves, and each shelf can accommodate 63 books. How many books can the bookstore display on all the shelves?
Use multiplication to solve word problems.
If there are 12 buses and each bus has 25 students, how many students are there? 12 × 25 = 300
Solve the equations using the strategy of your choice.
Solve the problems below. 93 × 15
153 × 24
× 25
Remember: You can use any multiplication strategy to solve.
Samuel picked 28 apples from each of his apple trees. If he has 15 apple trees, how many apples does he pick altogether?
× 52
Aaron wanted to know about how many students were in his school. If there were 24 students in each class and 16 classes, about how many students are in Aaron’s school?
If there are 26 students and each student reads 34 pages, how many pages are read in all?
Jacob is selling pumpkins. He has 8 pumpkins that he sells for $4.75 each. How much money will he earn if he sells all of the pumpkins?
There are 128 ounces in one gallon of milk. How many ounces would be in 16 gallons of milk?
A city has 27 roads. Each road has 58 houses. How many houses are in the city?
× 3 = 6
× 3 = 15
Multiply by 3
Emma is making gift baskets for a charity event. Each gift basket includes 10 chocolates and 15 candies. If Emma plans to make 20 gift baskets, how many chocolates and candies will she need to purchase? Fill in the table to solve for the number of chocolates and candies for each gift basket.
Mike is preparing goody bags for a kids’ party. Each goody bag contains 5 small toys and 8 stickers. If Mike plans to make 15 goody bags, how many small toys and stickers will he need to purchase? Fill in the table to solve for the number of small toys and stickers for each goody bag.
Write the rule, then fill in the missing numbers.
Ann’s Flower Shop is expanding its floral arrangements. In January, they created 5 arrangements, and in February, they made 15 arrangements. In March, the number increased to 45 arrangements, and in April, they crafted 135 arrangements. If this pattern continues, how many floral arrangements will Ann’s Flower Shop create in May?
Donna’s Candy Shop is introducing a new candy assortment. In the first week, they made 10 candy bags. The second week’s production increased to 40 bags. The third week saw a further increase to 160 bags. If this pattern continues, how many candy bags will Donna’s Candy Shop produce in the fourth week?
Marc’s Lemonade Stand is growing its lemonade production. On the first day, they squeezed 15 lemons. On the second day, the production increased to 75 lemons. The third day saw a further increase to 375 lemons. If this pattern continues, how many lemons will Marc’s Lemonade Stand squeeze on the fourth day?
John is stacking building blocks to create a tower. On the first level, he uses 8 blocks. On the second level, he uses 16 blocks. The third level increases to 32 blocks. If this pattern continues, how many blocks will John use on the fourth level?
Complete the following problems using the strategy of your choice.
Multiply the ones. Add a 0.
Multiply the tens. Add.
Write the rule, then fill in the missing numbers.
David has a rectangular room in his house that is 15 feet long and 20 feet wide. He wants to find the total area of the room. How many square feet is the room?
John is building a rectangular swimming pool in his backyard. The pool is 42 feet long and 56 feet wide. What is the total area of the swimming pool in square feet?
Ruth is planning a fundraising event where participants will arrange rectangular tables for a banquet. Each table has 15 seats in one row and 12 seats in another. What is the total seating capacity of one table?
Andrew is organizing a rectangular shelf for his matchbox car collection. Each shelf can hold 25 cars in a row and 18 cars deep. What is the total amount of cars on one shelf?
Chapter 5
Chapter 5
In Chapter 5, we will be introduced to
Long Division
In Chapter 5, we will be introduced to
Long Division
Students will use models and mental math to gain proficiency in solving division problems.
Students will use models and mental math to gain proficiency in solving division problems.
• Problem solve
• Estimate quotients
• Problem solve
• Interpret remainders
• Estimate quotients
• Use divisibility rules
• Interpret remainders
• Divide with long division
• Use divisibility rules
• Divide with long division
• Use error analysis for multiplication and division
• Use error analysis for multiplication and division
We can solve multi-step word problems that use multiple operations.
We can solve multi-step word problems that use multiple operations.
We can list the factors of a number and determine if it is prime or composite.
We can list the factors of a number and determine if it is prime or composite.
We can find compatible numbers and use them to estimate quotients.
We can find compatible numbers and use them to estimate quotients.
We can use divisibility rules to list the numbers a number is divisible by.
We can use long division to divide.
We can use divisibility rules to list the numbers a number is divisible by.
We can find errors in multiplication and division problems.
We can use long division to divide.
We can find errors in multiplication and division problems.
Use multiplication and division to solve problems.
Write related fact statements using the numbers 36, 4, and 9.
4 × 9 = 36
9 × 4 = 36
36 ÷ 4 = 9 36 ÷ 9 = 4
Sophia is knitting scarves for a craft fair. Each scarf requires 10 balls of yarn. She wants to make 30 scarves to sell. How many balls of yarn will Sophia need in all?
Jake is baking cookies for a bake sale. Each batch of cookies requires 12 eggs. He wants to bake 20 batches of cookies. How many eggs will Jake need in all?
Ann purchased 4 packs of notebooks at $3 each. Then, she bought 3 sets of colored pencils that cost $6 each. Finally, she purchased 2 sketchbooks for $8 each. How much money did she spend?
Rose went to the store and bought 5 packs of crayons at $2 each. Then, she purchased 3 sets of paintbrushes for $7 each. Finally, she bought 2 easels for $20 each. How much money did she spend?
Mike went shopping for school supplies. He bought 6 notebooks at $2 each, and then he picked up 4 packs of pens for $3 each. Finally, he grabbed 5 folders priced at $2 each. How much did he spend in total?
Sam went to the grocery store to buy some fruits and vegetables. He bought 2 kilograms of apples for $4 per kilogram, 3 kilograms of oranges for $3 per kilogram, and 1 kilogram of tomatoes for $2 per kilogram. How much money did Sam spend in total?
Use compatible numbers to estimate division.
Use compatible numbers to estimate 34 ÷ 7
Multiples of 7: 7, 14, 21, 35
34 is close to 35
34 ÷ 7 is close to 5
Estimate. List the multiples of the divisor and write the equation you used to estimate.
Sam needs to divide 25 pounds of sand into 3 containers. About how much sand should he put in each container? Write a compatible number sentence to help you solve.
David has 38 cupcakes to put on 6 plates. About how many cupcakes should he put on each plate? Write a compatible number sentence to help you solve.
Justin needs to mow 19 lawns in 5 days. About how many lawns does he need to mow a day? Write a compatible number sentence to help you solve.
Richard has 21 cups of feed to give to 2 horses. About how much feed does he need to give to each horse? Write a compatible number sentence to help you solve.
Understand the meaning of remainders.
There are 5 students and 22 pencils. How many pencils will be left over if the pencils are divided by the number of students? Multiples of 5: 5, 10, 15, 20 20 divides evenly by 5. 22 - 20 = 2 There are 2 left over.
Solve and write “Drop”, “Use,” or “Round” on the line under each problem. Explain your answers.
Option 1: Drop the remainder.
• Do this if you only need the number of equal groups.
Option 2: Use the remainder.
• Do this if you only need to know how many are left over.
Option 3: Round the quotient to the next whole.
• Do this if you need to include the left over pieces in your groups.
A water jug can hold 8 cups of water. If there are 234 cups of water that need to be placed into the same size jugs, how many jugs will be needed to carry all of the water?
It takes 9 pieces of chocolate to make 1 full candy bag. If there are 452 pieces of chocolate, how many full candy bags can be created?
There are 127 jelly beans in a container. If a teacher gives their students 5 jelly beans each, how many students can have five jelly beans?
A bakery is packing 109 muffins into containers. They can fit 9 muffins into each container. They will not sell any muffins that cannot make a pack of 9. How many muffins can they not sell?
George’s mom made 30 cookies and is having him put 7 cookies on each plate. She told him he can eat the leftover cookies. How many full plates can he make? How many does he get to eat?
If Frank divides 52 cards among 6 people, how many will be left over?
Jeffrey has 67 marbles he puts in 8 equal groups. How many marbles are not in a group?
Phillip has 38 nickels that he puts in stacks of 5. How many stacks does he make, and how many does he have left over?
Use divisibility rules for 2, 3, 5, 6, 9, and 10.
36 is divisible by what numbers?
2 (ends in 6)
3 (3 + 6 = 9. 9 ÷ 3 = 3)
6 (divisible by 2 and 3)
9 (3 + 6 = 9. 9 ÷ 9 = 1)
Circle the digits that the target number is divisible by.
Remember the rules:
2 - ends in 2, 4, 6, 8, or 0
3 - digits add to a multiple of 3
5 - ends in 5 or 0
6 - divisible by 2 and 3
9 - digits add to a multiple of 9 10 - ends in 0
3, 5, 6, 9, 10
List which numbers, 2, 3, 5, 6, 9, or 10, the given number is divisible by.
2, 3, 5, 6, 9, 10 36: 45: 14:
Mr. Matthews is arranging desks in a classroom. There are 24 desks. He is thinking about putting them in 2, 3, 5, 6, 9, or 10 rows. Which ways will come out evenly?
Nathan’s class is assigned to draw a new design for the American flag. It needs to have 50 stars in even rows. He is wondering what his options are. Would he be able to put them in 2, 3, 5, 6, 9, or 10 rows?
Peter is thinking of a number that is divisible by 9 and 6 but not 5. He said the number is smaller than 50 but bigger than 20. What number is it?
There are 45 squares for making a quilt. If the quilt has equal rows, can it have 2, 3, 5, 6, 9, or 10 rows? List all of the options that will make equal rows.
There are 72 students in a school’s ball game, divided evenly into 8 teams. How many players are there on each team?
There are 120 books in the school library, and they are evenly distributed among 6 bookshelves. How many books are there on each bookshelf?
In a classroom, there are 96 cookies to be distributed equally among 8 students. How many cookies will each student get?
A farmer has 144 apples, and he wants to pack them equally into 12 baskets. How many apples will he put in each basket?
There are 56 students in fourth grade. They are put in groups of two for science projects. How many groups are there?
There are 52 drinks on the table. There is an equal amount of 4 different flavors. How many of each flavor are there?
If Anthony walks 2 miles each day with his family, how long will it take them to walk 36 miles?
There are 80 pieces in a puzzle. If Gregory and his three friends each put together the same number of pieces, how many pieces does each person put together?
Use divisibility rules for 2, 3, 5, 6, 9, and 10.
Rewrite and divide. Show your work.
Tim’s teacher asked him to solve 24 × 42. He used the standard algorithm to solve. His final product of 144 was wrong. What was his mistake?
Judy’s teacher asked her to solve 36 × 28. She used the area model below to solve. Her final product of 788 was wrong. What was her mistake?
Write an explanation for what the student did wrong to get the incorrect answer and include the correct answer.
Write an explanation for what the student did wrong to get the incorrect answer and include the correct answer.
Complete each fact family.
Fact family:
2 × 3 = 6
3 × 2 = 6
6 ÷ 3 = 2
6 ÷ 2 = 3
List which numbers, 2, 3, 5, 6, 9, or 10, the given number is divisible by.
