Cumulative List of Learning Goals Unit 1 Learning Goals (to be spiraled) 1. Reading and writing numbers 2. Intro to Powers 3. Intro to Fractions 4. Add/Subtract Fractions 5. Fractions, Decimals, and Percents Unit 2 Learning Goals (to be spiraled) 1. Multiply decimals and fractions 2. Intro to Division 3. Divide Decimals & Fractions 4. Read, write, and describe ratios, rates, and proportions. 5. Read, write, represent, and operate with integers.
Unit 4 Learning Goals (to be spiraled) 1. Intro to Sampling 2. Intro to Graphs 3. Measures of Center 4. Intro to Probability 5. Real World Data
Unit 3 Learning Goals (to be spiraled) 1. Intro to Equations 2. Intro to Properties 3. Solve Equations 4. Function Tables 5. Coordinate Plane
MAP prep/Test Taking Strategies[1] 1. Guess, Check and Revise (Geometry, Number Sense) 2. Work Backward (Number Sense, Algebra) 3. Use Logical Reasoning (Fractions, Ratios, Probability, Data & Graphing) 4. Make an Organized List (Probability, Data & Graphing) 5. Write an Equation (Fractions, Algebra, Probability, Measurement)
Page 1 of 40
Unit 5 Learning Goals (new) 1. Intro to Angles 2. Intro to Shapes 3. 3D Figures 4. Perimeter/Area 5. Measurement
Report Period 1 Calendar KSS-‐no class Spiraled MW: operation actions DN: whole # + and TC: whole # + and OD: whole # + and -
MW: place value DN: whole # mult TC: whole # mult OD: whole # mult MW: exponents DN: place value TC: whole # div OD: whole # div MW: fractions DN: exponents TC: whole # m & d OD: whole # m & d MW: fractions DN: place value TC: whole # all operations OD: whole # operations MW: exponents DN: fractions TC: whole # operations OD: whole # operations
Monday
Tuesday
Wednesday
Thursday
Friday
August 7th
August 8th
August 9th
August 10th
Visually represent and describe the place value of digits in whole numbers and decimals.
Read, create, and use number lines to compare whole numbers and decimals.
Add and subtract decimals.
Round whole numbers and decimals. Estimate whole number and decimal sums and differences.
August 13th
August 14th
August 15th
August 16th
August 17th
Describe and compare numbers as powers of ten.
Read, expand, and evaluate exponents.
Evaluate cubes and squares.
Evaluate roots (cubes and squares).
Multiply and divide using exponents.
August 20th
August 21st
August 22nd
August 23rd
August 24th
Visually represent fractions.
Calculate and compare equilvalent fractions.
Read, create, and use fractional number lines.
Compute and visually represent fractions of groups.
Visually represent equilvalent fractions.
August 27th
August 28th
August 29th
August 30th
August 31st
Add and subtract like fractions.
Add and subtract like fractions with regrouping. September 4th
Add and subtract unlike fractions.
Add and subtract unlike fractions with regrouping.
Visually represent addition and subtraction of fractions.
September 5th
September 6th
September 7th
Visually represent and create number lines with percents.
Convert between FDP.
Create shared number lines with FDP.
Compare numbers using shared number lines with FDP.
September 10th
September 11th
September 12th
September 13th
Eliminate answer choices in multiple choice questions.
Answer CR questions excellently using the rubric.
No class-‐Staff PD
September 3rd Labor Day-‐no school
Benchmark: CR
Benchmark: MC
Learning Goal #1: Read, write, and visually represent whole numbers and decimals and find their sums and differences. Students will KNOW…
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That visually represent means draw a picture of that number.
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Each number has at least one digit in it. o The placement of the digit in a number gives the digit and the number its value. o
o
Short word form is a way of writing a number that uses digits and place values in words. Word form uses only words to write numbers.
•
Equivalent means that the two numbers being compared have the same value.
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A number line is a visual way to compare the value of numbers. o
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To add and subtract numbers, you add and subtract digits that have the same place value. o
o
o
A number line has intervals, tick-marks, and benchmarks.
Regrouping means carrying over the extra (ten or more values in a single place value) so that there is always only one digit in each place value. Borrowing happens when the value of the digit being subtracted from is too small to subtract the value of the place value in the other digit(s). Rounding means find the closest number to the original number but has less digits that are significant.
Students will BE ABLE TO…
1. Visually represent and describe the place value of digits in whole numbers and decimals.
• •
2. Read create and use number lines to compare whole numbers and decimals. 3. Add and subtract decimals. 4. Round whole numbers and decimals. Estimate whole number and decimal sums and differences.
Paired Math and/or Literacy Strategies:
Students will UNDERSTAND…
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•
•
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The order of the digits and operations matter. Decimals can only be combined or separated part by part – this means that their place values must be combined with the same place value aka “line up the decimal points.” When there is ten or more in one place value, the “extra” has to be carried over to the next largest place value. You can borrow from the next larger place value to get more digits to subtract. The question the problem asks determines whether you have to compute exactly (paying attention to all place values) or estimate (pay attention to less than all of the place values). Match the place value of the answer to the place value in the question. To compare numbers, stack them by lining up their decimal points and then compare the digits in each place value from largest to smallest value.
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• • • •
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Identify the characters and setting (activate schema) Identify the main question and supporting details in word problems Identify inferences in word problems Write analogies (ex. 2 tens is to 0.2 hundredths as 4 ten is to 0.4 hundredths) Semantic Maps Math Rubric (from last year) Use anticipatory guide for key points. Make text to self/text/world connections. Word Wall
Learning Goal #2: Compute fluently with powers. Students will KNOW…
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•
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Power of ten notation is the new expanded form because it tells the place value of each digit using a factor of a base ten. An power is a kind of number notation (language) that uses bases (factors) and exponents (count of factor uses) to write numbers. o A base is the normalsized number in an exponent that is the factor that is being multiplied. o An exponent is the tiny superscript number that tells the count of how many times the base should be multiplied. A square is a number that is multiplied by itself. Think length x width = square. A cube is a number that is multiplied by itself two times. Think length x width x height = cube. A radical (√) is the symbol for a root. o A square root is a number that can be multiplied by itself to give another number. o A cube root is a number that can be multiplied by itself TWICE to give another number. o If the symbol itself has a three exponent, it means find the cube root.
Students will BE ABLE TO…
1. Describe and compare numbers as powers of ten. 2. Read expand, and evaluate exponents. 3. Evaluate squares and cubes. 4. Evaluate square roots and cube roots. 5. Multiply and divide using exponents.
Paired Math and/or Literacy Strategies:
Students will UNDERSTAND…
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A root means separate using multiplication.
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A square means multiply twice.
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A cube means multiply three times.
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To evaluate, multiply the base the number your exponent demands.
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To expand, just write the base the number of times the exponent.
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A square root will have about half of the digits of the original number (because if 1002 = 100 x 100 = 10,000).
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You can multiply and divide exponents that share a base because the exponents tell you the count of how many times you multiply the same number.
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To multiply a shared base, add the exponents, then evaluate.
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To divide a shared base, subtract the exponents, then evaluate.
• • • • • • •
Identify the characters and setting (activate schema) Identify the main question and supporting details in word problems Visualize the pattern Summarize the steps Venn Diagrams Word maps Use anticipatory guide for key points. Make text to self/text/world connections. Word Wall
Learning Goal #3: Read, write, and visually represent fractions. Students will KNOW…
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That visually represent means draw a picture of that number (a whole shape split into different but equally sized portions with the important parts shaded in). A fraction has three parts: a numerator that shows the portion we have, a division bar, and a denominator that tells us how many parts the whole is split into. o
The numerator is on the top of the division bar and the denominator is on the bottom.
o
The denominator is read with the –th suffix.
•
A mixed number has both a whole number and a fraction part.
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An improper fraction has a numerator bigger than its denominator.
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Equivalent means that the two numbers being compared have the same value.
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To find a fraction of a group/set, you divide the set into groups, then multiply by the number of groups.
Students will BE ABLE TO…
1. Visually represent fractions.
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2. Calculate and compare equivalent fractions. 3. Read, create, and use fractional number lines. 4. Compute and visually represent fractions of groups. 5. Visually represent equivalent fractions.
Paired Math and/or Literacy Strategies:
Students will UNDERSTAND…
Fractions represent a part of a whole. Fractions with different denominators can have the same value.
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To compare fractions, they must have the same / a common denominator.
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Converting fractions means finding the factor that will make one fraction have the same denominator of the other.
