PHILOSOPHY PHILOSOPHY
The curriculum to Alpha Math was developed with the notion that Math extends beyond the classroom. Children need to understand the purpose of what they’re doing, the logic behind their procedures, and the reasonableness of their solutions. Each lesson is aligned with the Common Core State Standards, encouraging children to approach math practically so that they are prepared for college and career. All too often children are asked to memorize mathematical concepts without ever fully understanding their function in math and in their real world application. In the past, the subject of math was often limited to the classroom, leaving children with the ever-burning question: “When will I ever use this in real life?” Alpha Math’s problems and World Connections place math in a real-world context, allowing children to gain a purpose to learning. There is always more than one way to reach a solution. One size does not fit all. Success comes from practice and understanding. Alpha provides multiple mathematical strategies and encourages students to choose the approach with which they are most comfortable. It is short sighted to demand a quick, right answer and to rely on this method as a measure of the student’s mathematical ability. Math is more than just numbers and math class is a perfect time to encourage literacy, writing, and communication. Classroom discussions provide an opportunity for each child to speak up and become engaged in the material so that no child is left behind. Writing provides children a chance to formulate their ideas and to analyze their reasoning. Student participation and writing provides teachers insight to how their students are progressing and in which areas they need support. We believe that hands-on activities and the use of manipulatives help otherwise abstract mathematical ideas to become concrete. Each lesson starts with a hands-on activity to introduce a new concept. Alpha Math was created with the child in mind. We firmly believe that math can be fun once children make sense of what they are doing in math and why. We hope that our readers enjoy using the program as much as we enjoyed creating it.
I
DOING MATH
A. Write an addition sentence. 1
2
+
Addition of equal groups. 4 × 6 = 24 6 + 6 + 6 + 6 = 24
+
3
Multiplication
1
+ 4
Multiplication sentence
2
A number sentence used to e×press multiplication. 3 × 7 = 21
Checks previous knowledge of children. At the beginning of each chapter, teachers can assess the prior knowledge of children and ensure their readiness for the new concepts.
Factor
3
+
+
+
+
+
+
One of two numbers that are being multiplied. 2 × 5 = 10
B. Use a number line to find the sum. 0 1 3 5
1
2
3
4
5
6
7
8
Factor
9 10 11 12 13 14 15 16 17 18 19 20
2+2+2+2=
2
4+4+4=
1+1+1+1+1=
4
3+3+3=
0+0+0+0+0=
6
6+6=
Factor
Product
4
The answer to a multiplication. 6 × 5 = 30 Product
C. Problem Solving.
Parentheses
5
A pair of brackets used to indicate that enclosed operations of a mathematical e×pression should be carried out first. (2 × 9) + 40 18 + 40 = 58
Avery and Isla went skating. Each one of them skated 4 rounds. How many rounds do they skate in all? Write an addition sentence to solve.
120
121
Defines new terms relevant to the chapter. Children will improve their math language skills when they are introduced to the new vocabulary words they will learn in the chapter.
Multiplication Patterns Do you know that... There are seven species of sea lions in the world. Sea lions live for about 20 to 30 years. They are considered to be highly intelligent animals. They play tricks for entertainment. There is a sea lion which is 24 years old. It moves to a different park every 3 years. In how many different places has this sea lion lived?
TIME TO LEARN Use the multiplication table. 1
Multiplying any number by 0 equals 0 “zero property”.
2
Multiplying any number by 1 equals that number “Identity property”
Red Squares × 0 1 2 3 4 5 6 7 8 9 10 3
0 0 0 0 0 0 0 0 0 0 0 0
1 0 1 2 3 4 5 6 7 8 9 10
2 0 2 4 6 8 10 12 14 16 18 20
3 0 3 6 9 12 15 18 21 24 27 30
4 0 4 8 12 16 20 24 28 32 36 40
5 0 5 10 15 20 25 30 35 40 45 50
Answer
Yellow Squares 6 0 6 12 18 24 30 36 42 48 54 60
7 0 7 14 21 28 35 42 49 56 63 70
8 0 8 16 24 32 40 48 56 64 72 80
9 10 0 0 9 10 18 20 27 30 36 40 45 50 54 60 63 70 72 80 81 90 90 100
Group of year
1
2
3
4
5
6
7
8
18
24 − 3
21 − 3
18 − 3
15 − 3
12 − 3
9−3
6−3
3−3
21
18
15
12
9
6
3
0
24 ÷ 3 = 8
8 places
STEP Show the quotient as repeated subtraction in two BY STEP different ways. 1
30 ÷ 8 = 5
4
−6
0
Use the multiplication table to complete the pattern.