Divisibility rules:
2 - ends in 2, 4, 6, 8, or 0
3 - digits add to a multiple of 3
5 - ends in 5 or 0
6 - divisible by 2 and 3
9 - digits add to a multiple of 9
10 - ends in 0
Divide. Show your work.
Divide the tens:
D- 5 ÷ 3 = 1
M- 1 × 3 = 3
S- 5 - 3 = 2 B- 4
Divide the ones:
D- 24 ÷ 3 = 8
M- 8 × 3 = 24
S- 24 - 24 = 0 B- (none) 3
William has 34 apples. He gives 5 to each of his six neighbors and brings the leftovers home. How many apples does William bring home?
There are three ears of corn on a plant. If James needs 24 ears of corn, how many plants should he pick?
Russell has 18 strawberry plants he wants to put in equal rows. Can he put them in 2, 3, 5, 6, 9, or 10 rows? List all the possible answers.
Tyler opened a bag of candy and found it had 58 pieces. He put it in bags of 6 pieces each. How many pieces were left over?
Chapter 6
In Chapter 6, we will expand on
Long Division with Remainders
In Chapter 6, we will expand on
Long Division with Remainders
Students will continue to build fluency in long division as they practice with larger numbers and remainders.
Students will continue to build fluency in long division as they practice with larger numbers and remainders.
• Divide multiples of 10
• Estimate quotients
• Divide multiples of 10
• Use long division with remainders
• Estimate quotients
• Use multiplication to check division
• Use long division with remainders
• Use multiplication to check division
We can use patterns of division to divide multiples of 10. We can use compatible numbers to estimate quotients. We can use long division to divide up to four-digit dividends and find quotients with and without remainders. We can use multiplication to check division.
We can use patterns of division to divide multiples of 10. We can use compatible numbers to estimate quotients. We can use long division to divide up to four-digit dividends and find quotients with and without remainders. We can use multiplication to check division.
Complete the pattern for dividing by powers of 10. Divide.
A candy factory is making gummy bears. It places 90 gummy bears in each individual package. If it made 72,000 gummy bears, how many individual packages can it make?
The candy factory has 84,000 packages of gummy worms. If it puts 40 packages in a box, how many boxes will it fill?
The candy factory has 36,000 packages of gummy worms. There are 600 packages in a crate. How many crates of gummy worms did it make?
The candy factory made 81,000 pounds of candy. If each truck can carry 9,000 pounds, how many trucks are needed to ship all the candy?
Use patterns of 10 in division.
What is 4,500 ÷ 9? Think 45 ÷ 9 = 5 4,500 ÷ 9 = 500
Circle the better estimate. Write the equation you used to solve for the answer.
Bob has $120 to spend on school supplies. Each set of notebooks costs about $6. How many sets of notebooks can Bob buy?
Amy is planning to spend $60 on art supplies. Each paintbrush costs about $5. How many paintbrushes can Amy buy with her budget?
Max is going to spend $45 on board games. Each board game costs about $9. How many board games can Max buy with his budget?
Sara has 30 candies. She wants to distribute them equally among her 5 friends. How many candies will each friend receive?
Tim has 18 stickers. He wants to share them equally among 3 notebooks. How many stickers will each notebook get?
Hannah has 24 pencils. She wants to divide them equally among 8 students. How many pencils will each student receive?
Eric has 44 marbles. He wants to distribute them equally among his 4 friends. How many marbles will each friend receive?
5
3
11 B) 14
Moses has 45 candies. He wants to divide them equally among 5 of his friends. How many candies will each friend receive?
Anna has 120 balloons. She wants to share them equally among 12 of her friends. How many balloons will each friend receive?
Mike has 20 stickers. He wants to distribute them equally among 5 of his classmates. How many stickers will each classmate receive?
Helen has 60 cookies. She wants to share them equally among 10 of her friends. How many cookies will each friend receive?
Emma purchased 15 gift bags to pack her chocolates. She has 68 chocolates. Each gift bag can hold 4 chocolates. Did Emma order enough gift bags?
Rose bought 18 packets of crayons to distribute among her students. She has 74 crayons in total. Each packet can hold 6 crayons. Did Rose buy enough packets?
If Emma has enough gift bags, will all of her bags have 4 chocolates? Why or why not?
If Rose has enough packets, will all of her packets have 6 crayons? Why or why not?
Timothy bought 20 containers to store his collection of marbles. He has 85 marbles in total. Each container can hold up to 6 marbles. Did Timothy purchase enough containers?
Eli purchased 18 boxes to store his collection of trading cards. He has 64 trading cards in total. Each box can hold up to 8 trading cards. Did Eli buy enough boxes?
If Timothy has enough containers, will all of his containers be completely filled with marbles? Why or why not?
If Eli has enough boxes, will all of his boxes be completely filled with trading cards? Why or why not?
Divide two- and three-digit numbers by one-digit numbers. Remember: Divide Multiply Subtract Bring down
Circle the digits that the target number is divisible by.
Alexander planted fruit trees for 104 minutes. If he planted 8 fruit trees, how long did it take him to plant each one?
Alexander then watered raspberry plants. If he gave 54 quarts to 9 plants, how many quarts did each plant get?
Alexander went on to pick peaches. He picked 196 peaches from 7 trees. How many did he pick from each tree?
Alexander finally put fencing around his trees. He spent 198 minutes putting fencing around 6 apple trees. How much time did it take him to put fencing around one tree?
A company is boxing up its cans of soup to go to grocery stores. It has 1,518 cans of chicken noodle soup and puts 6 in each box. How many boxes can it fill?
A company is boxing up its cans of soup to go to the grocery stores. It has 3,418 cans of cream of mushroom soup and puts 8 in each box. How many boxes can it fill? How many cans will be left over?
A company is boxing up its cans of soup to go to grocery stores. It has 5,648 cans of tomato soup and puts 9 in each box. How many boxes can it fill? How many cans will be left over?
A company is boxing up its cans of soup to go to the grocery stores. It has 2,496 cans of alphabet soup and puts 5 in each box. How many boxes can it fill? How many cans will be left over?
At a large race, there are 832 runners. If they are divided into 4 different groups, how many runners are in each group?
The principal has 954 students in his school. He likes to give a positive note to each one. If he gave out the same number of notes to students each month for 9 months, how many would he give out each month?
Sam has 324 feet of ribbon for making bookmarks. How many yards is this?
Albert ran 621 miles this year. He runs 3 miles each day. How many days did he run this year?
Divide. Check your work by multiplying.
Divide. Use multiplication to check your work.
Andy divided 555 by 8 and got 69 remainder 6. Jake did the same problem and got 69 remainder 3. Which boy is correct? Multiply to check their work.
Benjamin divided 402 by 7 and got 57. Is he right? Explain. Use multiplication to check his answer.
Arthur is volunteering at a shelter. He’s told to divide 128 ounces of water evenly into 8 dog bowls. How much water should he put in each bowl? Divide and then multiply to check your answer.
Gerald is carrying feed for his horses into the barn. If there are 176 pounds of feed and each bucket holds 8 pounds, how many bucketfuls will he need to carry into the barn?
At a city zoo, there are 225 visitors. The zoo offers a guided tour on safari buses, and each bus can accommodate 9 visitors. How many safari buses will the zoo need for the guided tour?
At a science fair, there are 180 science projects on display. The projects are arranged on tables, and each table can hold 6 projects. How many tables are needed to display all the science projects?
In a bookstore, there are 240 books to be arranged on shelves. Each shelf can hold 12 books. How many shelves are needed to display all the books?
At a picnic, there are 150 sandwiches to be distributed to the participants. Each basket can hold 10 sandwiches. How many baskets are needed to distribute all the sandwiches?
Chapter 7
In Chapter 7, we will explore
In Chapter 7, we will explore
Fraction Concepts
Fraction Concepts
Understanding concepts about fractions has a lot of practical application in real-world situations and higher level operations with fractions.
Understanding concepts about fractions has a lot of practical application in real-world situations and higher level operations with fractions.
• Find prime factors
• Find prime factors
• Generate equivalent fractions
• Simplify fractions
• Generate equivalent fractions
• Simplify fractions
• Compare and order fractions
• Compare and order fractions
• Convert between improper fractions and mixed numbers
• Convert between improper fractions and mixed numbers
Numerator Denominator 3 5 2 3 1
Numerator Denominator 3 5 2 3 1
We can use factor trees and factor ladders to find the prime factors of a number.
We can use factor trees and factor ladders to find the prime factors of a number.
We can use models, multiplication, or division to generate and represent equivalent fractions.
We can use models, multiplication, or division to generate and represent equivalent fractions.
We can use a common factor to simplify fractions. We can compare and order fractions.
We can use a common factor to simplify fractions.
We can write, represent, and convert between improper fractions and mixed numbers.
We can compare and order fractions.
We can write, represent, and convert between improper fractions and mixed numbers.
Create factor trees and write the prime factors as an equation.
Finish the factor ladders and write the prime factors as an equation.
Sara received a mysterious gift from her aunt. The gift was a locked box, and the only clue provided was a note that mentioned the prime factorization of a number.
The note read: “Dear Sarah, your gift is a number less than 100. Its prime factorization has exactly three prime factors, and the sum of these prime factors is 18. Use your mathematical detective skills to find the number inside the box!”
In the Enchanted Garden, magical creatures called Flora Sprites tend to the growth of unique flowers. The Head Sprite recently planted a special flower with a secret number of petals. To discover the mystery, they left a clue in the form of its prime factorization. The clue says: “Dear Gardener, the enchanted flower in your care has a prime factorization with four prime factors. The product of these prime factors is 150. Can you determine the number of petals on this extraordinary flower?”
Emma received a coded message from her pen pal, and it seems to be based on the prime factorization of a number.
The only information provided is a clue that reads: “Dear Emily, your secret code is a number less than 50. Its prime factorization has exactly two prime factors, and the product of these prime factors is 35. Use your decoding skills to unveil the hidden message!”
Ann discovered an old chest in her attic locked with an intricate mechanism that seemed to involve the prime factorization of a number. A faded note inside provided a cryptic clue: “Dear Explorer, the secret to unlocking this chest lies in a number less than 70. Its prime factorization has exactly four prime factors, and the product of these prime factors is 56. Unravel the mystery to reveal the treasures within!”
Write two equivalent fractions that can represent the shaded part of the figure.
Find an equivalent fraction. Sample answer provided.
Robert has 2 3 of a pizza left. Is this equivalent to 3 5 or 4 6 ?
To make an equivalent fraction, Phillip multiplies 2 5 by 3 3 . What equivalent fraction does he get?
Walter has 1 3 of a container of ice cream. If he wants to make an equivalent fraction with a denominator of 12, what would the numerator be?
Vincent needs 3 4 pound of strawberries to make jam. He wants to convert it to ounces by making an equivalent fraction with the denominator 16. What will the numerator be?
Of the 28 guests that were invited to the party, 24 came. What fraction of the invited guests came to the party? Write your answer in simplest form.