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“What you do to the top, you have to do to the bottom.” – when you split or combine the parts on either the top or the bottom of the fraction, the other side has to be converted to be fairly.
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To fix an improper fraction, divide the numerator by the denominator. The denominator stays the same, the numerator is the remainder and the whole number is the quotient.
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A fraction can be simplified if both the numerator and denominator have a common factor. To simplify a fraction most efficiently, divide both the numerator and denominator by their greatest common factor.
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Identify the characters and setting (activate schema) Identify the main question and supporting details in word problems Write analogies (ex. 2 tenths is to 1 fifth as 4 tenths is to 2 fifths) Semantic Maps Use anticipatory guide for key points. Make text to self/text/world connections. Word Wall
Learning Goal #4: Add and subtract fractions. Students will KNOW…
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Adding and Subtracting fractions means to add the similar parts of the fractions, then simplify. o
o
o
Regrouping/Borrowing means splitting the parts of the group to share with other fractions. Reducing fractions means to make the fractional parts have the smallest value separately, while still having whole numbers in the numerator and denominator. Simplifying fractions means to make any improper fraction into a mixed number.
Students will BE ABLE TO…
1. Add and subtract fractions.
Students will UNDERSTAND…
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2. Add and subtract fractions with regrouping. 3. Add and subtract unlike fractions.
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4. Add and subtract unlike fractions with regrouping. 5. Visually represent addition and subtraction of fractions.
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Numbers with parts less than one can only be fairly combined or separated if they are split into the same number of parts. Numbers have to be in the same form before they can be compared, combined, or separated. You carry from a fraction to a whole number by subtracting the same value of the denominator (when you have an improper fraction) when you carry it into the whole number.
Paired Math and/or Literacy Strategies:
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Semantic Maps
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Identify the characters and setting (activate schema)
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Identify the main question and supporting details in word problems
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Visualize the pattern
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Summarize the steps
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Word maps
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Use anticipatory guide for key points. Make text to self/text/world connections. Word Wall
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Learning Goal #5: Compare fractions, decimals, and percents. Students will KNOW…
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Percent means “per cent” or out of one hundred. o
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Students will BE ABLE TO…
Percents can be worth more than 100% (whole numbers and decimals greater than one).
Any digits after a decimal represent a digit value less than one. An inequality is a number sentence that shows which an order of the value of numbers and uses the following symbols to indicate value: < = >.
•
When representing a comparison, use the original forms (the way the numbers were given to you).
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Check the directions to know if you need to order them from greatest to least or least to greatest.
Paired Math and/or Literacy Strategies:
Students will UNDERSTAND…
1. Visually represent and create number lines with percents.
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Semantic Maps
2. Convert between fractions, decimals, and percents.
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To compare numbers fairly, they have to be in the same form.
Identify the characters and setting (activate schema)
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3. Create shared number lines with fractions, decimals, and percents.
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Decimals and percents are base ten functions, so an efficient representation is a grid.
Identify the main question and supporting details in word problems
4. Compare numbers using shared number lines with fractions, decimals, and percents.
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Visualize the pattern
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FDPs have their own place value: anything for fractions, base ten for decimals, and the hundredths place for percents.
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Summarize the steps
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Word maps
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Use anticipatory guide for key points. Make text to self/text/world connections. Word Wall
FDPs are ways to write values that represent a part of a whole.
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A percent is the same as a decimal to the hundredths place.
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Sometimes numbers in different forms can have the same value; you’ll know because when you convert them to the same form, they will be the exact same number.
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Learning Goal #6: Use test-taking strategies to solve math problems on standardized tests. Students will KNOW…
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A multiple choice question has three lies and one truth. o
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"Look alike options" probably one is correct; choose the best but eliminate choices that mean basically the same thing, and thus cancel each other out
o
If two alternatives seem correct, compare them for differences, then refer to the stem to find your best answer
o
Compare digits in the numbers for correct place value.
The rubric allows you do get more points by showing on paper what you know in your head. You should do this for EVERY CR problem. o
Show more than one step
o
Show your calculations
o
Explain the process
o
Describe using vocabulary
o
Make a visual or a drawing
Students will BE ABLE TO…
Paired Math and/or Literacy Strategies:
Students will UNDERSTAND…
1. Eliminate answer choices in multiple choice questions.
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Eliminating foolish answer choices make the test easier for you.
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2. Answer CR question excellently using the rubric.
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Showing all parts of the rubric’s requirements will earn you more points and allow you to create more correct answers.
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Use anticipatory guide for key points. Make text to self/text/world connections.
  Daily Objectives for This Unit: 1. Read, write, and visually represent whole numbers and decimals and find their sums and differences. a. Visually represent and describe the place value of digits in whole numbers and decimals. (analysis) b. Read create and use number lines to compare whole numbers and decimals. c. Add and subtract decimals. d. Round whole numbers and decimals. Estimate whole number and decimal sums and differences. 2. Compute fluently with powers. a. Describe and compare numbers as powers of ten. b. Read expand, and evaluate exponents. c. Evaluate squares and cubes. d. Evaluate square roots and cube roots. 3. Read, write, and visually represent fractions. a. Visually represent fractions. b. Calculate and compare equivalent fractions. c. Read, create, and use fractional number lines. d. Compute and visually represent fractions of groups. e. Visually represent equivalent fractions. 4. Add and subtract fractions a. Add and subtract fractions. b. Add and subtract fractions with regrouping. c. Add and subtract unlike fractions. d. Add and subtract unlike fractions with regrouping. e. Visually represent addition and subtraction of fractions. 5. Compare fractions, decimals, and percents. a. Visually represent and create number lines with percents. b. Convert between fractions, decimals, and percents. c. Create shared number lines with fractions, decimals, and percents. d. Compare numbers using shared number lines with fractions, decimals, and percents. 6. Use test-taking strategies to solve math problems on standardized tests. a. Eliminate answer choices in multiple choice questions. b. Answer CR question excellently using the rubric.
Comparing and Contrasting Comparing and Contrasting Pattern Finding Predicting Comparing and Contrasting Comparing and Contrasting Classifying Classifying Comparing and Contrasting Comparing and Contrasting Comparing and Contrasting Comparing and Contrasting Comparing and Contrasting Recognizing Attributes Recognizing Attributes Recognizing Attributes Recognizing Attributes Comparing and Contrasting Comparing and Contrasting Seeing Relationships Seeing Relationships Comparing and Contrasting Comparing and Contrasting Comparing and Contrasting
Report Period 2 Instructional Calendar Spiraled MW: Estimate/Round DN: Equivalent Fractions TC: Whole # Multiplication OD: Powers MW: FDP DN: Equivalent Fractions TC: Whole # Multiplication OD: Powers and Roots MW: exponents DN: Divide Numbers TC: Whole # Mult and Div OD: Powers and Roots
MW: Add & Subtract Fractions DN: Divide All Numbers TC: Whole # Mult and Div OD: Powers and Roots
MW: Ratios, Rates, & Proportions DN: Add & Subtract Fractions TC: Whole # all operations OD: Integers
MW: Add & Subtract Integers DN: Add & Subtract Fractions TC: Whole # all operations OD: Integer Addition
Monday
Tuesday
Wednesday
Thursday
Friday
Sept 17
Sept 18
Sept 19
Sept 20
Sept 21
Add and subtract unlike fractions with regrouping.
Multiply decimals.
Multiply simple fractions.
Multiply mixed numbers.
Convert between FDP.
Sept 24
Sept 25
Sept 26
Sept 27
Sept 28
Divide whole numbers with no remainders.
Divide by two digit numbers.
Divide whole numbers with remainders.
Interpret remainders.
Represent remainders as fractions.
Oct 1
Oct 2
Oct 3
Oct 4
Oct 5
Divide decimals.
Represent remainders as decimals.
Divide simple fractions (across and reciprocal).
Divide mixed numbers.
Multiply and divide decimals using 10 x 10 grids.
Oct 8
Oct 9
Oct 10
Oct 11
Oct 12
Read and write ratios given information (pics, descriptions).
Identify and solve proportions.
Find unit rates.
Find fractions of whole numbers.
Add and subtract unlike fractions with regrouping
Oct 15
Oct 16
Oct 17
Oct 18
Oct 19
Read and represent integers in verbal examples and number lines.
Compare and order integers.
Add integers.
Subtract integers.
Convert rational integers to different forms.
Oct 22
Oct 23
Oct 24
Oct 25
Oct 26
Eliminate answer choices in multiple choice questions.
Answer CR questions excellently using the rubric.