2
0 , 9 , 18 , 27 , 36 , 45 , 54 , 63 , 72
3
−6
6
2
−6
12
1
−6
18
Starting
−6
24
30
30
24
14 ÷ 2 = Starting
pattern
14
159
247
TIME TO LEARN Introduces the concept and various mathematical approaches. With the examples provided, children can have rich classroom discussions. The vocabulary is used within context so children can use it as a reference when solving the exercises.
2
Shows students how math is relevant and extends beyond the classroom. Students can apply abstract mathematical concepts as they learn about the world around them.
P R AC T I C E A. Circle the fraction that represents the colored part.
Do you know that...
1
3
1 4
2 4
2 3
2 3
1 2
1 3
2
4
1 8
5 8
7 8
2 4
2 6
4 6
Answer 6 × 3 = 18 wheels
B. Color the fraction of the whole. 1
STEP BY STEP
A. Find each product.
3
× 1
3×7
= (2 × 7) + (1 × 7)
2
3×8
= (3 × 4) + (3 × 4)
4
3 3
3 9
×
2
3× 3×
= 30
3
3
×
= 18
3
3 4
2
4
5 8
2 3
C. Write the fraction.
B. Find the missing factor. 1
4 6
9
4
×
5 15 183
1
Numerator is two, denominator is six.
2
Denominator is 8 , numerator 3.
3
Denominator is two, numerator is one.
DOING MATH
Tricycle is a three-wheeled vehicle that was invented by two French inventors in 1789. In the United States and Canada, tricycles are used for recreation, shopping, and e×ercise. In Asia and Africa, they use tricycles to transport passengers and make deliveries. If there are 6 tricycles on your street. How many wheels do the 6 tricycles have in all?
308
Step by Step and Practice As children progress, they will become familiar with mathematical concepts through practice to reinforce their understanding of math. In each lesson, there are two sections of practice problems: Step by Step and Practice.
STEP BY STEP • Provides a guided practice following the initial introduction of new skills which engage children in the learning process. • Teacher encourages children and provides full guidance. • Teacher helps children facilitate discussion by providing suggestions and ideas. • Children reach a conclusion with teacher supervision.
1
2
3
P R A C T I C E • Provides an independent practice for children to apply their understanding and mastery of the new skills. • Children can confidently solve problems independently. • Children ask questions and express their own ideas independently. • Children reach their own solutions independently.
Max has 8 trading cards. 5 cards are baseball cards and the rest are football cards. What fraction of the trading cards are football cards?
Is finding a fraction of a whole differs from a fraction of a set? Explain.
Includes a wide range of word problems to demonstrate the use of generic problem solving methods. Children can hone in on both their mathematical and literacy skills as they learn how to reason and justify their answers.
Nolan says the fraction of the leaves that is green is 8 . 6 Do you agree? Explain.
Vocabu lary Ch ec k
Complete. is the number of equal parts in the whole. 313
3
DOING MATH
V oc abular y Chec k (Mathematics language builder) Refreshes student’s memory of important mathematical terminology presented throughout the chapter.
1
Zoe started shopping at 5:06 p.m. She finished shopping at 7:45 p.m. How much time did Zoe spend shopping?
2
If Ian started eating his lunch at 1:35 p.m. and finished his lunch at 2:10 p.m. Explain how you can find how long he spent eating.
3
Natalia was baking 2 dozens cupcakes for her party. It takes 25 minutes to bake 1 dozen cupcakes. She needs 45 minutes to decorate her home and 20 minutes to get ready. If she starts at 2:10 p.m. What time will she be ready for the party?
V o c a b u l a r y Ch e c k
Match.
The time between midnight and noon
Elapsed time
The time that passes from the start to the end of any activity
p.m.
The time between noon and midnight
a.m. 361
TIME TO LEARN Steps to problem solving
Problem Solving Strategies
1
Read and understand the problem.
Circle what you need to find, and underline the given information
2
Make a plan.
3
Carry out the plan.
4
Check.
How can you solve the problem? Solve the problem by: Drawing a picture. Making a table. Does your answer make sense? Is the math correct?