Tyler ate 6 16 pieces of a chocolate bar. Write this fraction in simplest form.
If 9 27 balloons were red, what fraction of the balloons were not red? Write your answer in simplest terms.
After dinner, 3 8 of a pizza remained. Write this fraction in simplest form.
Use benchmark numbers to determine if the fraction is closer to 0, 1 2 , or 1.
Compare fractions by shading the figures or plotting the number line. Use the following symbols: <, >, =
Elijah ate 3 8 of a candy bar at lunch. Is this fraction closer to 0, 1 2 , or 1?
Mark studied for 1 2 of an hour. Thomas studied for 3 5 of an hour. Which boy studied longer?
Willie filled up 7 of the 8 water bottles. Is this fraction closer to 0, 1 2 , or 1?
Andrew spent 1 2 his allowance on a game and 4 10 of it on candy. Did he spend more on the game or the candy?
Decompose fractions into sums of fractions. Decompose the fraction 3
Decompose each fraction into a sum of fractions using the fraction models.
Which of the following sets of fractions add up to 5 6 ?
Which of the following sets of fractions add up to 4 9 ?
Rachel has 5 6 of a cake left over from her birthday party, and she wants to share it with her friends. However, she’s not sure how many friends will join her, so she wants to plan for all possibilities. Rachel decides to decompose the fraction 5 6 into smaller parts to figure out how much each person will get if she has different numbers of friends.
What if Rachel has 5 friends who want cake? What are five fractions that can be added to make 5 6 ?
Jack has 9 12 of a pie left over from his family gathering, and he wants to share it with his cousins who are coming over. However, he is not sure how many cousins will be joining him, so he decides to break down the fraction 9 12 into smaller parts to ensure he has enough pie for everyone. How many ways can 9 12 decompose?
Donna has 4 5 of a batch of cookies left from her baking session and wants to share them with her friends who are coming over for a study session. She decides to decompose the fraction 4 5 into smaller parts to determine how many cookies each friend will get.
Moses has 3 4 of a bag of candies left after and wants to divide them among his siblings. To ensure fairness, he decides to break down the fraction 3 4 into smaller parts to figure out how many candies each sibling will receive.
Write improper fractions.
Write as an improper fraction. Think: There are 8 pieces. Each bar is divided into 5. The improper fraction is 8 5 .
Write the improper fraction that matches the fraction bars in each row.
Picture
Improper Fraction
Label each part in the fraction circle. Write the number of wholes and the fraction left. Then, write the improper fraction.
Wholes:
Fraction: Improper fraction: Wholes:
Fraction: Improper fraction:
Wholes:
Fraction: Improper fraction:
Danny ordered 6 pizzas for his family, which were cut into 12 slices each. There were 6 slices left over after dinner. How much pizza did Danny’s family eat? Show the amount as an improper fraction.
A store received a shipment of 50 boxes of chocolates. Each box contains 12 chocolates. After the sale, there were 57 chocolates left unsold. How many boxes of chocolates are left? Represent the answer as an improper fraction.
A bakery received a shipment of 60 boxes of cookies. Each box contains 20 cookies. After a big event, there were 88 cookies left unsold. How many boxes of cookies are left? Represent the answer as an improper fraction.
A toy store received a shipment of 45 boxes of puzzles. Each box contains 15 puzzles. After a weekend sale, there were 63 puzzles left unsold. How many boxes of puzzles are left? Represent the answer as an improper fraction.
Write as a mixed number.
Think: 1 whole and 4 5
Remember: To go from mixed number to improper fraction, use: Multiply, Add, Denominator. To go from improper fraction to mixed number, use division.
Mixed number: 1 4 5
Write the mixed number that matches the fraction bars in each row.
Change the mixed numbers to improper fractions.
Change the improper fractions to mixed numbers.
Harold is baking banana bread. The recipe calls for 2 1 2 cups of flour. What is this as an improper fraction?
Harold is baking banana bread. He needs 4 3 of a cup of butter. What is this fraction as a mixed number?
Harold is baking banana bread. He needs 6 1 4 bananas. Write this fraction as an improper fraction.
Harold is baking banana bread. He uses 6 4 of a tsp of baking soda. Write this fraction as a mixed number.
Complete the chart to represent each fraction. Simplify the fraction.
Create factor trees or factor ladders and write the prime factors as an equation.
A pie has 7 slices. Elijah ate 2 slices, and Danny ate 3 slices. What fraction of the pie did they eat in all?
A pie has 7 slices. Elijah ate 2 slices, and Danny ate 3 slices. What fraction of the pie was left when they were done?
Jack gave a sunflower 3 10 of a gallon of water and a row of daisies 5 10 of a gallon of water. What was the total amount he gave the all the plants? Write your answer in simplest form.
Carl was cleaning up from a pizza party. Each pizza had been cut into 8 slices. Carl picked up 23 slices. Convert this fraction to a mixed number.
Chapter 8
In Chapter 8, we will learn how to
In Chapter 8, we will learn how to
Add, Subtract, and Multiply Fractions
Add, Subtract, and Multiply Fractions
Many measurement problems, such as with cooking, length, and time, involve fractions.
• Add and subtract fractions with like denominators
Many measurement problems, such as with cooking, length, and time, involve fractions.
• Add and subtract mixed numbers with like denominators
• Add and subtract fractions with like denominators
• Problem solve with fractions
• Add and subtract mixed numbers with like denominators
• Multiply fractions by a whole number
• Problem solve with fractions
• Multiply fractions by a whole number
We can add and subtract fractions and mixed numbers with like denominators.
We can add and subtract fractions and mixed numbers with like denominators.
We can use models and number lines to multiply a fraction by a whole number.
We can use models and number lines to multiply a fraction by a whole number.
We can solve word problems with addition, subtraction, and multiplication of fractions.
We can solve word problems with addition, subtraction, and multiplication of fractions.
Add and subtract fractions with like denominators.
Use the number lines to add or subtract.
Add or subtract the fractions. Simplify.
Remember: If denominators are the same, add or subtract the numerators and leave the denominator.
At Peter’s Pizzeria, each type of pizza is cut into a different number of slices. The pepper pizza is cut into 9 slices. If Raymond eats 4 slices, and James eats 2 slices, what fraction of the pizza did they eat in all?
At Peter’s Pizzeria, each type of pizza is cut into a different number of slices. The veggie pizza is cut into 6 slices. If Mark eats 2 slices, and John eats 3 slices, what fraction of the pizza did they eat in all?
At Peter’s Pizzeria, each type of pizza is cut into a different number of slices. The cheese pizza is cut into 8 slices, but only 6 are left. If Joseph eats 2 slices, what fraction of the pizza is left?
At Peter’s Pizzeria, each type of pizza is cut into a different number of slices. The mushroom pizza is cut into 12 slices, but only 9 are left. If Joseph eats 4 slices, what fraction of the pizza is left?
Add. Simplify if necessary.
On Wednesday, Jonesville received 3 1 4 inches of snow. On Thursday, Jonesville received 6 3 4 inches of snow. How much snow fell in all?
It rained 1 1 4 inches every day for 5 days. How much rain fell in all?
Sam grew 2 5 8 inches last year. Henry grew 1 2 8 inches last year. How much did the boys grow in all?
Tom grew 3 4 inches last year and 1 1 4 inches this year. How much did he grow?
Add or subtract. Draw pictures to represent the problems. Simplify if necessary.
Add or subtract. Simplify if necessary.
On Monday, Greenfield experienced 5 1 2 inches of rainfall, and on Tuesday, Greenfield received 8 1 2 inches of rainfall. How much less rainfall occurred on Monday than on Tuesday?
On Wednesday, Jonesville received 3 1 4 inches of snow. On Thursday, Jonesville received 6 3 4 inches of snow. How much more snow fell on Thursday than on Wednesday?
On Thursday, Maplewood recorded 7 2 5 inches of rainfall, and on Friday, they received 4 3 5 inches of rainfall. How much less rainfall was there on Friday compared to Thursday?
Samuel grew 2 5 8 inches last year. Henry grew 1 2 8 inches last year. How much more did Sam grow than Henry?
Lesson instructions 4 Solve story problems by adding or subtracting fractions.
In an art room, one bucket has 5 3 7 pounds of clay. Another bucket has 2 1 7 pounds of clay. How much clay is there in all? 7 4 7 pounds
Leo has 9 10 pounds of oranges. Max has 5 10 pounds of oranges, and Eric has 3 10 pounds of oranges. How many pounds of oranges do they have altogether?
Mike is constructing a model of a bridge. He has 6 3 8 pounds of wood. He needs 10 3 4 pounds of wood. How much more wood does he need?
Hannah can’t work more than 15 3 5 hours per week. On Monday, she worked 3 hours. On Tuesday, she worked 4 2 5 hours. On Wednesday, she worked 5 1 5 hours. How many hours can she work on Thursday without exceeding 15 3 5 hours?
The horses on the ranch consume horse feed 3 times per day. At 7:00 am, they eat 3 10 of a ton of feed. At 12:00 pm, they eat 5 10 of a ton of feed. At 5:00 pm, they eat 6 10 of a ton of feed. How much feed do they eat per day?
Eddie spent 5 3 8 hours studying on Tuesday. On Thursday, he spent 2 5 8 hours studying. How many hours did he spend studying both days?
Ruth runs 3 1 4 miles every week. On Monday, she runs 1 3 8 miles. On Thursday, she runs 5 8 of a mile. How many more miles does she have left to run to meet her weekly goal?
Helen has 7 8 pounds of bananas. Mia has 3 8 pounds of bananas, and Ava has 4 8 pounds of bananas. How many pounds of bananas do they have altogether?
Judy is building a model airplane. She has 5 5 8 pounds of plastic. She needs 8 3 8 pounds of plastic. How much more plastic does she need?
Ann can’t work more than 18 4 7 hours per week. On Monday, she worked 4 hours. On Tuesday, she worked 3 3 7 hours. On Wednesday, she worked 5 2 7 hours. How many hours can she work on Thursday without exceeding 18 4 7 hours?
The cats in the shelter consume cat food 4 times per day. At 8:00 am, they eat 2 5 of a pound of food. At 12:00 pm, they eat 3 5 of a pound of food. At 3:00 pm, they eat 4 5 of a pound of food. At 6:00 pm, they eat 1 5 of a pound of food. How much food do they eat per day?
Kayla spent 4 5 8 hours practicing piano on Monday. On Wednesday, she spent 3 3 8 hours practicing. How many hours did she spend practicing both days?
Leo swims 2 7 8 miles every week. On Tuesday, he swims 1 5 8 miles. On Friday, he swims 3 4 of a mile. How many more miles does he have left to swim to meet his weekly goal?
Multiply fractions by whole numbers.
Multiply the fractions and simplify.
Remember: When multiplying a fraction by a whole number, multiply the numerator by the whole number and leave the denominator.
5
Kane had 4 buckets of rocks that were 5 6 full, and Eli had 3 buckets of rocks that were 3 4 full. Who had more rocks?