Benchmark: CR
Benchmark: MC
Staff PD Day (No Kids)
Learning Goal #1: Multiply Fractions and Decimals Students will KNOW… •
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To multiply decimals, you must multiply each digit in the top number to each digit in the bottom number. To multiply fractions, you multiply the numerators together and then multiply the denominators together. If you have a mixed number, you must make it an improper fraction to multiply it. o
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Multiply the denominator to the whole number, then add the numerator. Put that number over the original denominator.
To simplify a fraction, you divide both the numerator and denominator by the same number.
Students will UNDERSTAND… •
To multiply decimals, you don’t have to line up the decimal points.
Students will BE ABLE TO DO… •
Multiply decimals. o
Line up decimals appropriately.
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To multiply fractions, you MUST make the fractions improper.
o
Multiply each digit by each digit in the other number.
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A final answer is one that is fully simplified.
o
Add the sums together.
Simplify always means divide.
o
Apply the correct number of decimal places to the final answer.
o
§ § o
Divide an improper fraction to make a mixed number.
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Divide a simple fraction in order to reduce it.
A simplified fraction is still an equivalent fraction – its just that you use division instead of multiplication.
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Multiply simple fractions. o
Multiply across on top and bottom.
o
Simplify/Reduce their final answers.
Multiply mixed numbers. o
Make mixed numbers into improper fractions.
o
Multiply the improper fractions together.
o
Simplify/reduce their final answers.
Learning Goal #2: Divide Whole Numbers Students will KNOW… • •
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When we divide, we are trying to scoop out a certain number (the number outside of the bridge), and we can count the number of scoops we take out on top.
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The number under the bridge is how many items we have in our bowl.
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The number outside of the bridge is how many items our magic scoop can take out – no more, no less.
When we are left with a number that is less than our scoop, that is called the remainder. o
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Students will UNDERSTAND…
To divide, you put the first number under the bridge and the second number on the outside.
The remainder can be a fraction – the number of items left over the number of items one scoop can take out.
Writing the first 9 multiples of our scoops to the side allows us to divide quickly and stay on track. We must line up the number of scoops we are taking from the number of items in the bowl we are taking it from. Remainders aren’t always dropped.
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To divide any number, you move from right to left under the bridge.
The bottom number (after we subtract) is the one we are trying to “take scoops” from. That’s how much is left in our bowl.
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We keep dividing until we can’t take out multiples of our scoop anymore.
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We can stop dividing when the bottom number is less than one scoop.
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The question lets you know whether the remainder affects the answer at all. o
“left over” – the remainder is the answer.
o
“How many total” – the remainder is the extra one, even though it is an incomplete group
o
“Completely full” – the remainder is dropped. (people are left behind/items are trashed)
Students will BE ABLE TO DO… •
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Divide whole numbers with no remainders. o
Identify and set up a long division problem from a given problem (in words and symbols).
o
Write the first 9 multiples of the outside number to the side to help.
o
Divide until no more “scoops” can be taken out.
Divide by two digit numbers. o
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Divide whole numbers with remainders. o
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Stop dividing when the bottom number is less than one scoop. (+ the above)
Interpret remainders. o
Identify whether the remainder changes the final answer to a question in the word problem.
o
The remainder (1) adds one to the final answer, (2) doesn’t affect the final answer, or (3) is the final answer. ( + the above)
Represent remainders as fractions. o
Write multiples for numbers more than 9. (+ the above)
Create a fraction with the remainder on top and the “scoop” as the denominator, writing the final answer as a mixed number. (+ the above)
Learning Goal #3: Divide Fractions and Decimals Students will KNOW… •
To divide decimals, keep the decimal place in the first number. The second number must be come a whole number. o
o
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You can always add zeros after the decimal point. It doesn’t change the value of the number at all.
If you have a remainder when dividing a decimal, add a zero to the decimal under the bridge then divide again.
To divide fractions, you can divide across if you can divide evenly on both the top and the bottom.
o
To divide fractions, you MUST make the fractions improper.
Move the decimal places in the outside number until the number is a whole number. Then move the decimal place in the second number the same number of places.
To make a remainder into a decimal, add decimal and a zero to the number under the bridge then divide again.
o
Students will UNDERSTAND… •
If you can’t divide evenly across, you can change the sign and the fraction behind (aka make a reciprocal and multiply). If you have a mixed number, you must make it an improper fraction to divide it.
o
You must add zeros and divide until the remainder is 0.
o
If the remainder keeps being a certain number, then you have a repeating decimal. You can stop dividing after you see this number 3 times.
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You must both flip the sign and the fraction behind – you can’t just do one or the other.
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Sometimes you can divide across – sometimes you can’t.
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Dividing or multiplying just the whole number part of a mixed number is not fair to its simple fraction partner.
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Multiplying and dividing decimals with 10 by 10 grids only works when both decimals are to the tenths or hundredths place.
Students will BE ABLE TO DO… •
Divide decimals. o Divide completely. o Add zeros to finish the division. o Bring the decimal point up.
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Represent remainders as decimals. o
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When there is a remainder, add a decimal point and a zero, then divide again. Repeat until the remainder is zero.
Divide simple fractions. o Try to divide across. o
If dividing across doesn’t work, flip the sign and the fraction behind.
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Divide mixed numbers. o Make mixed numbers into improper fractions first.
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Multiply and divide decimals using 10 x 10 grids. o Multiply: § Shade one decimal in columns. § § o
Shade the other decimal in rows. The overlap (its count) is the answer.
Divide:
To multiply decimals using 10 x 10 grids, you must shade in each decimal (one in columns, one in rows), then count the overlap.
§
Shade one decimal into columns.
§
To divide decimals using 10 x 10 grids, you must shade in one decimal, then outline that decimal in groups of the second decimal, then count the groups to get your final answer.
§
Outline the decimal into groups of the second decimal. The count of the groups is the final answer.
Learning Goal #4: Ratios, Proportions, and Rates Students will KNOW… •
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A ratio is a comparison in one of these forms. Number names and the word “to”
o
Number names and the word “to”
o
Number names and a colon
o
Number names and a colon
o
As a fraction
o
As a fraction
A ratio can compare two different ways. o
One Part to another part
o
Part to the whole
A proportion is two equivalent fractions separated by an equal sign.
o
We know that the fractions are equivalent because the conversion from the first numerator to the second numerator is the same as the conversion from the first denominator to the second denominator. Proportions can have number names and they are equivalent if the number names/units are the same across the ratio.
A rate is a special kind of ratio that has a 1 at the bottom. o
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A ratio is a comparison in one of these forms.
o
o
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Students will UNDERSTAND… •
Rates are made by taking one ratio and using the original denominator as a division conversion.
Finding a fraction of a whole number is the same as dividing by the denominator and then multiplying that result by the numerator.
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It’s not a proportion unless the two fractions are equivalent.
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A rate can be read in two different ways. o
Something “for every” something else
o
Something “per” something else
Students will BE ABLE TO DO… •
Read and write ratios. o Write in all three forms. o Draw the ratio. o Describe the ratio as a part to a part or a part to a whole.
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Identify and solve proportions. o
Find the conversion to tell whether the example is actually a proportion.
o
Fill in a numerator or denominator (or the equivalent in different forms) to complete the proportion.
o
Solve word problems by writing ratios and completing the proportion.
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Find unit rates. o Divide by the given denominator to determine the unit rate.
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Find fractions of whole numbers. o
Divide by the denominator and multiply by the numerator.
Learning Goal #5: Intro to Integers Students will KNOW… • •
A integer is any number that has a positive or negative sign. A positive integer is a number that has a positive/addition sign (or no sign) in front of it. o
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A negative integer is a number that has a negative/subtraction sign in front of it. o
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A positive integer is always located to the right of the zero on a number line.
A negative integer is always located to the left of zero on a number line.
The absolute value is the number of jumps from zero to that number.
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Adding same signed integers results in an integer with the original sign.
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Adding different signed integers is the same thing as subtracting two integers.
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Subtracting negative integers is the same as adding the (second) positive. o
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(-2) – (-3) = (-2) + 3 = 1
Subtracting different signed integers is the same as changing the sign and the sign behind. o
Pos – Neg = Pos + Pos
o
Neg – Pos = Neg + neg
Students will UNDERSTAND… •
Zero is neither positive or negative.
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Numbers that have no sign are actually positive integers.
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Negative integers can be written with or without the parentheses. Example: (-2) = -2
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Negative integers are always smaller than positive integers.
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The larger a negative number, the less its integer is worth. (think negative as going under water)
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Adding and subtracting positive numbers is the same as regular addition or subtraction.