STEP BY STEP
The final lesson in each chapter teaches and encourages children to use the design process to solve problems. 1. Read and understand the problem. By reading the problem thoroughly and underlining the given information, students will be able to identify the most important and necessary details in the problem solving process. 2. Make a plan. Students will make a plan to solve the given problem based on the information they gathered above. 3. Carry out the plan. Students apply problem-solving abilities to carry out the plan they made. 4. Check. Discovering the way to self-evaluation for their solution and overall work.
Paige has 24 smiley faces. She shared them with 2 and two of her friends. How many smiley faces will each one of the 3 friends have?
1
Read and understand the problem.
24 smiley faces. Shared among 3 friends How many smiley faces will each one have?
2
Make a plan.
Use multiplication to help you divide. 24 shared among 3 What number times 3 equals 24?
3
Think multiplication
Carry out the plan.
× 3 = 24
8 × 3 = 24 4
Check.
Divide 24 ÷ 3 = smiley faces
Check. Revise your calculations if necessary. 263
A. Match.
1×3
2×4
8×3
3×9
B. Write addition and multiplication sentences.
A formative assessment in the middle of each chapter to evaluate students’ progression of understanding the first half of the chapter.
1
2
3
4
C. Complete. 1
9 + 9 + 9 + 9 + = 9 × ______
2
3 groups of 2 =______
3
6 × 3 = ______ + ______ + ______
4
4 rows of 5 = ______
D. Problem solving. Luke bought 5 notebooks for $ 4 each. How much money did he pay? Use a number line to show your answer. 142
4
Thousands Hundreds
The value:
Tens Ones
2
3
4
5
2000
300
40
5
B. Read and write 4-digit numbers to show the number in 3 different ways Expanded form: 3000 + 200 + 5 Standard form: 3,205 Word form: three thousand, two hundred and five.
C. Ordering numbers To order 2563 , 2,635 , 2,548 you can use a number line or a place value chart. 2,000
2,548
2,563
2,635
Place value chart Thousands Hundreds Tens 2 5 6 2 6 3 2 5 4
3,000
From least to greatest: 2,548 , 2,56,3 , 2,635 From greatest to least: 2,635 , 2,563 , 2,548
Ones 3 5 8
Briefly summarizes mathematical concepts for students to review and reference.
D. Rounding to the nearest 10 or 100 To round 3,472 to the nearest 10 and 100, you can use a number line or a place value chart. Place value chart Thousands Hundreds Tens 3 4 7
3,472
3,000
3,500
Ones 2
DOING MATH
Place value chart
A. 4-digit numbers
3,472 rounded to the nearest 10 is 3,470 3,472 rounded to the nearest 100 is 3,500 39
CHECK Multiply. 1
2×4=
2
3
2×7=
4
6×4= 9×4=
5
2×5=
6
10 × 3 =
7
5×6=
8
10 × 8 =
9
3×3=
10
6×3=
11
3×5=
12
6×7=
13
7×4=
14
7×8=
15
8×3=
16
8×6=
17
9×5=
18
9×9=
19
30 × 5 =
20
2×9=
CHECK Assesses children’s comprehension of the chapter.
232
Vocabulary Review
A. Match. 4000 + 200 + 5
Word form
12, 14, 16, 18, ...
Odd numbers
Two thousand, three hundred eleven
Expanded form
15, 17, 19, 21, ...
Standard form
1,568
Even numbers
B. Complete each sentence with one of these words: pattern
chart
diagonal
round
To
, replace a number with a number that tells about how many.
A
is the way something happens repeatedly.
A
connects opposite corners of a figure.
A
is a way to show information in a simple way.
Provides various fun activities for students to review the chapter vocabulary words.
45
A. Write the time shown on each clock.
B. Draw the hands on the clock to show the time given. Twenty-two to four
12 past five
C. Solve. A train takes 2 hours and 9 minutes to travel from London to Liverpool. The table shows the time the train leaves London. Find the time the train arrives in Liverpool. Leaves London
05:36
09:28
01:54
11:15
Arrives Liverpool
D. What is the mass?
E. What is the capacity of the measuring cup?
Provides a formative assessment at the end of the chapter to test students’ understanding of the content.