Debra is making fruit salad for a picnic. She needs 4 bowls of fruit salad. Each bowl requires 3 5 pound of strawberries. If Debra has 5 pounds of strawberries, how many pounds of strawberries will she use to make the fruit salad?
Eddie is making batches of cookies for a bake sale. Each batch requires 3 4 cup of chocolate chips. If Eddie plans to make 6 batches of cookies, how many cups of chocolate chips will he need?
Judy is making bracelets for a craft fair. She estimates that each bracelet will require 2 3 yards of thread. If she plans to make 8 bracelets, how many total yards of thread will she need?
Multiply fractions by whole numbers.
Multiply the fractions and simplify.
Remember to simplify fractions if necessary!
Abe drinks 1 4 of a gallon of juice. Jack drinks 5 times more juice. How many gallons of juice did Jack drink?
Anthony walks 3 5 of a mile to school. His friend John walks 4 times more miles than Anthony. How many miles does John walk to school?
Steven bakes 2 3 of a dozen cookies for a party. His friend Tom bakes 3 times more cookies than Steven. How many cookies does Tom bake for the party?
Charlie has a book with 200 pages. He reads 3 4 of the book in one week. In the same week, his friend Jake reads 2 times more pages than him. How many pages does Jake read in one week?
Solve word problems by multiplying a fraction and a whole number.
Helen has 16 cookies. Judy has 1 5 of the number of cookies
Helen does. How many cookies does Judy have? 16 5 cookies
Chad spends 9 hours studying for his exams. David spends 1 3 of that time reviewing his notes. How much time does David spend reviewing his notes?
Think: 16 × 1 5 = 16 5
Amy owns a toy store. She sells 4 times as many dolls as she does action figures. Today, she sold 3 4 of a shelf of action figures. How many shelves of dolls did she sell?
Helen owns a flower shop. She sells 5 times as many roses as she does lilies. Of the flowers sold today, 2 3 were lilies. How many roses did she sell?
Sara gives each of her dogs 3 4 of a cup of dog food every day. She has 6 dogs. How many cups of dog food does she feed her dogs per day?
Emma makes cookies. On Monday, she made 3 4 of a dozen cookies. On Tuesday, she made 4 times more cookies. How many dozen cookies did she make on Tuesday?
John makes pizzas. On Monday, he made 2 3 of a pizza. On Tuesday, he made 6 times more pizzas. How many pizzas did he make on Tuesday?
Justin has 12 pencils. Ben has 1 3 of the amount of pencils Justin does. How many pencils does Ben have?
Helen has 16 cookies. Judy has 1 5 of the number of cookies Helen does. How many cookies does Judy have?
Jake has 20 marbles. Morris has 1 2 of the number of marbles Jake does. How many marbles does Morris have?
Leo has 24 candies. Max has 1 3 of the number of candies Leo does. How many candies does Max have?
Donna is making sandwiches for a picnic. She uses 1 4 of a pound of cheese in each sandwich. She has 12 friends coming to the picnic. How many pounds of cheese does she use in total?
Henry is baking cupcakes for a party. He uses 1 3 of a cup of frosting on each cupcake. He has 15 guests coming to the party. How many cups of frosting does he use in total?
Emma fills a container with 1 3 gallon of water. She needs 5 times more water to completely fill the container. How many more gallons of water does she need to fill the container?
Tom puts 1 5 pound of sand into a bucket. He needs 7 times more sand to fill the bucket completely. How many more pounds of sand does he need to fill the bucket?
Emma has 1 2 of a pound of strawberries. Sara has 1 3 of a pound of strawberries. Lisa has 1 4 pounds of strawberries. How many pounds of strawberries do they have altogether?
Tom studied for 3 1 2 hours. Victor studied for 1 3 4 hours. How many more hours did Tom study than Victor?
Anna sold 10 flower arrangements on Monday. On Wednesday, she sold 1 4 as many flower arrangements. How many arrangements did she sell on Wednesday?
William sold 12 cupcakes on Monday. On Wednesday, he sold 1 3 as many cupcakes. How many cupcakes did he sell on Wednesday?
In Chapter 9, we will be introduced to
Decimals
In Chapter 9, we will be introduced to
Decimals
Decimals are another way to write fractions and can be a helpful way of showing exact amounts.
• Understand decimals
Decimals are another way to write fractions and can be a helpful way of showing exact amounts.
• Name the place value of decimals
• Understand decimals
• Add fractions with denominators of 10 and 100
• Name the place value of decimals
• Compare and order decimals
• Add fractions with denominators of 10 and 100
• Locate decimals and fractions on a number line
• Compare and order decimals
We can show decimals with models and number lines.
• Locate decimals and fractions on a number line
We can write parts of a whole as a decimal, as a fraction, and in word form.
We can show decimals with models and number lines.
We can write parts of a whole as a decimal, as a fraction, and in word form.
We can find equivalent denominators to add fractions with denominators of 10 and 100.
We can use place value to compare and order decimals.
We can find equivalent denominators to add fractions with denominators of 10 and 100.
We can use place value to compare and order decimals.
Lesson instructions 1
Identify decimal place values. Don’t forget to say the word “and” at the decimal when reading the number.
Circle the place value of the underlined digit in each number. Write
Mr. Thomson wrote a check for $6.35. What is this number in word form?
Ryan ran a race in 38.794 seconds. What number is in the thousandths place?
The fourth grade class raised $3,296.75 for the animal shelter. What is the value of the 5 in this number?
If one and four tenths inches of rain fell this week, what is that number in standard form?
Lesson instructions 2
Identify the relationship between fractions and decimals and learn the decimal notation for fractions with denominators of 10 and 100.
We can write fractions with denominators of 10 as a decimal:
We can write fractions with denominators of 100 as a decimal:
Amy says she has 5 10 of a dollar and shows 5 dimes in her hand to her sister. Her sister tells her she has 50 cents. Who is correct?
David has 40 dimes and 25 pennies. He wants to buy a coffee that costs $4.10. Does he have enough money?
Steven runs sixty-five hundredths of a mile around the park. Write this number as a decimal.
Helen has a red ribbon that is 6 10 feet long and a blue ribbon that is 60 100 feet long. She thinks both ribbons are the same length. Write these fractions as decimals to see if she’s correct.
Lesson instructions 3
Add fractions with denominators 10 and 100.
We can use models to help us add fractions. 4 10 + 7 100
When we add fractions, they must have a common denominator.
Write the equivalent fractions and show both fractions visually on the grids.
Write the word form of each number. Complete the equivalent fractions and add to solve.
Six tenths inches of snow fell on Monday, and six hundredths inches of snow fell on Tuesday. How much snow fell altogether? Write an equation and solve.
Anna has five dimes and 11 pennies. How much money does Anna have in total? Write an equation and solve.
Max has 3 dimes, and his brother George has 77 pennies. How much money do they have together? Do they have enough to buy a candy bar that costs one dollar?
Debra has 123 pennies. Write this amount as a fraction.
Represent tenths and hundredths with pictures, words, and numbers.
This hundred flat = 1 whole
This shows 3 rows = 3 tenths
What is a decimal for this? 0.3
One row = 1 tenth (0.10)
One cube = one hundredth (0.01)
This shows 4 cubes or 4 hundredths
Circle the place value that correctly identifies the place value of the quotient or product.
Write the decimals shown. Color in the correct decimal amount.
Three tenths of an inch of snow fell last night. Write this amount as a decimal.
0.13 inches of rain fell on Tuesday. Write this amount in word form.
Terry bought a candy bar. He paid $1.00 and got back $0.70 in change. Write the amount of the change in word form.
Roy has 57 pennies. Write how much money he has as a decimal.
Lesson instructions 5
Compare decimals and use the notation <, >, or =.
When comparing decimals, start with the whole numbers and work your way down to the right. 5.63 and 7.39: 7.39 > 5.63 because 7 wholes is greater than 5 wholes.
Compare each set of decimals using <, >, or =.
Fill in the amount shown and compare using <,>, or =.
Nathan ran the race in 13.61 seconds the first time and 13.69 seconds the second time. In which race was he faster?
Peter and Paul are saving money to go skating. Peter has saved $2.09, and Paul has saved $2.40. Which boy has saved more?
Scott bought 3.9 kilograms of bananas. James bought 3.788 kilograms of bananas. Who bought more bananas?
Jack ran 5.2 miles today and 5.20 miles yesterday. On which day did he run more?
Lesson instructions 6
Locate decimals and fractions on a number line.
Step 1: Find the two wholes that the decimals are between.
Step 2: Make a number line that shows all the tenths between those two wholes.
Step 3: Find two tenths that the decimal is between.
Step 4: Make a number line that shows all the hundredths between those two tenths.
Write the decimal, fraction, and word form for the number on the number line that matches each letter.
Rewrite the fractions as decimals. Plot the decimals on the number line or write the matching letter.
Fill in the missing improper fraction or mixed number and plot the matching letter on the number line.
Leo is 2.30 meters tall, and Tim is 2.65 meters tall. Rick’s height is in between Leo’s and Tim’s. Write two possible heights for Rick in meters.
Anna has four dollars and fifty cents, and Ruth has 40 dimes. Who has more money? What two whole numbers do these amounts fall in between on a number line?
The roses in the garden grew 70 100 cm, and the tulips grew 0.7 cm. Plot these numbers on a number line to determine if they grew the same amount.
Chad ate 550 100 pieces of candy. How many whole pieces of candy did Chad eat?
Write 550 100 as a mixed number and a decimal.
Lesson instructions 7
Order decimals in the tenths and hundredths place.
Step 1: Write the numbers by lining up the decimal points vertically.
Step 2: Start on the left with the largest place value and compare numbers. The smallest value here will be the smallest number between the different numbers you are comparing.
Step 3: Look at the remaining numbers. If all of the whole numbers are the same, go to the next place value to the right of the decimal point, the tenths place.
Step 4: Keep moving right one place value at a time until you have compared all digits. Rewrite the numbers in order.
Order each decimal group from smallest to largest.
0.63, 0.17, 0.93 3.21, 1.91, 2.36 0.72, 1.35, 1.82 0 1 2
Write the smallest number from each problem 1 - 4 and plot them on the number line below.
Rewrite each group of numbers from largest to smallest.
Select one problem from 6 - 9 and explain how you put the decimals in order.
Eddie and his friends are planning a dog relay race in their neighborhood. Since the dogs are different sizes, they will each run a different distance. Put the distances in order from shortest to longest.
Sparky 80.65 meters
Bailey 8.97 meters
Tuffy 80.5 meters
Chad is comparing three recipes for bread. The first recipe calls for 0.4 kg of flour, the second calls for 0.385 kg of flour, and the third recipe calls for 0.43 kg of flour. Which recipe asks for the least flour?
Ms. Mills went shopping and bought shampoo for $3.45, lotion for $6.99, and a snack for $4.35. List the prices in order from least to greatest.
Lisa is measuring three bags of sugar. Put these weights in order so Lisa can use the bag with the least sugar first.
10.26kg, 1.26kg, 12.06 kg
Write the decimal form for each number.