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The final answer in adding or subtracting always has the sign of the largest absolute value.
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An absolute value is written between two lines, |89|, and never has a positive or negative sign.
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Students will BE ABLE TO DO… •
Read and represent integers. o Write a real life situation as an integer. o Write an integer as a real life situation. o Write the absolute value of an integer. o Locate an integer on a number line.
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Compare and order integers. o Use number lines to compare and order integers.
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Add integers. o
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Use SMARTcuts and number lines to add integers.
Subtract integers. o Use SMARTcuts and number lines to subtract integers.
Unit 2 Benchmark Questions Lisa’s Running Distances
Unit 1 Week 2: Intro to Powers
Unit 1 Week 1: Reading and writing numbers
Day
Distance
Monday
2.05
Tuesday
What is the value of the 5 in the number below? 6,523,091,487 A.
five billion
4.1
B.
five million
Wednesday
3.8
C.
five hundred million
Thursday
1.95
D.
five hundred thousand
Friday
4.05
Which is the greatest distance Lisa ran? a. four and one tenth b. four and one hundredth c. four and five hundredths d. four fifths
Which of the following is 9.423 written in expanded notation? A.
(9 × 1) + (4 × 10) + (2 × 100) + (3 × 1000)
B.
(9 × 1) + (4 × 0.1) + (2 × 0.01) + (3 × 0.001)
C.
(9 × 0.1) + (4 × 10) + (2 × 100) + (3 × 1000)
D.
(9 × 0.1) + (4 × 0.01) + (2 × 0.001) + (3 × 0.0001)
Pat bought one of each of the items in the table below. Items Pat Bought Item Cost Blender $34.88 Coffeemaker $29.95 Can Opener $14.29 Rice Cooker $30.25 Which of the following sums is closest to the total cost, in dollars, of the four items that Pat bought? A. B. C. D.
Which of the following is equivalent to the expression below?
A. B. C. D .
Hazel shaded the circles shown below.
In Edward’s class, of the students like swimming better than they like running. What is
Yuan needs cups of milk for a recipe. Which of the following is another way to write
in simplest form?
?
Mario shaded of the shapes in a group. Which of the following could be Mario’s group? A.
A. A.
B. B.
Unit 1 Week 3: Intro to Fractions
B. Which of these shows how many circles Hazel shaded? A.
1 3/4
B.
2 1/3
C.
2 3/4
D.
3 1/3
D. C.
C.
D.
C.
D .
 Which of the following is equivalent to the expression below?
Which of the following is equivalent to the expression below?
Angie used 20 inches of ribbon to wrap a gift. She also used 15
Which of the following is equivalent to the expression below?
inches of ribbon to tie a bag. A.
B.
A.
What is the total number of inches of ribbon that Angie used?
B.
3 A. 4
35
Unit 1 Week 4: Add/Subtract Fractions
A. C.
C.
D .
D .
B. 4 35 B. C. 5 36 C.
D .
36
D . 5
+1
€
Week 1: Multiply Decimals and Fractions
Unit 1 Week 5: Fractions, Decimals, and Percents
Which number is the largest? ½ 33% 0.57 a. ½ b. 33% c. 0.57
On Tuesday, 80% of the students bought lunch at school. The other 20% of the students brought lunch from home. What fraction of the students bought lunch at school on Tuesday?
Which of the following numbers is not equivalent to 40%?
Order the numbers from greatest to least: 156% 0.56 5/6
0.0 A. 4
a. 156% 0.56 5/6
0.4 B. 0
b. 156% 5/6 0.56 c. 5/6 156% 0.56
A.
d. 0.56 5/6 156%
C. B.
D .
C. D .
0.06 ×9.2 a. 0.0052 b. 5.52 c. -5.52 d. 0.552
4 3 × = 5 9
3
Reduce your answer to lowest terms.
€
12 a. 45 12 c. 15
€
€
€
€
4 b. 15 7 d. 14
10 1 × = 12 2
10 11 b. 3 24 14 10 2 c. 3 d. 1 24 21 a. 3
Bonnie bought a 13-pound turkey for $0.85 per pound. How much money did she pay for the turkey? a. $11.05 b. $13.85
c. $130.05 d. $12.15
On Wednesday the farmers at the Boone Farm picked 4/5 of a barrel of tomatoes. Thursday, the farmers picked 1/10 as many tomatoes as on Wednesday. How many barrels of tomatoes did the farmers pick on Thursday? Simplify your answer.
5 15 4 c. 50 a.
2 25 1 d. 3 b.
€
Week 4: Ratios, Rates, and Proportions
Week 3: Divide Decimals and Fractions
Week 2: Divide W hole Numbers
Jackson County has $408 to buy new stop signs. If each sign costs $17, how many new stop signs will the county be able to buy?
Divide 4,687,635 by 5 a. 1,111,101 b. 911,501 c. 157,525 d. 935,727
12 672
A teacher took 52 photos during the visit to the amusement park. She wants to place all of the photos in an album. Each album page will hold 8 photos. What is the least number of pages the teacher needs for all her photos?
=
a.
54 b. 56 c. 560 d. 540
a. 17 b. 20 c. 24 d. 31
Represent your remainder as a fraction: 139 ÷ 6 =
24 65 b. 24 65 a. c. d.
2 4
25
a. 7 pages b. 6 pages c. 60 pages d. 416 pages Cody received a total of $10 for the cans he returned last week. If he received $0.50 for each can he returns, what was the total number of cans Cody returned last week? a. 5 b. 20 c. 10 d. 100
A sixth-grade class will clean 1 a beach that is 3 2 miles long.
They divided the beach into
7 sections of 8 of a mile. How € many groups will be needed to clean the entire beach? a. €2 groups b. 3 groups
What is the value of n in the following proportion?
4 n = 5 20 a. 12 b. 4
c. 16 d. 8
2 9 12 c. 6 a. 1
b. 2 d. 1
1 1
In this problem, how many zeros will we still have to add after the decimal point to have a zero remainder? (hint: finish the problem) a. none b. one c. two d. three
c. 4 groups d. 5 groups
Suppose you need to make a batch of purple clay. The recipe says you need to eight cups of red clay and twelve cups of blue clay. What is the simplest form of this ratio? a. 12:8 b. 8:12 c. 4:6 d. 2:3
Divide 1 1/3 by 2/3. Simplify your answer.
If KIPP students travel 1155 miles in 25 hours to get to Utah, how fast were they traveling per hour?
Which of the following proportions are equivalent?
a.26.2 miles per hour b. 20.0 miles per hour c. 46.2 miles per hour d. 50.0 miles per hour
1 34 = c. 2 17
€ €
24 3 = a. 24 2
€ €
2 32 = b. 1 16 50 52 = d. 15 17
A class of 25 students went to a zoo. IF each ticket was the same price and the total price for the class to go was $56.25, What was the ticket price for each student? a. $2.15 b. $2.20
c. $2.25 d. $2.50
20 x 2/5 = a. 8 c. 50
b. 40 d. 4
Week 5: Integers
–6 + (–3) = a. 9 b. -9 c. 3 d. -3
19 + (–19) = a. 0 b. -38 c. 38 d. -0
Week 1: Multiply decimals and fractions
Week 2: Divide Whole Numbers
Week 3: Divide decimals and fractions Week 4: Ratios, Proportions, and Rates
7 – (– 9) = a. 2 b. -2 c. 16 d. -16
–7 + (–3) - 6 = a. 4 b. -4 c. 16 d. -16
Which list orders the integers from least to greatest? a. -5, -7, 9, 12 b. -7, -5, 9, 12 c. 12, 9, -5, -7 d. 12, 9 -7, -5
Christopher has 3 5/6 cups of powdered sugar. He sprinkles 1/4 of the sugar onto a plate of brownies and sprinkles the rest onto a plate of lemon cookies. a. How many cups of sugar does Christopher sprinkle on the brownies? b. What is the fraction of sugar Christopher sprinkles on the lemon cookies? c. How many cups of sugar does Christopher sprinkle on the lemon cookies? There are 190 guests at a wedding. The couple has circles tables and each table seats 8 people. 1. What is the least amount of tables the couple must use to seat everyone? 2. Does this problem ask you to find the number in a group or the number of groups? 3. How many people are sitting at the last table? Mr. Esposito is trying to show his answer to 0.18 ÷ 0.06 by splitting a decimal grid into groups. 1. 0.18 ÷ 0.06 means splitting _____ into groups of ______. 2. Shade in the appropriate decimal grids to show 0.18 ÷ 0.06. 3. How many groups will he have? The Fish Bowl store had a sale. During the sale, the store gave away two kinds of fish, goldfish and catfish. • Every 5th customer received a free goldfish. • Every 12th customer received a free catfish. There were 134 customers on the day of the sale. a. How many customers received a free goldfish? Show or explain how you got your answer. b. How many customers received a free catfish? Show or explain how you got your answer. c. How many customers received both a free goldfish and a free catfish? Show or explain how you got your answer.