600 ml 500 400 300 200 100
_____________ kg
_____________ milliliter
382
5
COMMON CORE STATE STANDARDS
Operations and Algebraic Thinking 3.OA Represent and solve problems involving addition and subtraction. 3.OA.1 Interpret products of whole numbers, e.g., interpret 5 × 7 as the total number of objects in 5 groups of 7 objects each. For example, describe a context in which a total number of objects can be expressed as 5 × 7. 3.OA.2 Interpret whole-number quotients of whole numbers, e.g., interpret 56 ÷ 8 as the number of objects in each share when 56 objects are partitioned equally into 8 shares, or as a number of shares when 56 objects are partitioned into equal shares of 8 objects each. For example, describe a context in which a number of shares or a number of groups can be expressed as 56 ÷ 8. 3.OA.3 Use multiplication and division within 100 to solve word problems in situations involving equal groups, arrays, and measurement quantities, e.g., by using drawings and equations with a symbol for the unknown number to represent the problem. 3.OA.4 Determine the unknown whole number in a multiplication or division equation relating three whole numbers. For example, determine the unknown number that makes the equation true in each of the equations 8 × ? = 48, 5 = ? ÷3, 6 × 6 = ?. Understand properties of multiplication and the relationship between multiplication and division. 3.OA.5 Apply properties of operations as strategies to multiply and divide.2 Examples: If 6 × 4 = 24 is known, then 4 × 6 = 24 is also known. (Commutative property of multiplication.) 3 × 5 × 2 can be found by 3 × 5 = 15, then 15 × 2 = 30, or by 5 × 2 = 10, then 3 × 10 = 30. (Associative property of multiplication.) Knowing that 8 × 5 = 40 and 8 × 2 = 16, one can find 8 × 7 as 8 × (5 + 2) = (8 × 5) + (8 × 2) = 40 + 16 = 56. (Distributive property.) 3.OA.6 Understand division as an unknown-factor problem. For example, find 32 ÷ 8 by finding the number that makes 32 when multiplied by 8. Multiply and divide within 100. 3.OA.7 Fluently multiply and divide within 100, using strategies such as the relationship between multiplication and division (e.g., knowing that 8 × 5 = 40, one knows 40 ÷ 5 = 8) or properties of operations. By the end of Grade 3, know from memory all products of two one-digit numbers.
6
Solve problems involving the four operations, and identify and explain patterns in arithmetic.
3.OA.9 Identify arithmetic patterns (including patterns in the addition table or multiplication table), and explain them using properties of operations. For example, observe that 4 times a number is always even, and explain why 4 times a number can be decomposed into two equal addends.
Number and Operations in Base Ten 3.NBT Use place value understanding and properties of operations to perform multi-digit arithmetic. 3.NBT.1 Use place value understanding to round whole numbers to the nearest 10 or 100. 3.NBT.2 Fluently add and subtract within 1000 using strategies and algorithms based on place value, properties of operations, and/or the relationship between addition and subtraction.
COMMON CORE STATE STANDARDS
3.OA.8 Solve two-step word problems using the four operations. Represent these problems using equations with a letter standing for the unknown quantity. Assess the reasonableness of answers using mental computation and estimation strategies including rounding.
3.NBT.3 Multiply one-digit whole numbers by multiples of 10 in the range 10–90 (e.g., 9 × 80, 5 × 60) using strategies based on place value and properties of operations.
Number and Operations – Fractions 3.NF Develop understanding of fractions as numbers. 3.NF.1 Understand a fraction 1/b as the quantity formed by 1 part when a whole is partitioned into b equal parts; understand a fraction a/b as the quantity formed by a parts of size 1/b. 3.NF.2 Understand a fraction as a number on the number line; represent fractions on a number line diagram. a. Represent a fraction 1/b on a number line diagram by defining the interval from 0 to 1 as the whole and partitioning it into b equal parts. Recognize that each part has size 1/b and that the endpoint of the part based at 0 locates the number 1/b on the number line. b. Represent a fraction a/b on a number line diagram by marking off a lengths 1/b from 0. Recognize that the resulting interval has size a/b and that its endpoint locates the number a/b on the number line.