Fraction Form: 1 2
Decimal Form: 0.5
Word Form: one half
Compare each set of decimals using <, >, or =.
Round each number to the underlined place value.
Mark ran 2 3 10 miles today. Write this number as a decimal.
Larry bought 2.64 kg of bananas. Write this decimal in word form.
Jason’s backpack weighed 6.34 pounds, and Adam’s backpack weighed 6.4 pounds. Which boy’s backpack weighed more?
Timothy ran a race in 22.96 seconds. Round this number to the nearest tenth.
Chapter 10
Chapter 10
In Chapter 10, we will learn about
Geometry
In Chapter 10, we will learn about
Geometry
Geometry is important because the world is made up of different lines, angles, and shapes.
Geometry is important because the world is made up of different lines, angles, and shapes.
• Identify points, lines, line segments, and rays
• Label angles
• Identify points, lines, line segments, and rays
• Measure and draw angles
• Label angles
• Solve for the unknown angle
• Measure and draw angles
• Solve for the unknown angle
• Identify perpendicular, parallel, and intersecting lines
• Classify triangles and quadrilaterals
• Identify perpendicular, parallel, and intersecting lines
• Classify triangles and quadrilaterals
We can draw and label points, lines, line segments, and rays.
We can draw and label points, lines, line segments, and rays.
We can find the angle of a fraction of a circle and identify it as acute, right, or obtuse.
We can find the angle of a fraction of a circle and identify it as acute, right, or obtuse.
We can use a protractor to measure and draw angles. We can add or subtract to solve for an unknown angle.
We can use a protractor to measure and draw angles.
We can add or subtract to solve for an unknown angle.
We can identify if lines are parallel, perpendicular, or intersecting.
We can identify if lines are parallel, perpendicular, or intersecting.
We can classify different types of triangles and quadrilaterals according to the measure of their sides and angles.
We can classify different types of triangles and quadrilaterals according to the measure of their sides and angles.
Identify geometric figures, such as lines, rays, points, and line segments.
Point - an exact location Line - a straight path that extends indefinitely both directions
Line segment - part of a line that has two endpoints Ray - part of a line that has one endpoint and the other side extends indefinitely
Draw a line to match the definitions to the geometry terms.
An exact location
Part of a line that has two endpoints
A straight path that extends indefinitely in both directions
Part of a line that has one endpoint and the other side extends indefinitely
Draw and label with the correct geometric term.
What is the difference between a line segment and a line?
Rose is hiking along a straight trail in a national park. She starts at the trail entrance and walks for 1.5 miles to Walker’s Peak. To show her distance on a map, which geometry term is being applied?
John is building a rectangular garden in his backyard. He decides to put a fence around the garden to keep out rabbits. He already has one side of the garden bordered by his house, so he only needs to install a fence along the other three sides. How many line segments is the fence made up of?
What is the difference between a line and ray?
Identify different types of angles.
An angle that creates a square corner is right angle. A right angle measures 90°. It is written as XYZ.
Draw and label the figures. Write the names of the figures.
An angle that has a measure less than 90° is called an acute angle. It is written as ABC.
An angle that has a measure greater than 90° is called and obtuse angle. It is written as JKL.
Donald measures an angle and finds that it is 98 degrees. What kind of angle is it: acute, right, or obtuse?
Max measures an angle and finds that it is 80 degrees. What kind of angle is it: acute, right, or obtuse?
How many degrees is a right angle?
Give a possible angle measurement for an acute angle.
Measure angles. A circle measures to 360°. In this example, line NOP splits the circle in half, so 1 2 of a full turn is 180°.
Solve for the angles.
Look at the circle below. DEF is 1 8 of a full turn.
How many degrees does DEF measure?
Look at the circle below. ABC is 1 3 of a full turn.
How many degrees does ABC measure?
Look at the circle below. NOP is 1 2 of a full turn.
How many degrees does NOP measure?
The circle is divided into 360 equal parts. Point X represents the center of the circle.
Which angle measures 45°?
The circle is divided into 360 equal parts. Point O represents the center of the circle.
Which angle measures 120°?
How many degrees does the caterpillar need to turn to be upright? Before After
If you turn the dial 135 degrees to the right, what setting will it be on?
How many degrees are in 1 8 of a full turn?
How many 30 degree angles does it take to make a full turn?
Identify and measure angle types.
To measure an angle, you can use a tool called a protractor. Line up the bottom of the protractor to one of the lines related to the angle you are trying to measure. The number that the opposite line points to tells you the degree of the angle.
Identify the type of angle and its measurement.
Type
Each hour on the clock is 30 degrees. If the clock says 5:00, what is the degree measurement of the angle and what type of angle is it?
Each hour on the clock is 30 degrees. If the clock says 2:00, what is the degree measurement of the angle and what type of angle is it?
What type of angle do perpendicular lines make?
Mark measured an angle but can't tell if it should be 85 degrees or 95 degrees. He can see that it is an acute angle, though. What is the correct measurement?
Use addition, subtraction, and background knowledge about angles to solve for an unknown, missing angle.
Solve for the missing angles.
Find the value of b.
Straight lines = 180°
Right angles = 90°
If the whole angle is 155°, subtract 110° to find a.
Find the value of x.
Find the value of x.
Find the value of x.
Find the value of x.
Find the value of x.
Find the value of y.
Find the value of k.
Find the value of f.
A hungry snake is eyeing a delicious mouse for its meal. The snake can currently open its mouth at an angle of 30 degrees. To successfully engulf the mouse, it needs to widen its jaw to an angle of 80 degrees.
What is the additional angle that the snake needs to open its mouth for the mouse to fit?
Write the equation that will help you find the missing angle. Then, solve for the missing angle.
A chef is preparing a dish and needs to cut a carrot. The chef can currently cut the carrot at an angle of 5 degrees. To achieve the desired thin strips, the chef needs to adjust the angle of the knife to 25 degrees.
What is the additional angle that the chef needs to adjust the knife for the carrot to be properly cut?
Write the equation that will help you find the missing angle. Then, solve for the missing angle.
A pelican is eyeing a school of fish swimming just below the water’s surface. The pelican can open its bill at an angle of 15 degrees. In order to scoop up the fish effectively, it needs to widen its bill to an angle of 45 degrees. What is the additional angle that the pelican needs to open its bill for the fish to fit?
Write the equation that will help you find the missing angle. Then, solve for the missing angle.
A giraffe is reaching for leaves on a tall tree. The giraffe can extend its neck at an angle of 10 degrees. To comfortably reach the highest leaves, it needs to extend its neck further to an angle of 50 degrees.
What is the additional angle that the giraffe needs to extend its neck for the leaves to be within reach?
Write the equation that will help you find the missing angle. Then, solve for the missing angle.
Lesson instructions 6
Identify and draw intersecting, parallel, and perpendicular lines.
Parallel lines lines that never touch
Intersecting lines lines that cross, but do not make right angles
Perpendicular lines lines that cross and make right angles
State whether the given pair of lines are parallel, perpendicular, or intersecting.
Answer:
Answer:
Answer:
Which statements appears to be true?
Answer:
A) AB is perpendicular to CD.
B) AB is perpendicular to EF.
C) CD is parallel to EF.
A) QR is perpendicular to ST.
B) ST is parallel to UV.
C) QR is parallel to ST.
Write three true statements about the figures below.
Write three true statements about the figures below.
Write three true statements about the figures below.
Write three true statements about the figures below.
Lesson instructions 7
Classify triangles and quadrilaterals. Parallelogram Rectangle Square Trapezoid
Equilateral triangle Isoscelas triangle Rhombus
Scalene triangle
Complete the chart.
1.
2.
3.
4.
Number of Right Angles Number of Parallel Sides
All Words That Apply
Parallelogram Rectangle
Rhombus Square Trapezoid Quadrilateral Polygon
Parallelogram Rectangle
Rhombus Square Trapezoid Quadrilateral Polygon
Parallelogram Rectangle
Rhombus Square Trapezoid Quadrilateral Polygon
Parallelogram Rectangle
Rhombus Square Trapezoid Quadrilateral Polygon
Terry is thinking of the only type of quadrilateral that has one set of parallel sides. What shape is Terry thinking of?
Zachary made a garden that is a parallelogram with all the sides measuring 25 feet. The angles are not all the same, though. What type of parallelogram is his garden?
Russell wants to build a doghouse. He knows that he wants the base to be a quadrilateral and the angles to all be right angles. What shapes are possible choices for the base of his doghouse?
Adam drew a shape that had four sides, but none of them were parallel. What is the name for Adam's shape?
Which statements appears to be true?
Which statements appears to be true?
Parallel:
Perpendicular:
A) OP is parallel to QR.
B) MN is parallel to OP.
C) MN is perpendicular to OP.
What is value of m?
155°- 110°= 45° a = 45°
A) TS is parallel to UV.
B) QR is perpendicular to UV.
C) QR is parallel to UV.
What is value of d?
What is value of j?
Equilateral: three equal angles and side lengths
Isosceles: two equal angles and side lengths
Scalene: no equal angles or side lengths
Is this triangle equilateral?
Is this triangle isosceles?
What kind of triangle is this?
A) equilateral B) isosceles but not equilateral C) scalene
A crafty spider is patiently waiting for an unsuspecting fly to come within its reach. The spider can currently open its web-trap at an angle of 20 degrees. In order to successfully capture the fly, it needs to expand its web-trap to an angle of 60 degrees.
What is the additional angle that the spider needs to open its web-trap for the fly to be ensnared?
A patient owl is perched on a branch, awaiting the perfect moment to swoop down and catch a passing vole. The owl can currently rotate its head at an angle of 45 degrees. To successfully spot and grab the vole, it needs to turn its head to an angle of 120 degrees. What is the additional angle that the owl needs to rotate its head for the vole to be within its line of sight and reach?
A curious chameleon is perched on a branch, eagerly eyeing a passing insect. The chameleon can currently swivel its eyes at an angle of 60 degrees. To successfully focus on the insect and capture it with its tongue, it needs to adjust its eyes to an angle of 110 degrees.
What is the additional angle that the chameleon needs to swivel its eyes for the insect to be in its line of sight and within striking distance?
A curious chameleon is perched on a branch, eagerly eyeing a passing insect. The chameleon can currently swivel its eyes at an angle of 60 degrees. To successfully focus on the insect and capture it with its tongue, it needs to adjust its eyes to an angle of 110 degrees.
What is the additional angle that the chameleon needs to swivel its eyes for the insect to be in its line of sight and within striking distance?
Chapter 11
In Chapter 11, we will learn about
Measurement
In Chapter 11, we will learn about
Measurement
Understanding the U.S. customary measurement system is important for accurately describing the size of objects or liquids.
Understanding the U.S. customary measurement system is important for accurately describing the size of objects or liquids.
• Estimate and convert length
• Find area and perimeter
• Estimate and convert length
• Estimate and convert weight
• Find area and perimeter
• Estimate and convert liquid capacity
• Estimate and convert weight
• Estimate and convert liquid capacity
We can understand the relative sizes of measurements in the U.S. customary measurement system. We can convert between different units of measurement. We can compare measurements and solve word problems with measurement.