Week 5: Operations with Integers
-‐
In Buffalo, New York, the temperature was 14°F at dawn. 1. If the temperature dropped 7°F by 9 am, what was the temperature at 9 am? 2. If the temperature rose another 3 degrees by noon, what was the temperature at noon? 3. What is the temperature at night, if the temperature dropped 10 degrees at night?
Report Period 4 Instructional Calendar Spiraled
Monday
Wednesday
Thursday
Friday
Jan 1
Jan 2
Jan 3
Jan 4
No School – Winter Break
No School – Winter Break
No School - PD
Reteach: Determine appropriate answers given different question types.
NWEA, Weekly Assessment, & Unit Benchmark Smart Goals
Jan 7
Jan 8
Jan 9
Jan 10
Jan 11
Distinguish between types of sampling.
Identify bias in sample or question and correct.
MW: All operations (decimals) DN: MAP ATTACK TC: Integers OD: Converting FDP
Jan 14
Jan 15
Jan 16
Jan 17
Compare and justify the use of a particular graph.
Read and intepret stemand-leaf plots.
Read and intepret line plots.
Read and interpret circle graphs.
MW: All operations (decimals) DN: MAP ATTACK TC: Integers OD: Solving Equations
Jan 21
Jan 22
Jan 23
Jan 24
No School – MLK Day
Calculate mean, median, mode, and range.
Identify quartiles, upper extreme, and lower extreme of data sets.
Read and create boxand-whisker plots.
Jan 28
Jan 29
Jan 30
Jan 31
Calculate possible outcomes using models and the fundamental counting principle.
Find the probability of an outcome.
Find the probability of independent compound events.
Find the probability of dependent compound events.
Feb 4
Feb 5
Feb 6
Feb 7
Calculate elapsed time.
Read and create Venn diagrams.
Solve logic problems.
Draw conclusions and make predictions from survey results from graph and data set.
Feb 11
Feb 12
Feb 13
Feb 14
Feb 15
Benchmark Sample – Take then Trade and Grade
Benchmark Study Session – based on Sample
Benchmark: CR
Benchmark: MC
Staff PD Day
MW: All operations (whole) DN: MAP ATTACK TC: Integers OD: Converting FDP MW: All operations (whole) DN: Proportions TC: Integers OD: Converting FDP
MW: All operations (fractions) DN: MAP ATTACK TC: Solving Equations OD: Converting FDP MW: All operations (fractions) DN: MAP ATTACK TC: Integers OD: Solving Equations MW: All operations (mixed) DN: MAP ATTACK TC: Solving Equations OD: Converting FDP
Tuesday
Dec 31
NWEA
Draw numeric conclusions about population based on sample.
• Study Session • Smart Goals Revisit • Assessment Jan 18 • Study Session • Smart Goals Revisit • Assessment Jan 25 • Study Session • Smart Goals Revisit • Assessment Feb 1 • Study Session • Smart Goals Revisit • Assessment Feb 8 • Study Session • Smart Goals Revisit • Assessment
(No Kids)
Learning Goal #1: Intro to Surveys Students will KNOW… •
A survey is when you ask a portion of the population a question. o
•
•
•
•
A population is a group of people whose opinion you care to find.
o
A sample is a part of the population.
o
A sample size is the amount of people you choose to survey.
•
•
You can take a percent or decimal from a graph and multiply it by the total population to make a prediction about the whole population.
Validity of your results depend on the kind and size of the sample as well as the questions in your survey.
•
A random sample is created when everyone in the population has the same chance of participating in the survey’s sample.
The questions you ask in a survey can influence the answers your sample person.
•
A convenience sample is created when the people asked are easily available to the researcher.
Samples are used in order to avoid asking EVERYONE the same question – because it’ll take a lot of time, or money, or concentration.
•
A difference in characteristics between the sample and the population can make the results biased.
A representative sample is a sample that has the same characteristics as the population you want to survey.
Bias happens in a survey when the results from the sample are different from what the whole population would say. A prediction is an opinion about the future judgment of a population.
•
A conclusion is a judgment about what is important to the population based on the sample’s results.
Students will BE ABLE TO DO… •
The sample should include people who have some kind of interest in the subject of the question.
•
•
Students will UNDERSTAND…
•
•
Analyze situations to determine whether and what type of sample is needed. o
Choose an appropriate sample size given the population.
o
Choose a sample similar to a given population.
Identify bias and its source in survey questions then correct. o
Distinguish between biased (leading/persuasive) and unbiased survey questions.
o
Compare characteristics between the sample and the population to check for bias.
Make predictions based on samples. o
•
Generalize results to a larger, but similar, population.
Draw numeric conclusions about a population based on a sample. o
Find the percent of the population using proportions.
Learning Goal #2: Intro to Graphs Students will KNOW…
Students will UNDERSTAND…
•
Axes are the vertical and horizontal number lines on the graph.
•
The higher the interval you choose, the longer the axes will be.
•
An interval is the way the data points are grouped.
•
Stems are always all the digits but the last. o
Leaves are always only the last digit.
A scale is the range of data points included in the graph.
o
Duplicates must be represented.
•
o
Leaves must be in numerical order.
A data set is the complete list of all of the data points
o
Include “blank” stems that make up a gap.
•
A data point is every piece of numerical data you put into a graph.
•
What you want to highlight from the data set determines the type of graph.
Categorical data is the information included in the graph that is not numerical.
•
The scale must start at zero, otherwise your graph is misleading.
•
The interval of an axis must be consistent.
•
In almost every graph, the horizontal axis is categorical data and the vertical axis is numerical data.
•
o
o
• •
•
•
Numerical data is the information included in the graph that is a count of the categorical data.
The key in a graph tells you what each symbol represents. These can represent numerical data. Stem-and-leaf plots are graphs that list the last digit of each data point on the right and the previous digits on the left. Line plots are graphs that use symbols to show how frequently each kind of data point shows up in the data set. Circle graphs are graphs that show the portion of the sample who answered in a certain way.
•
•
Students will BE ABLE TO DO… •
•
•
Line plots should include on the horizontal axis the complete range of data points, even those that are not represented in the data set. Stem-and-leaf plots should include duplicates. •
Identify purpose and create parts appropriate for specific graphs (picture, line graph, line plot, circle). o
Identify categorical and numerical data in a graph.
o
Label parts of a graph that are missing.
o
Create a table from information in a graph.
Draw complex conclusions from graphs. o
Make conclusions about the sum of or difference between two or more data points.
o
Compare the sum of or difference between two or more data points and the rest of the data set.
Read and create stem-and-leaf plots and line plots. o
Draw conclusions a stem-and-leaf plot.
o
Create a stem-and-leaf plot from a given set of data.
o
Create a line plot from a given data set.
o
Draw conclusions from a line plot.
Justify the appropriate graph given the kind of data and the purpose. o
Identify the kind of information each graph shows.
o
Choose a graph that matches the purpose of the point the researcher is trying to make.
Learning Goal #3: Measures of Center Students will KNOW…
Students will UNDERSTAND…
Students will BE ABLE TO DO…
•
A median is the middle data point in a data set.
•
•
The mean is the average of a data set. Adding all of the data points together then dividing by the count of the data set finds the mean.
Intervals should not overlap, or include the same numbers.
o
Identify the min and max.
•
Intervals should be equal, or include the same amount of data points.
o
Find the difference between the min and max to find the range.
The mode is the most frequently occurring data point.
•
The boxes and whiskers don’t have to be the same size.
o
Count the number of data points.
o
Find the sum of all of the data points.
•
The range is the difference between the upper extreme and the lower extreme.
•
In a box-and-whisker plot, duplicate data points DO matter.
o
Find the mean of the data points using the count and sum of the data points.
•
A gap is an area in the data set that has no data points. This is evident when you plot the data points on a line plot.
•
The boxes include all of the data points between the upper and lower quartiles.
•
•
A cluster is an area in the data set that has the most data points. This is evident when you plot the data points on a line plot.
The larger the box/whisker, the more data points that exist in that box/whisker.
o
Find the lower and upper extremes to find the median.
•
The whiskers include all of the data points between the extremes and the quartiles.
o
•
Find the median of the data halves to find the quartiles.