7
MATHEMATICAL PRACTICE
Mathematical Practice MP1 Make sense of problems and persevere in solving them. Mathematically proficient students start by explaining to themselves the meaning of a problem and looking for entry points to its solution. They analyze givens, constraints, relationships, and goals. They make conjectures about the form and meaning of the solution and plan a solution pathway rather than simply jumping into a solution attempt. They consider analogous problems, and try special cases and simpler forms of the original problem in order to gain insight into its solution. They monitor and evaluate their progress and change course if necessary. Older students might, depending on the context of the problem, transform algebraic expressions or change the viewing window on their graphing calculator to get the information they need. Mathematically proficient students can explain correspondences between equations, verbal descriptions, tables, and graphs or draw diagrams of important features and relationships, graph data, and search for regularity or trends. Younger students might rely on using concrete objects or pictures to help conceptualize and solve a problem. Mathematically proficient students check their answers to problems using a different method, and they continually ask themselves, “Does this make sense?” They can understand the approaches of others to solving complex problems and identify correspondences between different approaches. MP2 Reason abstractly and quantitatively. Mathematically proficient students make sense of quantities and their relationships in problem situations. They bring two complementary abilities to bear on problems involving quantitative relationships: the ability to decontextualize —to abstract a given situation and represent it symbolically and manipulate the representing symbols as if they have a life of their own, without necessarily attending to their referents—and the ability to contextualize, to pause as needed during the manipulation process in order to probe into the referents for the symbols involved. Quantitative reasoning entails habits of creating a coherent representation of the problem at hand; considering the units involved; attending to the meaning of quantities, not just how to compute them; and knowing and flexibly using different properties of operations and objects. MP3 Construct viable arguments and critique the reasoning of others. Mathematically proficient students understand and use stated assumptions, definitions, and previously established results in constructing arguments. They make conjectures and build a logical progression of statements to explore the truth of their conjectures. They are able to analyze situations by breaking them into cases, and can recognize and use counter examples. They reason inductively about data, making plausible arguments that take into account the context from which the data arose. Mathematically proficient students are also able to compare the effectiveness of two plausible arguments, distinguish correct logic or reasoning from that which is flawed, and—if there is a flaw in an argument—explain what it is. Elementary students can construct arguments using concrete referents such as objects, drawings, diagrams, and actions. Such arguments can make sense and be correct, even though they are not generalized or made formal until later grades. Later, students learn to determine domains to which an argument applies. Students at all grades can listen or read the arguments of others, decide whether they make sense, and ask useful questions to clarify or improve the arguments.
8
MP5 Use appropriate tools strategically. Mathematically proficient students consider the available tools when solving a mathematical problem. These tools might include pencil and paper, concrete models, a ruler, a protractor, a calculator, a spreadsheet, a computer algebra system, a statistical package, or dynamic geometry software. Proficient students are sufficiently familiar with tools appropriate for their grade or course to make sound decisions about when each of these tools might be helpful, recognizing both the insight to be gained and their limitations. For example, mathematically proficient high school students analyze graphs of functions and solutions generated using a graphing calculator. They detect possible errors by strategically using estimation and other mathematical knowledge. When making mathematical models, they know that technology can enable them to visualize the results of varying assumptions, explore consequences, and compare predictions with data. Mathematically proficient students at various grade levels are able to identify relevant external mathematical resources, such as digital content located on a website, and use them to pose or solve problems. They are able to use technological tools to explore and deepen their understanding of concepts.
MATHEMATICAL PRACTICE
MP4 Model with mathematics. Mathematically proficient students can apply the mathematics they know to solve problems arising in everyday life, society, and the workplace. In early grades, this might be as simple as writing an addition equation to describe a situation. In middle grades, a student might apply proportional reasoning to plan a school event or analyze a problem in the community. By high school, a student might use geometry to solve a design problem or use a function to describe how one quantity of interest depends on another. Mathematically proficient students who can apply what they know are comfortable making assumptions and approximations to simplify a complicated situation, realizing that these may need revision later. They are able to identify important quantities in a practical situation and map their relationships using such tools as diagrams, two-way tables, graphs, flowcharts and formulas. They can analyze those relationships mathematically to draw conclusions. They routinely interpret their mathematical results in the context of the situation and reflect on whether the results make sense, possibly improving the model if it has not served its purpose.
MP6 Attend to precision. Mathematically proficient students try to communicate precisely to others. They try to use clear definitions in discussion with others and in their own reasoning. They state the meaning of the symbols they choose, including using the equal sign consistently and appropriately. They are careful about specifying units of measure, and labeling axes to clarify the correspondence with quantities in a problem. They calculate accurately and efficiently, express numerical answers with a degree of precision appropriate for the problem context. In the elementary grades, students give carefully formulated explanations to each other. By the time they reach high school they have learned to examine claims and make explicit use of definitions.
9
Place Value and Patterns Addition & SubtractionWithin 1000
Chapter 1 Chapter 2
SCOPE SEQUENCE
Chapter
Lesson
Understanding Multiplication Multiplication Tables Division
Chapter 6 Chapter 4 Chapter 5
Vocabulary
Material
CCSS
Mathematical Practice
Lesson 1
4-Digit Numbers
Recognize 4-digit numbers
4-digit number, thousand, place value chart
thousand, hundreds, and tens blocks.