We can understand the relative sizes of measurements in the U.S. customary measurement system. We can convert between different units of measurement. We can compare measurements and solve word problems with measurement.
Lesson instructions 1
Understand the relative sizes of the customary system of length and how to convert between units of length, including expressing the conversion as a fraction.
Find the conversion on the chart to help convert units.
Eric was studying the tadpoles in his backyard pond. The small tadpoles moved so quickly and were fun to watch. If Eric wanted to measure the tadpoles, what would be the best unit of measurement?
Alice had a ribbon that was 3 feet in length, and her sister Rachel had a ribbon that was 36 inches in length. Rachel said her ribbon was longer, but Alice said they were the same length. Who was correct?
Jeffrey is building a sandbox. He measures it to be 60 inches wide. How many feet would that be?
Tom loves running around the park. His father asks him to run 100 yards. How many feet is that?
Lesson instructions 2
Understand how to convert between units of length, including expressing the conversion as a fraction and estimating the conversion as a fraction
Find the conversion on the chart to help convert units.
the best estimate. Estimate the best answer for each conversion. Compare using <, >, or =.
The length of a desk
The length of a soccer field
length of a picture frame
Mickey has 180 inches of ribbon to use on a project. How many yards does he have?
Victor would like to measure around the perimeter of his house. Should he use inches or feet?
If Charlie has 3 yards of fabric, and Ann has 15 feet of fabric, how much fabric do they have altogether?
Howard wants to create a frame for his art project. His project has a perimeter of 124 inches. About how many feet of of wood will he need to make a frame?
Calculate the area and perimeter of rectangles .
Find the perimeter of each shape.
Perimeter: add up all the sides together
Area: length × width
Find the area and perimeter of each shape.
Harold’s bedroom measures 12 feet by 11 feet. What is the area of his bedroom?
The community pool is shaped like a rectangle. One side is 48 feet long and the other is 27 feet long. What is the perimeter of the pool?
The playground is 97 yards long and 35 yards wide. What is the area of the playground?
The table on the patio is a square. The sides are each 60 inches. What is the perimeter of the table?
Circle the best unit to measure each object. Convert. Use the conversion charts to help.
Ben was helping a neighbor carry sticks that had fallen over the winter. They packed them in the truck to take to the local waste center. All the sticks weighed 450 pounds. Is that more or less than a ton?
Rachel was making cookies. The recipe called for 2 pounds of flour. How many ounces would that be?
George was at the store and bought 48 ounces of bananas. How many pounds of bananas did he buy?
Larry was at the airport and had a personal bag with him. The personal bag could not weigh more than 1 pound. If Larry’s bag was 8 ounces, could he bring it on the plane? Explain.
Estimate the best answer for each measurement.
Convert using multiplication or division.
Complete the conversion table.
Compare the measurements using <, >, =. Use the conversion tables or multiplication/ division to help.
Mannie wants to know how much his bag of apples weighs. What unit should he measure the bag of apples in?
Joseph has a bag of candy that weighs 18 ounces. Solomon has a bag that weighs one pound. Which bag of candy weighs more?
Eli said his book bag weighed a ton when he arrived home from school. Is this a good estimate for the weight of a bookbag? Explain.
Sara was making muffins and putting them into boxes of 6 for a bake sale. If each muffin weighed 4 ounces, how many pounds did the box of 6 muffins weigh?
Measure liquid capacity.
Find the conversion on the chart to help convert units.
Steven was hoping to make a large recipe of cookies for his class trip. He needed 1 quart of oil but only has an 8 ounce measuring cup. How many cups should he use?
Jack wants to drink 40 fluid ounces of water. If he has a water bottle that holds 2 cups, how many times will he have to fill his water bottle?
The Stark family bought 5 gallons of juice for a celebration. How many cups of juice can they serve?
Abe gets out a jug of maple syrup. He notices it is smaller than a gallon but larger than a pint. What size could the jug of maple syrup be?
Complete the conversion tables.
Circle the greater unit of measurement.
Find the equivalent measurements.
Jeremy measured out 10 ounces of milk for a recipe. Mark measured out 1 cup of water for the recipe. Who measured out more?
Anthony needed 4 gallons of juice for a party. He bought 14 quarts. Does he have enough?
Brian needs to give each of his 16 tomato plants 1 quart of water. How many gallons is this?
Thomas is filling up a wading pool. He wants to do it as fast as possible. He has a container that holds 11 quarts and one that holds 25 pints. Which one is bigger?
1
1
1
1
1
1
Perimeter: add all side lengths together
Area: length × width
Perimeter:
6 + 6 + 2 + 2 = 16in
Area: 6 × 2 = 12in
Joseph is 6 feet tall, and Daniel is 60 inches tall. Who is taller?
Erika had 1 gallon of juice. She divided it between her 16 friends. How much juice did each friend get?
A hook will hold 64 ounces. How many pounds will it hold up?
A rectangle has an area of 40 square feet. If the length is 8 feet, what is the width?
Chapter 12
Chapter 12
In
Chapter 12, we will expand on
In Chapter 12, we will expand on
Measurement and Geometry
Measurement and Geometry
The metric measurement system is an easy system to use and is used all over the world.
The metric measurement system is an easy system to use and is used all over the world.
• Estimate and convert length
• Estimate and convert weight
• Estimate and convert length
• Estimate and convert weight
• Estimate and convert liquid capacity
• Estimate and convert time
• Estimate and convert liquid capacity
• Find elapsed time
• Estimate and convert time
• Find lines of symmetry
• Find elapsed time
• Problem solve
• Find lines of symmetry
• Problem solve
We can understand the relative sizes of measurements in the metric measurement system.
We can understand the relative sizes of measurements in the metric measurement system.
We can convert between different units of measurement, including time.
We can convert between different units of measurement, including time.
We can compare measurements and solve word problems with measurement.
We can compare measurements and solve word problems with measurement.
We can find the elapsed time from two analog clocks or a word problem.
We can find and count lines of symmetry.
We can find the elapsed time from two analog clocks or a word problem.
We can solve measurement word problems with whole numbers and fractions.
We can find and count lines of symmetry.
We can solve measurement word problems with whole numbers and fractions.
Lesson instructions 1 Convert, compare, and estimate between metric units of length.
A pencil tip is about 1 mm in length. A staple is about 1 cm in length.
A door is about 1 m in length. A road bridge could be 1 km in length.
Eli measured his pencil and said that it was 15 centimeters long. Henry measured his pencil and said that it was 110 millimeters long. Whose pencil is longer? How do you know?
Judy measured her ribbon and said it was 2 meters long. Kelly measured her ribbon and said it was 200 centimeters long. Whose ribbon is longer? How do you know?
Justin measured the length of his driveway and found it to be 3 kilometers long. Kane measured his driveway and found it to be 4,500 meters long. Whose driveway is longer? How do you know?
Rick measured the length of a hiking trail and found it to be 2.5 kilometers long. Sam measured the same trail and found it to be 2,500 meters long. Whose measurement is longer? How do you know?
Lesson instructions 2 Convert, compare, and estimate between metric units of weight.
A pencil tip is about 1 mm in length. A staple is about 1 cm in length.
A door is about 1 m in length. A road bridge could be 1 km in length.
1 kilogram (kg) = 1,000 grams (g)
If one small apple weighs 65,000 milligrams, how many grams does it weigh?
If one packet of sugar weighs 75,000 milligrams, how many grams does it weigh?
If a box of chocolates weighs 120,000 milligrams, how many grams does it weigh?
If a bag of flour weighs 95,000 milligrams, how many grams does it weigh?
Convert, compare, and estimate between
milliliters
to milliliters.
To convert from milliliters to liters, multiply by 1,000. To convert from liters to milliliters, divide by 1,000.
Ruth and Sara each poured some juice into their glasses. Ruth had 1,500 milliliters in her glass. Sara had 1.7 liters in her glass. Who had more juice? How do you know?
Marc and Sam each filled their water bottles. Marc’s water bottle contained 750 milliliters of water, while Sam’s water bottle contained 1.2 liters. Who had more water? How do you know?
Tom and Eli each filled their cups with milk. Tom’s cup contained 600 milliliters of milk, while Eli’s cup contained 0.8 liters. Who had more milk? How do you know?
Kelly and Lisa each filled their bottles with orange juice. Kelly’s bottle contained 1,300 milliliters of orange juice, while Lisa’s bottle contained 1.5 liters. Who had more orange juice? How do you know?
Lesson instructions 4
Multiply to convert to a shorter unit of time.
Divide to convert to a longer unit of time.
seconds in 8 minutes
hours in 3 days seconds in 3 minutes days in 24 hours hours in 10 days
minutes in 6 hours seconds in 4 minutes seconds in 7 minutes seconds in 2 minutes
hours in 540
hours in 5 days
minutes in 120 seconds minutes in 1 hour
minutes in 240 seconds minutes in 6 hours hours in 5 days minutes in 9 hours
minutes in 10 hours hours in 7 days minutes in 480 seconds
Emma practiced playing the guitar for 40 minutes 5 days out of the week. How many hours and minutes did she practice guitar?
It took a chef 10 days to prepare a banquet. He worked for 8 hours each day. He charges 60 dollars per hour. How much money should he bill his client?
It took a gardener 5 days to complete landscaping for a large garden. He worked for 7 hours each day. He charges 40 dollars per hour. How much money should he bill his client?
Jack practiced piano for 30 minutes 6 days out of the week. How many hours and minutes did he practice piano?
What time is on this clock?
What time is on this clock?
What time will it be in 45 minutes?
What time will it be in 4 hours and 45 minutes?
What time is on this clock?
What time is on this clock?
What time is on this clock?
What time is on this clock?
What time is on this clock?
What time is on this clock?
What time will it be in three hours and thirty minutes?
What time will it be in 4 hours and 15 minutes?
What time is on this clock?
What time is on this clock?
What time is on this clock?
What time is on this clock?
George took his dog for a walk. He left at 11:00 a.m. and walked around the neighborhood and through the park. He got home at 11:30 a.m. How long did George walk his dog?
The train arrives at the station every 30 minutes. The first train arrived at 7:00 in the morning, but Sara missed it. When will the next train arrive?
Kelly woke up 1 hour and 15 minutes late today at 8:45 a.m. What time was she supposed to wake up?
Judy starts from home at 8:00 a.m. to get to work by 9:00 a.m. when her workday starts. Work is nine hours long. What time will work be over?
Lesson instructions 6 Find line of symmetry.
Line of symmetry
Not a line of symmetry
A line of symmetry is a line that divides a shape or object into two identical parts. If you were to fold the shape on the line, it would match up perfectly.
Is the dotted line on each shape a line of symmetry? Write yes or no.
How many lines of symmetry do these figures have?
Sara is designing a pattern for a quilt. She wants to create a symmetrical design for the quilt’s center. She decides to use a butterfly shape. If she draws half of the butterfly’s shape on one side of the quilt, how many lines of symmetry does the butterfly shape have?