An outlier is a data point that is far away from the rest of the data points in a data set.
•
•
A box-and-whisker plot is a graph that shows how far the extreme data points are from the other data points.
To find the median in an even numbered data set, find the mean of the middle two data points.
•
A data set can have more than one outlier, gap, and cluster (or have none at all).
•
The lower extreme is the smallest value in a data set.
•
•
The upper extreme is the largest value in a data set.
Gaps, clusters, and outliers can exist only between the upper and lower extremes, aka only in the range of the data.
•
The lower quartile is the median of the lower half of the data set.
•
The upper quartile is the median of the upper half of the data set.
•
•
•
•
Calculate mean, median, mode, and range.
Identify quartiles, upper extremes, and lower extremes from data sets.
Read and create a box-and-whisker plot from a data set. o
Draw the five points on a number line.
o
Draw the boxes and whiskers.
o
Identify where the most data points lie in a box-and-whisker plot.
Learning Goal #4: Intro to Probability Students will KNOW… •
Students will UNDERSTAND…
An outcome is one possible result of a given experiment.
•
•
A sample space is visual of all possible outcomes of an experiment.
•
You list the first action of the event first in these sample spaces.
•
A favorable outcome is an outcome that is possible that you actually want to see.
•
You multiply in a compound event because the number of options grows when you include more events.
•
A combination is an outcome where the order doesn’t mater – like in a fruit salad or the kinds of materials in a backpack.
You can use a table, grid, or tree diagram to list all of the possible outcomes of an event.
•
Independent events include: rolling a dice, spinning a spinner, etc.
•
Probability of an event can be described as likely, unlikely, impossible, or certain.
•
Dependent events include: pulling a card/marble, choosing a person, etc.
•
Theoretical probability is the ratio of the count of favorable outcomes to the total number of outcomes.
•
Probability can represented as a ratio from 0 to 1.
•
P(event) means the probability of choosing what is in the parentheses.
•
A compound event is the combination of two or more events. o
o
•
Students will BE ABLE TO DO… •
o
•
•
•
A dependent event is when the first outcome takes options away from subsequent outcomes.
•
Create a sample space to illustrate the possible outcomes using a list, grid, or tree.
Find the probability of a single outcome. o
Write and compare probability as a ratio, decimal, and percent.
o
Describe probabilities using likely, unlikely, impossible, or certain.
Find the probability of independent compound events. o
An independent event is when the first outcome doesn’t take away options from subsequent outcomes.
The fundamental counting principle tells you only the number of possible outcomes in an event. You just multiply together the number of possible outcomes in each part of the event.
Calculate possible outcomes using models.
Identify the probability of both events and multiply.
Find the probability of dependent compound events. o
Describe how a compound event is limited by the choices that precede each choice.
o
Calculate the probability of each subsequent event.
o
Write the probability of compound events.
Calculate the number of possible outcomes using the fundamental counting principle. o
Multiply the number of possible outcomes in each category.
Learning Goal #5: Real World Data Students will KNOW… • •
•
Elapsed time is the number of minutes and hours between a start time and an end time. Venn Diagrams have at least six different parts: o Universe: The whole box o Classification: titles of groups o Group 1: The area of group 1 o Group 2: The area of group 2 o Both Groups: The area the groups share o Neither Group: In the universe, but not in either group Logic problems give you parameters and circumstances. o
Parameters are the rules.
o
Circumstances are the options.
Students will UNDERSTAND… •
•
Both elapsed time and actual time can be written with a colon, but actual time also includes AM or PM.
•
There are 60 minutes in 1 hour (base 60).
•
Minutes and hours can be written as fractions.
• • • •
Add minutes to the next hour. Add hours to the appropriate hour. Add the minutes you still need. (Minute, hour, minute)
Students will BE ABLE TO DO… •
•
Calculate elapsed time. o
Count up from a start time to an end time.
o
Count down from an end time to a start time.
o
Describe elapsed time in words.
Read and create Venn Diagrams. o
Read Venn Diagrams.
o
½ hour = 30 minutes
o
Complete Venn Diagrams.
o
1/3 hour = 20 minutes
o
Create Venn Diagrams.
o
¼ hour = 15 minutes
o
1/6 hour = 10 minutes
o
1/12 hour = 5 minutes
Write your shared portion first (so you don’t count the same people twice). The count of the universe should be the same as the count of the four groups. Write all of the circumstances next to each answer space. Cross out circumstances that don’t fit into the parameters as you go through the parameters.
•
Solve logic problems. o
Create answer spaces.
o
Write the circumstances next to the answer spaces.
o
Cross out circumstances as the parameters dictate.
Â
Aligned Benchmark Questions
Unit 4 Week 1
A frozen-food company wans to conduct a survey to find out what flavor of ice cream people like best. Which of the following would give them the best sample? a. Ask people who work at the frozen-food company b. Survey every other first-grade student who attends the nearest elementary school c. Ask a local grocery store to announce the survey and have shoppers give their answers. d. Choose 5 neighbors to record their preferences. Which question would be best to use in finding out your neighborsâ&#x20AC;&#x2122; favorite local restaurant? a. When was the last time you went to a restaurant for lunch? b. How often do you go to a restaurant for dinner? c. How do you like that new restaurant that opened down the street? d. What restaurant in our neighborhood do you eat at the most? Teachers at a school asked a sample of their students which subject was the best. When the teachers got back together, they figured out that they asked 50 students out of the total population of 250 students. 20 of those students said that math was the best subject. If 20 out of 50 students said math was the best subject, how many students in the population would probably say that math was the best subject? a. 100 students c. 50 students b. 20 students d. 200 students Which of the following samples would be biased? a. Asking people who walk out of a restaurant if they prefer beef, chicken, or lamb for dinner. b. Calling every 10th name in the phone book and asking which candidate they would vote for in the next presidential election. c. Asking your classmates which type of school lunch they like best. d. Asking baseball fans at a St. Louis cardinals game which is the best professional baseball team. How can you tell when a sample is random? a. when it does not represent any of the characteristics of the whole population b. when it represents just one characteristic of the whole population c. when at least half of the population is equally likely to be chosen d. when every member of the population is equally likely to be chosen
 Mr. Nunez drives a bus. The line plot below shows the number of passengers that were on his bus for each of the last 10 trips he made. Which number of passengers did he have the most? a. 1 c. 8 b. 6 d. 9
In a survey of 250 sixth graders, the following items were found to be the studentsâ&#x20AC;&#x2122; favorite drinks for lunch. How many sixth-graders liked tea the best?
Unit 4 Week 2
tea 12% milk 38%
soda 27% juice 23%
a. 12 students b. 20 students
c. 26 students d. 27 students
Mr. Mayes asked 24 of his students how many miles they live from the The stem-and-leaf plot shows how far each student lives from the
school. school.
Which of the following is true conclusion based on the stem-and-leaf a. Five students live 1 mile from the school. b. Ten students lives 2 miles from the school. c. Eleven students live more than 20 miles from the school. d. The maximum distance a student lives from the school is 15
plot?
miles.
G R What is the median of the following data set? a. 27.83 c. 30 b. 29 d. 20
A D E 12,
7
42, 15, 25, 33, 40
5
Math
CA L I F O R N I A S TA N DA R D S T E S T
The table below shows the scores of 9 students on a history test.
Released Test Questions
!
a. 22 b. 32
c. 39 d. 46
DO NOT WRITE HERE
The following table shows test score for Mr. Jackson’s History class. 78 The following data represent the number of What is the range of test scores?
years different students in a certain group have 26 gone to school together: 12, 5, 8, 16, 15, 9, 19. These data are shown on the box-and-whisker plot below.
What is the mean of the turkey sandwiches sold? a. 11 turkey sandwiches b. 16 turkey sandwiches
8
HISTORY TEST SCORES The table shows the number of turkey and ham sandwiches sold days 18 46 by Derby’s 30 Deli for 46 several35 in one week.
50
48
What is the range for this set of data? 12
16
c. 50 turkey sandwiches d. 10 turkey sandwiches
19
22 32 39
C
12
DO NOT WRITE HERE
This box-and-whisker plot displays information about scores 25 students. What isthe the test median of the for data? 46 Based on the plot, which of the following statements is true? A 5 a. The highest score on the test is 90. c. The median test score is 85. B 8 b. The range of the test scores is 15. d. The interquartile range is 75 - 85.
What is the difference between the median number of turkey sandwiches sold and the median number of ham sandwiches sold?