MP.2, MP.4, MP.6, MP.7
Lesson 2
Read And Write 4-Digit Numbers
Read and write the 4-digit number using three different forms
expanded form, standard form, word form
thousand, hundreds, and tens blocks.
MP.2, MP.4, MP.6, MP.7
Lesson 3
Ordering Numbers
Ordering 4-Digit numbers from least to greatest and vice versa
order, least, greatest
number line
MP.2, MP.4, MP.6, MP.7
Lesson 4
Rounding To The Nearest 10
Rounding whole numbers to the nearest 10.
round, closer, half way
number line
3.NBT.1
MP.2, MP.4, MP.6, MP.7
Lesson 5
Rounding To The Nearest 100
Rounding whole numbers to the nearest 100.
number line
3.NBT.1
MP.2, MP.4, MP.6, MP.7
Lesson 6
Problem Solving
Use problem solving strategy to Solve word problem concerning Reading and writing 4- digit numbers., Round numbers to the nearest 10 and 100.
3.NBT.1, 3OA.9
MP.2, MP.4, MP.6, MP.7
Lesson 1
Estimate Sums
Estimate the sum of two or three numbers
3.NBT.1, 3.OA.8
MP.1, MP.2, MP.3, MP.4, MP.7
Lesson 2
Using A Place Value To Add
Add two 3-digit numbers using place value.
hundreds, tens, and ones models 3.NBT.2
MP.1, MP.2, MP.3, MP.4, MP.7
Lesson 3
Using A Number Line To Add
number line
3.NBT.2
MP.1, MP.2, MP.3, MP.4, MP.7
Lesson 4
Breaking Down To Add
Add two 3-digit numbers using a number line Add two 3-digit numbers within 1000 using decomposing strategy Add two 3-digit numbers within 1000 using compensation Use addition properties to add, 3-digit numbers within 1000.
3.NBT.2
MP.1, MP.2, MP.3, MP.4, MP.7
3.NBT.2
MP.1, MP.2, MP.3, MP.4, MP.7
3.NBT.2
MP.1, MP.2, MP.3, MP.4, MP.7
3.OA.9
MP.1, MP.2, MP.3, MP.4, MP.7
3.OA.9
MP.1, MP.2, MP.3, MP.4, MP.7
3.NBT.1, 3.OA.8
MP.1, MP.2, MP.3, MP.4, MP.7
Lesson 5
Breaking Apart To Add
Lesson 6
Addition Properties
Lesson 7
Number Patterns
Lesson 8
Addition Pattern
Lesson 9
Estimate Differences Using A Place Value To Subtract Using A Number Line To Subtract
Lesson 10 Lesson 11 Lesson 12
Breaking Down To Subtract
Lesson 13
Breaking Apart To Subtract
Lesson 14
Think Addition To Subtract
Lesson 15
Problem Solving Strategy
Lesson 1
10
Objective
Lesson 2 Lesson 3 Lesson 4 Lesson 5
Multiplication As Equal Groups Multiplication As Repeated Addition Multiplication As Arrays Multiplication By Drawing Multiplication On A Number Line
Identify number patterns Identify arithmetic patterns including patterns in the addition table using properties of operations Estimate the difference of two or three numbers
break apart, compensation, fluently property, commutative, associative, identity pattern, increase, rule, even numbers, odd numbers diagonal
hundred chart, addition chart
hundreds, tens, and ones models 3.NBT.2
MP.1, MP.2, MP.3, MP.4, MP.7
Subtract two 3-digit numbers using a number line
number line
3.NBT.2
MP.1, MP.2, MP.3, MP.4, MP.7
3.NBT.2
MP.1, MP.2, MP.3, MP.4, MP.7
3.NBT.2
MP.1, MP.2, MP.3, MP.4, MP.7
3.NBT.2
MP.1, MP.2, MP.3, MP.4, MP.7
3.NBT.2, 3.OA.8
MP.1, MP.2, MP.3, MP.4, MP.7
3.OA.1, 3.OA.3
MP.1, MP.2, MP.3, MP.4, MP.7
3.OA.1
MP.1, MP.2, MP.3, MP.4, MP.7
arrays
3.OA.1, 3.OA.3 3.OA.3