Lisa is arranging tiles on the floor to create a symmetrical pattern. She has square tiles that are each 1 foot by 1 foot. If she wants to create a symmetrical pattern that is 4 feet wide, how many square tiles does she need to place along the width to achieve symmetry?
Emma is arranging candles on a circular birthday cake. She wants to create a symmetrical pattern with the candles. If she has 12 candles in total, and she wants to place them in a symmetrical arrangement around the perimeter of the cake, how many candles will she place on one side of the cake?
John is arranging tiles to create a symmetrical design on his kitchen floor. He has rectangular tiles that measure 6 inches by 12 inches. If he wants to create a symmetrical pattern that is 4 feet long, how many tiles does he need to place along the length to achieve symmetry?
Solve word problems with measurement.
1. Read the problem.
2. Decide which operation to use.
3. Convert the measurement and solve. Metric Length 1 meter = 100 cm 1 cm = 10 millimeters Metric Weight 1 gram = 1,000 milligrams 1 kilogram = 1,000 grams Metric Capacity 1 liter = 1,000 milliliters
Sarah’s pencil is 18 centimeters long. Emma’s pencil is half as long as Sarah’s. How many millimeters long is Emma’s pencil?
Leo spends 9 hours on reading each week. Max spends 1 4 of the time that Leo spends on reading. How many minutes does Max spend on reading each week?
A bag of apples weighs 8 kilograms. A bag of oranges weighs 1 3 of the weight of the bag of apples. How many grams does the bag of oranges weigh?
There are 6 bottles of juice in the fridge, each containing 1.5 liters of juice. How many milliliters of juice are in the fridge?
There are 30 days in April. It took 1 3 of the month for the flower seeds to germinate. How many hours did it take for the seeds to germinate?
George has 700 milliliters of orange juice and 450 milliliters of lemonade. Harry has 1.5 liters of apple juice. Who has more to drink?
7
Anna’s pencil is 18 centimeters long. Donna’s pencil is 2 3 as long as Anna’s. How many millimeters long is Donna’s pencil?
Rachel spends 7 hours on painting each week. Lisa spends 1 3 of the time that Rachel spends on painting. How many minutes does Lisa spend on painting each week?
A bag of apples weighs 10 kilograms. A bag of oranges weighs 1 5 of the weight of the bag of apples. How many grams does the bag of oranges weigh?
There are 6 bottles of juice in the fridge, each containing 1.5 liters of juice. How many milliliters of juice are in the fridge?
Fill in the tables to convert the measurements.
Look at these clocks.
What is the time on this clock? 6:40
What time will it be in 3 hours and 12 minutes? 9:50
What time will it be in 8 hours and 15 minutes?
What time will it be in one hour and thirty minutes?
What time is on this clock?
What time is on this clock?
What time is on this clock?
What time is on this clock?
Write how many lines of symmetry each shape has. Draw the lines of symmetry.
3 lines of symmetry
Rachel leaves her house to walk to school at 7:20 a.m. She walks for 1 hour and 15 minutes before arriving at school just as the first bell is ringing. What time does the first bell ring?
Jake spends 8 hours on studying each week. Abe spends 1 3 of the time that Jake spends on studying. How many minutes does Abe spend studying each week?
An eight-year-old girl is 1.3 meters tall. Her four-year-old brother is 0.9 meters tall. How many centimeters taller is the girl than her brother?
Emma’s basket holds 8 liters. Sara’s basket holds 2 5 as much as Emma’s. How many milliliters does Sara’s basket hold?
Chapter 13
In Chapter 13, we will work with
Data
In Chapter 13, we will work with
Data
We will learn how to organize and graph information we collect about the world.
We will learn how to organize and graph information we collect about the world.
• Create and interpret bar graphs, picture graphs, and tally graphs
• Create and interpret frequency charts
• Create and interpret bar graphs, picture graphs, and tally graphs
• Create and interpret frequency charts
• Create and interpret dot plots with and without fractions
• Create and interpret line and double-line graphs
• Create and interpret dot plots with and without fractions
• Create and interpret line and double-line graphs
We can understand the relationship between bar graphs, picture graphs, tally graphs, and frequency charts.
We can understand the relationship between bar graphs, picture graphs, tally graphs, and frequency charts.
We can use a dot plot to understand data and create a dot plot from a frequency chart.
We can create dot plots with fractions.
We can use a dot plot to understand data and create a dot plot from a frequency chart.
We can draw a line graph and double-line graph given a frequency chart.
We can create dot plots with fractions.
We can draw a line graph and double-line graph given a frequency chart.
Make a bar graph.
Use the data in the chart to make a bar graph.
Answer the questions below. Packages Delivered Monday 15
12
9
16
23
15
1. What day had the most packages delivered?
2. How many packages were sold on Tuesday?
3. What day had the least amount of packages delivered?
4. What two days had the same number of packages delivered?
5. How many packages were delivered in total?
6. What is the average number of packages delivered?
Favorite Seasons
Winter Spring Summer Fall
= 2 students
1. 2. In the pictograph, how many students does each smiley face represent?
How many more students chose summer than spring?
How many students chose fall?
How many students voted in all?
A frequency tables shows us how often something happened. Here, three students ordered French fries, and five students ordered ice cream.
A teacher recorded the favorite fruits of students in the class. Fill in the missing tally marks to match the frequencies on the table. Then, use the frequency table to answer questions 1-3.
How many students were in the class? How do you know?
What was the most popular fruit? How do you know?
How many more students like watermelon than like grapes?
If you combined other categories, what two fruits would give you as many votes as watermelon?
A park ranger kept track of the animals that could be seen from the ranger station. Fill in the missing frequencies to match the tally marks on the table. Then, use the frequency table to answer questions 5-8.
How many more squirrels than deer were seen? Explain.
What is the most common animal that the rangers see?
What is the least common animal that is seen?
How many animals besides birds were seen?
What is the most common house color on the block?
What is being measured in the frequency table below?
What is the least common shirt color in the class?
Did the group have more students older or younger than 10? Explain.
Lesson instructions 3
A frequency table has three columns: one each for the category, the tallies, and the frequency.
Flipping a Coin Coin Flip Tallies Frequency Heads Tails
• The coin landed on heads 11 times.
• It landed on tails 9 times.
• It was flipped 20 times (11+9).
• It landed on heads 2 more times than tails (11-9).
Fill in missing parts on the frequency tables for the given data sets and answer the questions that follow.
A teacher is keeping track of the color of student backpacks and gets the following results: black, black, green, black, blue, black, black, green, green, black, black, blue, black, black, red
How many students are in this class?
How many more students have black backpacks than red backpacks?
A child was measuring the length of rocks (in inches) that were found in the park:
3, 5, 4, 3, 3, 2, 3, 2, 4, 2, 2, 3, 3, 1, 3, 5, 3, 3, 4, 2, 3, 2
What is the most common length of rock found?
What was the least common rock length found?
If you lined all the rocks up end to end, how long would your line of rocks be in inches?
Bonus: How long would it be in feet?
Color Tallies Frequency
Rock Lengths Length
What is missing from the frequency table below, and why are those parts important?
Show the tally marks for a frequency of 23. Why are tally marks typically shown in groups of 5?
A city worker counted the number of tall trees in each park. If there were a total of 20 trees, what number should go in the blank spot on the table?
A student was tracking the results of flipping a coin 30 times. The first row of the table is finished. What should go in the second row?
Lesson instructions 4
Interpret dot plots to answer questions.
A dot plot shows information or data along a number line. This dot plot shows 1 student (1 dot) read 0 books, 3 students (3 dots) read 1 book, 2 students (2 dots) read 2 books.
Use the dot plots to answer each question.
A gardener kept record of how many bees visited the garden each day. The results were graphed on the dot plot.
How many days were the bees counted?
How many days had 11 bees?
What were the most common numbers of bees in the garden?
How many more days had 15 bees visiting than 12 bees visiting?
All the students in fourth grade were given one snack size bag of candy. They opened and counted the candies in their bag, and the results were graphed.
How many bags of candy were given out?
What was the difference between the most candies per bag and the least candies per bag?
How many students had more than 20, but less than 23 candies in their bag?
What was the most common number of candies per bag?
In a dot plot, what does the key show?
Why does a dot plot need a title above the plot and a label under the number line?
Tim said that there were 3 days that had 5 cars in the parking lot, but Solomon said there were 6 days with 5 cards in the parking lot. Who was right? How do you know?
Analyze the dot plot below. What number of bee represents 1 9 of the total data collected? Explain how you arrived at your answer.
Lesson instructions 5
Number frequency can be recorded with tally marks and graphed on a dot plot.
Tally how many times each of the following numbers occur.
2, 3, 2, 2, 2, 3, 2, 2, 2, 4, 4, 4
2 occurs 7 times; tally IIII II 3 occurs 2 times: tally II 4 occurs 3 times; tally III
Create tally charts and dot plots of the given information.
Number of picnic tables per park in town: 0, 3, 2, 4, 4, 6, 5, 4, 4, 6, 4, 5
Then use a number line. Place 7 dots above 2. Place 2 dots above 3. Place 3 dots above 4.
Number of spots per ladybug: 4, 4, 6, 5, 3, 3, 7, 0, 1, 2, 7, 5, 5, 4, 3, 6, 6, 5
Create dot plots using the following information.
Number of strawberries per container: 22, 25, 25, 24, 23, 23, 26, 23, 22, 27, 24, 24, 25, 26
Ages of students in a school band: 14, 15, 14, 16, 17, 16, 17, 18, 15, 16, 16, 17. Each dot should represent two students.
A class was surveyed about the number of siblings they have, and below is the dot plot displaying the data. Answer the question using the dot plot.
A class was surveyed about the number of siblings they have, and below is the dot plot displaying the data. Answer the question using the dot plot.
Number of siblings
What is the most common number of siblings Mrs. Alpine’s class has?
Number of siblings
How many more people had 1 sibling than 5 siblings?
The number of donuts left after each class’ end of the school year celebration party is recorded below. Answer the question using the dot plot.
End of the Year Party Donuts
The number of donuts left after each class’ end of the school year celebration party is recorded below. Answer the question using the dot plot.
End of the Year Party Donuts
Number of donuts
How many classes are there? Hint: count the number of dots.
Number of donuts
How many donuts are left over altogether?
Lesson instructions 6
Interpret dot plots with fractions to answer questions. A dot plot shows information or data along a number line. This dot plot shows 1 beetle measured 1 4 inch, 3 beetles measured 1 2 inch, and 2 beetles measured 3 4 inch.
Answer the questions about the dot plot below.
What is the dot plot tracking?
How many students were counted?
What was the difference between the most amount that students read and the least amount of reading time?
How many students read more than one hour but less than three hours?
What fraction of the total students read less than 2 hours?
Create the dot plots for the given information. In your dot plots, remember to include a title and a label.