D 16 Jillian works at a ski resort. She recorded the number of snowboards6thatMandy were rented each day for two weeks in the stem-and-leaf plot below. bought packs of trading cards that contain 8 cards each. She gave away 5 cards. CSN00082
A
0
B
1
C
2 x !3number of packs of trading cards D
DO NOT WRITE HERE
CSM21123
What is the mode of the data in the stem-and-leaf plot? a. 53 c. 86 b. 66 d. 75
!
Which expression shows the number cards numbers that Mandy has left? 80 Jared scored the of following of points 8x " 5 5x " 8
in his last 7 basketball games: 8, 21, 7, 15, 9, 15, and 2. What is the median number of points scored by Jared in these 7 games? A
9
5 " 8x
B
11
8 " 5x
C
15
D
19 CSN00200
DO NOT WRITE HERE
Unit 4 Week 3
5
79 ! 39
— 28 —
This is a sample of California Standards Test questions. This is NOT an operational test form. Test scores cannot be projected based on performance on released test questions. Copyright © 2008 California Department of Education.
Morgan rolls a die. What is the probability she will roll a three? a. 1/6 c. 2/6 b. 1/36 d. 9/36
Unit 4 Week 4
Julius has a bag with some marbles in it. • There are 6 red marbles. • There are 8 white marbles. • There are 12 blue marbles. Julius will take a marble from the bag without looking. What is the probability that Julius will take either a red marble or a white marble?
a.
c.
b.
d.
At Teresa’s Burrito Shop, Jim always chooses 1 item from each column in the table below. Wrap Filling Topping plain wheat
beans beef chicken
sour cream guacamole
What is the total number of ways that Jim can order a burrito at Teresa’s Burrito Shop by choosing 1 wrap, 1 filling, and 1 topping? a. 6 c. 10 b. 7 d. 12 Christina shows her friend Jennifer a deck of cards. What is the probability that Christina draws an ace and does not replace it, and then draws another ace? a. 2/52 c. 2 b. 1/221 d. 12
A contest is being held at a school fair for 40 fifth-grade and 30 sixth-grade students. Each student’s name was written on one card and placed into a box. The principal will reach into the box and pick one card without looking. The student named on the card will be the winner of the contest. What is the probability that the winner of the contest will be a sixth-grade student?
A.
C.
D. B.
Rashid read a book for 2 hours, 10 minutes. He finished reading at 5:00 p.m. What time did Rashid start reading? a. 2:50 am c. 2:50 pm b. 3:50 am d. 3:50 pm
Tanesha’s soccer game started at 11:43 a.m. and finished at 2:09 p.m. How long was Tanesha’s soccer game? a. 2 hours and 17 minutes c. 3 hours and 17 minutes b. 2 hours and 26 minutes d. 3 hours and 26 minutes In the Venn diagram below, how many people speak either Russian or German only? a. 22 b. 18
c. 12 d. 34
Unit 4 Week 5
The Venn diagram below shows the number of seventh-grade students who are in the choir, the choir and the band, or in neither.
in the band, in both
What is the total number of seventh-grade students who are not in the band? A.
41
B.
55
C.
63
D.
95
Samuel, Dylan, Nicholas, and James each own a car. One has a green car, one has a pink car, one has a yellow car, and one has a red car. Who has the pink [2] car? • • • • • • •
James favorite colors are green and yellow. His car is one of his favorite colors. Nicholas favorite colors are red and green. His car is one of his favorite colors. Samuel favorite colors are yellow and red. His car is one of his favorite colors. Nicholas borrowed the red car, because Dylan was using his car. Samuel doesn't like yellow cars. Nicholas borrowed the red car, because James was using his car. Dylan doesn't like red cars. a. Samuel b. James
c. Nicholas d. Dylan
Constructive Response
1. The following survey question is biased: “Don’t you agree that planting more trees around the school will make it even more beautiful?” a. Explain why the survey question is biased. b. Rewrite the question so that it won’t be biased at all. c. The researcher wants to know the preferences of people who look at the school. Choose which sample is the most biased and explain why he shouldn’t use that sample. i. Sample 1: people who live on the street the school is located on ii. Sample 2: people who like flowers iii. Sample 3: people who go to school or work in the school building 2. Josie has three different pairs of shoes: tennis shoes (T), boots (B), and loafers (L). She also has two different colored pairs of socks: white (W) and red (R). a. Make a tree, list, or grid to show all the possible combinations of one pair of shoes and one pair of socks. b. What is the number of possible combinations she can have with white socks? Show or explain how you got your answer. 3.
In health class, students were asked to hold their breath for as long as they can. The raw data box shows their results. a. Create a stem-and-leaf plot for the data in the box. b. Which data value is the mode? Explain how you know it’s the mode.
4. For snack today, KIPPsters got raisins. Ms. Taylor asked each student to count the number of raisins in each box. The raw data set is below.
a. Create a line plot form this raw data set. b. Which data value is the median? Show or explain how you got your answer. c. What is the mean from this data set? Show or explain how you got your answer.
5
W e e k
4
U n i t
5. A teacher looks into her phone bin and notices that there are lots of different phones in there. She counts that out of 44 phones, 22 have touchscreens and 18 have phone covers, but only 5 have both touchscreens and phone covers. a. Create a Venn diagram to illustrate what she found. b. How many phones have either touchscreens or phone covers but not both? Explain how you know. c. How many phones have neither touchscreens nor covers? Explain how you know. Rashid read a book for 2 hours, 10 minutes. He finished reading at 5:00 p.m. What time did Rashid start reading? a. 2:50 am c. 2:50 pm b. 3:50 am d. 3:50 pm Tanesha’s soccer game started at 11:43 a.m. and finished at 2:09 p.m. How long was Tanesha’s soccer game?
Report Period 5 Instructional Calendar Spiraled MW: All operations (decimals) DN: MAP ATTACK TC: Adding Fractions
MW: All operations (decimals) DN: MAP ATTACK TC: Subtracting Fractions
Monday
Tuesday
Wednesday
Feb 19
Feb 20
Feb 21
No School – President’s Day
Reteach: Divide decimals (TC)
Reteach: Add and Subtract Fractions (TC)
Reteach: Multiply and Divide Fractions (TC)
Feb 25
Feb 26
Feb 27
Feb 28
Name lines, angles, and polygons.
Measure and classify angles.
Identify a 3D figure based on it attributes.
Read and identify mat plans from isometric representations and vice versa.
Mar 4
Mar 5
Mar 6
Mar 7
Identify similar and congurent figures as well as corresponding sides.
Recognize, describe, and apply rotational symmetry.
Recogonize and apply transformations.
Manipulate tangrams.
Mar 11
Mar 12
Mar 13
Mar 14
Describe and distinguish between perimeter and area.
Calculate perimeter using coordinate planes and side lengths.
Calculate area using coordinate planes and side lengths.
Identify and justify correct unit of measure of perimeter, area, and volume.
MW: All operations (decimals) DN: MAP ATTACK TC: Adding Integers
MW: All operations (decimals) DN: MAP ATTACK TC: Subtracting Integers
Thursday
Feb 18
Friday Feb 22 • Study Session • Smart Goals Revisit • Assessment Mar 1 • Study Session • Smart Goals Revisit • Assessment Mar 8 • Study Session • Smart Goals Revisit • Assessment Mar 15 • Study Session • Smart Goals Revisit • Assessment
SPRING BREAK – Mar 16 - 22 MW: All operations (decimals) DN: MAP ATTACK TC: Decimal Addition
MW: All operations (decimals) DN: MAP ATTACK TC: Decimal Subtraction
Mar 25
Mar 26
Mar 27
Mar 28
Mar 27
Identify and use appropriate units of measure (including volume).
Convert measures within the customary system.
Convert measures within the metric system.
Compute with measures.
No School – Good Friday
Apr 1
Apr 2
Apr 3
Apr 4
Apr 5
Benchmark Sample Test
Benchmark Study Session on IXL
Benchmark: CR
Benchmark: MC
Staff PD Day
(No Kids)
Calendar until the state test Directions: Use the template below to plan how you will organize the instructional days you have before the state test. The goal should be to use today’s data to create the most complete, strategic plans possible.
Monday #1 (4/8) Guess Check and Revise Use similar sides to construct ratios and solve for a missing side. Monday #2 (4/15)
Guess Check and Revise Identify parts of a circle and discover the origin of pi. Tuesday #2 (4/16)
Wednesday #1 (4/10)
Thursday #1 (4/11)
Friday #1 (4/12)
Guess Check and Revise
Guess Check and Revise
Guess Check and Revise
Calculate circumference and area given diameter or radius.
Calculate perimeter and area of irregular shapes.