MP.1, MP.2, MP.3, MP.4, MP.7 MP.1, MP.2, MP.3, MP.4, MP.7
number line
3.OA.3
MP.1, MP.2, MP.3, MP.4, MP.7
3.OA.5
MP.1, MP.2, MP.3, MP.4, MP.7
3.OA.5
MP.1, MP.2, MP.3, MP.4, MP.7
3.OA.5
MP.1, MP.2, MP.3, MP.4, MP.7
3.OA.5
MP.1, MP.2, MP.3, MP.4, MP.7
3.OA.9
MP.1, MP.2, MP.3, MP.4, MP.7
3.OA.3, 3.OA.5
MP.1, MP.2, MP.3, MP.4, MP.7
3.OA.7, 3.OA.4
MP.1, MP.2, MP.3, MP.4, MP.7
3.OA.7, 3.OA.4 3.OA.7, 3.OA.4 3.OA.7, 3.OA.4 3.OA.7, 3.OA.4 3.OA.7, 3.OA.4 3.OA.7, 3.OA.4 3.OA.7, 3.OA.4 3.OA.7, 3.OA.4 3.OA.7, 3.OA.4
MP.1, MP.2, MP.3, MP.4, MP.7 MP.1, MP.2, MP.3, MP.4, MP.7 MP.1, MP.2, MP.3, MP.4, MP.7 MP.1, MP.2, MP.3, MP.4, MP.7 MP.1, MP.2, MP.3, MP.4, MP.7 MP.1, MP.2, MP.3, MP.4, MP.7 MP.1, MP.2, MP.3, MP.4, MP.7 MP.1, MP.2, MP.3, MP.4, MP.7 MP.1, MP.2, MP.3, MP.4, MP.7
3.NBT.3
MP.1, MP.2, MP.3, MP.4, MP.7
3.OA.8
MP.1, MP.2, MP.3, MP.4, MP.7
3.OA.7, 3.OA.4, 3.OA.8
MP.1, MP.2, MP.3, MP.4, MP.7
3.OA.2, 3.OA.3
MP.1, MP.2, MP.3, MP.4, MP.7
3.OA.2, 3.OA.3
MP.1, MP.2, MP.3, MP.4, MP.7
3.OA.2, 3.OA.3
MP.1, MP.2, MP.3, MP.4, MP.7
3.OA.5
MP.1, MP.2, MP.3, MP.4, MP.7
3.OA.4, 3.OA.6
MP.1, MP.2, MP.3, MP.4, MP.7
Subtract two 3-digit numbers within 1000 using partitioning decomposing strategy Subtract two 3-digit numbers within 1000 using compensation Subtract using the relationship between addition and subtraction. Use the problem solving strategy to Solve word problems concerning estimate, adding and subtracting within 1000. Interpret products as equal groups Interpret products as repeated addition Interpret products as, Arrays. Interpret products by drawing
equal groups, times, size, multiplication repeated addition, multiplication sentence array, factor, product
Interpret products using number lines
Order Property
Apply commutative property as strategy to multiply
Lesson 7
Grouping Property
Apply Associative property as strategy to multiply
Lesson 8
Breaking Property
Apply Breaking property as strategy to multiply
Lesson 9
Multiplication By 0 And 1
Lesson 10
Multiplication Patterns
Lesson 11
Problem Solving
Lesson1
Multiplication Facts Of 2
Drive and recall multiplication facts of 2
Lesson 2 Lesson 3 Lesson 4 Lesson 5 Lesson 6 Lesson 7 Lesson 8 Lesson 9 Lesson 10
Multiplication Facts Of 3 Multiplication Facts Of 4 Multiplication Facts Of 5 Multiplication Facts Of 10 Multiplication Facts Of 6 Multiplication Facts Of 7 Multiplication Facts Of 8 Multiplication Facts Of 9 Mixed Multiplication Facts
Drive and recall multiplication facts of 3 Drive and recall multiplication facts of 4 Drive and recall multiplication facts of 5 Drive and recall multiplication facts of 10 Drive and recall multiplication facts of 6 Drive and recall multiplication facts of 7 Drive and recall multiplication facts of 8 Drive and recall multiplication facts of 9 Fluently multiply within 100, using different strategies.
Lesson 11
Multiply With Multiples Of 10
Multiply one-digit whole numbers by multiples of 10
Order Of Operation
break down, decompose
Subtract two 3-digit numbers using place value.