A tailor has leftover buttons. The buttons have the following widths (in inches):
A child is collecting twigs and wants to keep track of how long they are in inches. The following measurements are recorded: 3, 5 1 2 , 3 1 2 , 5, 5, 4 1 2 , 5, 6, 3 1 2 , 5 1 2 , 3, 4, 3, 5 1 2
In the dot plot below, what is the difference between the oldest and youngest child in the daycare? Explain.
What is the total number of cookies eaten as show on this dot plot below?
What is missing from the dot plot below?
Analyze the dot plot below. How many days had at least 2 inches of snow fall?
Use the data in the chart to make a double line graph.
Hint: The days of the week go on the x-axis, and the number of quarts goes on the y-axis. Berries Picked Last Week
Answer the questions below.
1. What was the total quarts of strawberries picked?
2. What was the total quarts of blueberries picked?
3. What day had the most amount of berries picked?
4. What two days had the same number of strawberries and blueberries picked?
How much warmer was Thursday than Tuesday?
What was the median temperature for the week?
What was the range of the data?
What was the average high temperature this week?
Answer the questions based on the information in each graph.
In a mixed fruit cup, the fruit was counted and graphed. How many cherries were in the fruit cup? 2 cherries
A. What was the most common fruit?
B. What was the least common fruit?
C. How many more blueberries were there than cherries? 1.
A teacher tracked how students got to school. How many students rode on the bus? 8 × 2 = 16 students
A. How many students rode a car?
B. How many students were counted in all?
C. How many more students rode the bus than walked or rode their bike?
B. Were there more plates or bowls? 3.
In a thrift store, a worker counted the types of dishes on a shelf. How many cups and plates were there?
Cup 22 Plate 4 22 + 4 = 26 cups and plates
A. How many dishes were there that were not cups?
C. Were there more 1-year-olds or 2-year-olds? 4. 1
A daycare counted the number of kids present in the room. How many 1-year olds were there? 3 1-year olds
A. What was the highest age in the room?
B. How many kids were in the room?
or Bike
2
8
Create a line plot for the following data. Distance traveled to school in miles: 1, 4, 4, 3, 5, 2, 4, 4, 5, 3, 7
Create a line plot for the following data. Length of pipe cleaners in inches: 4, 4 1 2 , 4, 4 1 2 , 5, 5, 5, 5 1 2 , 5 1 2 , 6, 6, 4 1 2 , 7 1 2 , 7, 7, 5, 5
Create a tally chart for the following data.
Favorite colors in the kindergarten classroom: red, red, blue, blue, green, red, blue, green, green, red, yellow, red, green, blue, yellow, blue, blue, blue
Create a frequency table for the following data.
Eye color: blue, blue, green, blue, brown, blue, brown, brown, brown, blue, blue, brown, brown, brown
Chapter 14
In Chapter 14, we will conclude with
Level D Review
In Chapter 14, we will conclude with
Level D Review
This chapter includes all concepts covered in this book.
This chapter includes all concepts covered in this book.
• Understand place value with large numbers and decimals
• Use all four operations with multi-digit numbers
• Understand place value with large numbers and decimals
• Add, subtract, and multiply fractions
• Use all four operations with multi-digit numbers
• Compare, order, and find decimals on a number line
• Add, subtract, and multiply fractions
• Identify and solve for unknown angles
• Compare, order, and find decimals on a number line
• Problem solve
• Identify and solve for unknown angles
• Problem solve
We can identify place value from millions to hundredths.
We can use all four operations to solve problems with multi-digit numbers.
We can identify place value from millions to hundredths. We can use all four operations to solve problems with multi-digit numbers.
We can add, subtract, and multiply fractions and mixed numbers and simplify our answers.
We can understand the size of decimals.
We can add, subtract, and multiply fractions and mixed numbers and simplify our answers.
We can describe an angle as acute, obtuse, or right, measure angles, and find a missing angle.
We can understand the size of decimals.
We can describe an angle as acute, obtuse, or right, measure angles, and find a missing angle.
We can solve multi-step word problems with all four operations.
We can solve multi-step word problems with all four operations.
Identify the place value of the underlined digit in each number.
854.12 Hundredths place
Write each number in word form.
854.12 Word Form: eight hundred fifty-four and twelve hundredths
Complete the charts by filling in the value of each digit.
854.12
Value of Digit 8: 800
Value of Digit 4: 4
Value of Digit 1: 0.1
Patrick thought of a number with a 7 in the hundreds place, a 5 in the ones place, 2 more tens than hundreds, and 3 fewer thousands than ones. What number did he think of?
Terry saw that 9,307,194 people lived in his city. Which number is in the ten thousands place?
The school fundraiser raised 34,295.18 for new playground equipment. What is the value of the 8?
Steven has $109.43 in his bank account. What number is in the tenths place?
+ 56,994
Rewrite the problem, then add or subtract the whole numbers.
+ 12,531 + 91,247 = 129,873 89,346 928,341 + 35,194 967,836 + 734,671 973,971 + 456,211 983,426 + 356,732 68,943 − 3,299 302,654 298,188 452,386 329,321 11 11 25,658 + 17,482 43,140 11 11 9,652 3,945 + 1,563 15,160
William is keeping track of his time to see where it all goes. It took him 5,621 seconds to clean his room and 1,294 seconds to do the laundry. How long did it take him to do both activities?
Tyler read recently that there are 83,906 people in his town, and 13,209 of them are children. How many are not children?
The school cafeteria served 3,476 breakfasts and 5,982 lunches this week. About how many meals did they serve in all? Estimate to the largest place value before solving.
Zachary used 12,645 blocks to build a castle. If he started with 30,000 blocks, how many blocks does he have left?
Use patterns of multiplication to solve each problem.
40 × 70 = 2800 1 95 × 25 475 + 1900 2375
There are 450 rubber bands in the bag. If you have 4 bags, how many rubber bands do you have?
If Walter practices making 5 backbends a day, how many would he make in 365 days?
Nathan divided a large bag of pretzels into smaller ones for snacks. He put 45 pretzels in each bag and made 29 bags. How many pretzels were in the large bag?
Bryan’s uncle has a farm. His uncle told him that there were 30,000 corn plants in an acre. If his uncle has 40 acres of corn, how many corn plants are there?
Use patterns of division to solve each problem.
Use compatible numbers to estimate.
25 ÷ 8 = 24 is close to 25 24 ÷ 8 = 3
25 ÷ 8 is about 3
Divide.
Divide: 5 ÷ 3=1
Multiply: 1 × 3 = 3
Subtract: 5 - 3 = 2
Bring down: 4
Divide: 24 ÷ 3 = 8
Multiply: 8 × 3=24
Subtract: 24 - 24 = 0 Bring
(none)
The teacher divides 36 students into 9 groups. How many students are in each group?
Jacob can bake a batch of 2 muffins in the oven at a time. If he wants to bake 108 muffins, how many batches will he need to make?
If 700 markers are put in packages of 10, how many packages are made?
Sara is organizing a community event and wants to place flyers around the neighborhood. She has a budget of $480 for printing flyers. Each flyer costs $8. How many flyers can she print?
Complete each equivalent fraction.
List the factors for each pair of numbers.
Simplify each fraction using the common factors from above.
Compare each set of decimals using <, >, or =.
Solve. Simplify if necessary.
Add the numerators. Keep the denominator.
Russell has 6 9 of a pie left. What fraction is this in simplest form?
Scott ate 1 3 of a pizza, and Roger ate 2 8 of a pizza. Which boy ate more?
Jordan is making a pizza crust. The recipe calls for 2 1 6 cups of flour. What is this amount as an improper fraction?
Alex is making muffins. The recipe calls for 3 2 3 cups of flour for the muffins and another 1 3 cup of flour for the topping. How much flour does Alex need in all?
Compare the decimals using <, >, or =.
Identify the place values of the underlined numbers.
854.123 Thousandths place
Write each number in its word form.
854.12 Word form: eight hundred fifty-four and twelve hundredths Line up place values.
Order each group from smallest to largest.
Create a number line and plot the following decimals.
Mrs. Ross’s fifth-grade class raised $4578.93 for a charity, and Mrs. Mill’s class raised $4599.75 for the same charity. Who raised more money? How much more?
Mrs. Miller’s third-grade class collected $7820.36 for a charity, while Mrs. Davis’s class raised $7801.25 for the same charity. Who raised more money? How much more?
The tomato plant grew 12.6 cm on Monday, 1.8 cm on Tuesday, 6.4 cm on Wednesday, and 0.9 cm on Thursday. Which day had the most growth for the plant?
The sunflower plant grew 14.2 cm on Monday, 2.5 cm on Tuesday, 8.9 cm on Wednesday, and 1.3 cm on Thursday. Which day had the most growth for the plant?
How much did the plant grow altogether?
How much did the plant grow altogether?
Identify the type of angle and its measurement.
Acute angle < 90°
Right angle = 90°
Obtuse angle > 90°
Type of angle: Acute
Measurement: 50°
Type of angle:
Measurement:
Type of angle:
Measurement:
Type of angle:
Measurement:
Type of angle:
Measurement:
Determine the value of A in each angle.
Type of angle:
Measurement:
Type of angle:
Measurement:
A water sprinkler covers 90° of a backyard lawn. How many times will the sprinkler need to be moved in order to cover the full 360° of lawn?
Two angles join to form a right angle. The first angle measures 35°. What is the measure of the second angle?
Two angles join to form a right angle. The measure of the first angle is 55°. What is the measure of the second angle?
This angle cuts out 1 9 of the circle. Find the measure of the angle.
Start by writing 1 9 as a fraction with a denominator of 360.
Solve each problem.
Solving word problems:
C Circle the numbers
U Underline the question
B Box the key words
At the grocery store, Joseph weighs 1 apple. If 1 apple weighs 3 4 pounds, how much would 8 apples weigh? 3.
E Eliminate what you don't need
S Does your answer make sense?
In the bee yard, there were 145,932 bees making honey. What is that number rounded to the nearest ten thousand?
1. 2. The tomato plant grew 18.7 cm on Monday, 3.8 cm on Tuesday, 7.1 cm on Wednesday, and 2.6 cm on Thursday. How much did the plant grow altogether?
5. 6. Emma practiced playing the piano for 45 minutes 5 days out of the week. How many hours and minutes did she practice the piano?
Zachary’s family wanted to put a fence around their yard. If their yard was a perfect square, and one side measured 37 feet, how much fencing would they need to fence the entire yard?
7. 8. At a band concert, chairs are set up in rows of 25. If there are 900 chairs set up, how many rows of chairs are there?
A local bakery uses 6,000 pounds of flour in a year. How many tons do they use?
It is 325 miles from James’s house to his grandparents, and it is seven times that amount to get to his aunt’s house. How many miles it is to James’s aunt’s house?
A bag of apples cost $3. How much would 6 bags of apples cost?
Sam read 7 20 of his weekly goal on Sunday and 3 20 of his weekly goal on Monday. How much more of his goal did he read on Sunday?
The train arrives at the station every 20 minutes. The first train arrived at 8:00 a.m., but Helen missed it. When will the next train arrive?
Alan puts 12 eggs in a carton. If he has 338 eggs, how many cartons can he fill?
How many will he have left over?
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