Assessment
Wednesday #2 (4/17)
Thursday #2 (4/18)
Friday #2 (4/19)
Work Backward
Work Backward
Work Backward
Work Backward
Work Backward
Calculate and compare rates.
Justify the better buy.
Solve for missing data point when the mean is given.
Predict from plotted data.
Assessment
Monday #3 (4/22) Use Logical Reasoning Write equivalent forms of algebraic expressions.
Tuesday #1 (4/9)
Tuesday #3 (4/23)
Wednesday #3 (4/24)
Thursday #3 (4/25)
Friday #3 (4/26)
Use Logical Reasoning
Use Logical Reasoning
Use Logical Reasoning
Use Logical Reasoning
Solve 2-step equations.
Identify a solid figure given its net and vice versa.
Calculate using measures.
Assessment
Learning Goal #1: Intro to Angles Students will KNOW… • • •
• • • •
•
•
A line has two arrows at the end. A ray has one endpoint and one arrow. An angle is 2 rays connected at their endpoint. o Acute angles are angles between 0 and 89 degrees. o Right angles have an exact measurement: 90 degrees. o Obtuse angles are angles between 91 and 179 degrees. o Straight angles have an exact measurement: 180 degrees. The shared end point of two rays (that make an angle) is called the angle’s vertex. A line segment has two end points. Those end points make the name of the line segment. A protractor is a tool that measures angles exactly and has two scales – an inside scale and an outside scale. 3D figures are named by their base then their face. o Platonic solids – faces and bases are all the same kind o Prisms – one kind of base and a different kind of face o Pyramids – one base that comes up to a point (an apex) o Circle solids – at least one circular base Figures have faces, edges, and vertices. o A vertex is a corner on a 3D figure. o An edge joins one vertex with another. o A face is an individual surface on a 3D figure. Isometric representations are 2D drawings of 3D figures.
Students will UNDERSTAND… • •
• • • •
• • • • • • •
Describing an angle (acute, right, obtuse, and straight) is different from measuring an angle’s degrees with a protractor. Acute, right, obtuse, and straight are angle measurements but they are less exact than the measurements you’d get from using a protractor. Figure names are created using the type of figure and the vertices or points (ex. Polygon ANFD). Which scale you use on a protractor depends on which side of the protractor your angle opens on. To find an angle measurement, you have to count up from the 0 degree that matches one of your rays. To set a protractor correctly, match one side of the protractor with one ray of the angle, then position the crosshairs on the vertex, keeping the ray on the 0 degree line. Finally count up from the 0 degree mark until you get to the next ray. A figure sits on its base and shows its face. You can count the number of faces, edges, and vertices a 3D figure has. Mat plans can be drawn from the front, side, back, or top. Mat plans include the number of blocks in the figure. Isometric representations are like drawing cubes.
Students will BE ABLE TO DO… •
•
•
•
Name lines, angles, and polygons. o Write names of figures (in multiple ways). o Identify figures given their names. o Draw figures given their names or descriptions freehand and in a coordinate plane. Measure and classify angles. o Describe angles using right, obtuse, straight, and acute. o Use a protractor to give exact angle measurements in simple and complex figures and polygons. Identify a 3D figure based on its attributes . o Describe angles using right, obtuse, straight, and acute. o Use a protractor to give exact angle measurements in simple and complex figures and polygons. Read, create, and identify mat plans from 3D figures and vice versa. o Describe mat plans. o Build a figure given its mat plan. o Choose a figure based on its mat plan. o Create a mat plan based on a given figure.
Learning Goal #2: Intro to Shapes Students will KNOW… • • •
• •
•
Similar means the figures have exactly the same shape, but the size is not the same. Congruent means that the figures have both exactly the same size and the same shape. Corresponding parts on a set of figures are parts of the figure that are in the same location (but they don’t have to be the same size). Rotations happen around a point. o The unit for rotation is degrees. Kinds of transformations include a slide/translation, turn/rotation, flip/reflection. o Reflections can happen across a line. o Slides are described in number of units. Tangrams are 7 shapes that you can use to create complex figures.
Students will UNDERSTAND… • • • • • • • •
Rotational symmetry means that the figure can be rotated into a matching figure in less than 360 degrees. Rotational symmetry describes the rotation in number of turns as well as the degrees (and each turn can be described in degrees as well). Rotational symmetry can be applied in two directions – clockwise (right) and counterclockwise (left). A figure can be transformed more than once. You can identify correspondence by comparing the names of the figure or comparing the marks on the figures. Figures must be similar or congruent for them to have corresponding parts.
Students will BE ABLE TO DO… •
•
•
You cannot overlap tangrams. You might not use every single tangram in a tangram puzzle.
•
Identify similar and congruent figures and describe corresponding parts of figures. o Use the names of the figures to identify corresponding parts. o Write the names of figures in correct order to describe corresponding parts. o Identify corresponding parts from visuals (with and without marks). Recognize and apply rotational symmetry. o Describe rotational symmetry in degrees. o Draw rotated figures given the degrees. o Identify which figure was rotated the appropriate amount of degrees. Recognize and apply transformations. o Contrast the kinds of transformations (slide, turn, flip). o Use math vocabulary to describe transformations (slide/translation, turn/rotation, flip/reflection). o Draw transformations on a coordinate plane given the number of units or the point/line by which the figure is transformed. Manipulate tangrams. o Fit all tangrams into a single shape. o Identify which tangrams are used to fit into a single shape.
Learning Goal #3: Perimeter and Area Students will KNOW… • • • • • •
Perimeter is the total length of the sides in units. The formula for perimeter = the sum of the side lengths. Area is the amount of units inside a closed figure (polygon). Volume is length times width times height. The formula for area is a figure’s height times the width (like a multiplication table). The units for any perimeter are units because you are just counting sides.
•
The units for any area are square units because the multiplication of each unit equals the SQUARE of that unit.
•
The units for any volume are cube units because the multiplication of each unit equals the CUBE of that unit.
Students will UNDERSTAND… • • • • •
Regular polygons have sides and angles that are all equal. The perimeter is the RIM of the polygon. Area is the amount of space inside of the perimeter. If a polygon is on a coordinate plane, find the perimeter by counting the lines that RIM the figure. If a polygon is on a coordinate plane, find the area by counting the boxes inside the figure. o If a figure’s sides don’t include the whole box, you can find an approximate area.
Students will BE ABLE TO DO… •
•
•
•
Describe and distinguish between perimeter and area. o Use a coordinate plane to describe the difference between perimeter and area. o Relate the formulas of perimeter and area to given figures. o Explain what the differences in formulas for perimeter and area mean. Calculate perimeter and area of regular figures using coordinate planes. o Count the distance around a figure in units. o Count the units inside a figure. Calculate perimeter and area of regular figures given side length. o Choose the correct formula for perimeter and area. o Substitute appropriate measures from the figure in the correct formula. o Identify the lengths of sides without measures in regular polygons. o Solve formulas to calculate perimeter and area. Identify and justify the correct unit of measure for perimeter, area, and volume. o Choose the correct units for volume. o
Choose the correct units for area.
o
Choose the correct units for perimeter.
Learning Goal #4: Measurement Students will KNOW… • • •
• • • • •
Weight can be measured: o Customary: pounds, ounces, tons o Metric: grams Length/Height/W idth can be measured: o Customary: inches, feet, yards, miles o Metric: meters Volume can be measured: o Customary: fluid ounces, cups, pints, quarts, gallons o Metric: liters Multiply in order to convert from a larger unit to a smaller unit. Divide in order to convert from a smaller unit to a larger unit. A conversion is a number sentence that describes a single unit as a number of another unit. Customary units are used in the US. Metric units are used almost everywhere else. o Metric units are base ten.
Students will UNDERSTAND… • • •
When converting, convert to 2 significant digits after the decimal. You can add or subtract units vertically, but you can’t borrow between different units without a whole other conversion. After conversion, check that your answer is in simplest form. This means that none of your units is more than the not-one conversion.
Students will BE ABLE TO DO… •
•
•
•
Identify and use the appropriate units of measure. o Relate the size of objects to a number of everyday objects. o Given an everyday object, determine the number of its count to another given object. Convert measures within the customary system. o Identify the correct conversion from a conversion chart. o Apply the correct conversion. o Simplify the converted answer into simplest terms. Convert measures within the metric system. o Identify the correct conversion from a conversion chart. o Apply the correct conversion. o Simplify the converted answer into simplest terms. Compute measures using operations. o Add same units and simplify. o Subtract same units and simplify o Borrow using the units.