Lesson 6
Lesson 12
estimate, actual, compatible, reasonable
Apply Identity and zero property as strategy to multiply Identify arithmetic patterns including patterns in the multiplication table. Use the problem solving strategy to Solve word problem concerning properties of operations as strategies to multiply
Apply order of operation when solving more than one operation Use the problem solving strategy to Solve two-step word problems concerning multiplication and addition
commutative, order property array parenthesis, grouping property, associative breaking, distributive property identity property, zero property pattern
fact, multiple, double, even number
naught
multiples of 10, skip counting, decompose order, operation unknown
Lesson 13
Problem Solving
Lesson1
Division As Equal Sharing
Interpret whole-number quotients of whole numbers as equal sharing
division, share, divided by, division sentence
Lesson 2
Division As Repeated Subtraction
Interpret whole-number quotients of whole numbers as repeated subtraction
distribute, dividend, divisor, quotient, repeated subtraction
Lesson 3
Division By Drawing
Interpret whole-number quotients of whole numbers by drawing
Lesson 4
Division By 0 And 1
Apply properties of 0 and 1 as strategies to divide.
Lesson 5
Think Multiplication To Divide
Divide by recalling multiplication facts
Lesson 6
Problem Solving
Use the problem solving strategy to solve word problem concerning division within 100.
3.OA.3
MP.1, MP.2, MP.3, MP.4, MP.7
Lesson 7
Dividing By 2 And 3
Dividing whole numbers within 100 by 2 and 3 by recalling multiplication facts of 2, 3
3.OA.4, 3.OA.7, 3.OA.8
MP.1, MP.2, MP.3, MP.4, MP.7
Lesson 8
Dividing By 4 And 5
Dividing whole numbers within 100 by 4 and5 by recalling multiplication facts of 4, 5
3.OA.4, 3.OA.7, 3.OA.8
MP.1, MP.2, MP.3, MP.4, MP.7
Lesson 9
Dividing By 6 And 7
Dividing whole numbers within 100 by 6and 7 by recalling multiplication facts of 6, 7
3.OA.4, 3.OA.7, 3.OA.8
MP.1, MP.2, MP.3, MP.4, MP.7
Lesson 10
Dividing By 8 And 9
Dividing whole numbers within 100 by 8 and 9 by recalling multiplication facts of 8, 9
3.OA.4, 3.OA.7, 3.OA.8
MP.1, MP.2, MP.3, MP.4, MP.7
Lesson 11
Order Of Operation
Using order of operation when solving math problems.
3.OA.8
MP.1, MP.2, MP.3, MP.4, MP.7
Lesson 12
Problem Solving
Use the problem solving strategy to Solve two-step word problems concerning the four operations
3.OA.8
MP.1, MP.2, MP.3, MP.4, MP.7
fact family, inverse relation
number line
Fractions Measurement Data Perimeter and Area Geometry
Chapter 7 Chapter 8 Chapter 9 Chapter 10
Lesson
Objective
Vocabulary
Lesson1
Fractions As A Part Of Whole
Divide the whole into equal parts.( half, third, fourth, sixth and eighth)
Lesson 2
Express Fractions
Write the fraction of the shaded part
Lesson 3
Fraction As A Part Of A Set
Write the fraction as the quantity formed by parts of a set
Lesson 4
Fractions On A Number Line
Write fractions on a number line
partition, space
Lesson 5
Whole Numbers As Fractions
Write whole number as a fraction., Write fractions that equivalent to whole number
whole numbers
Lesson 6
Equivalent Fractions
Understand two fractions as equivalent fractions., Find and generate simple equivalent fractions
equivalent fractions
Lesson 7
Comparing Fractions With Common Denominators
Recognize that comparisons are valid only when the two fractions refer to the same whole., Compare two fractions with the same denominator
Lesson 8
Comparing Fractions With Common Numerator
Recognize that comparisons are valid only when the two fractions refer to the same whole., Compare two fractions with the same Numerator.
Lesson 9
Problem Solving Strategy.
Use the problem solving strategy to Solve word problem concerning Fractions.
Lesson1
Telling Time
Tell and write time to the nearest minute
telling time, hour, minute, half an hour, quarter an hour
Lesson 2
Time Intervals
Measuring time intervals in minutes
time interval
Lesson 3
Time Real Situations
Relate telling and writing time to real situations, recognize AM-PM, calculate time intervals
Lesson 4
Capacity
Measure and estimate liquid volumes of objects using standard units of liters (L).
Lesson 5
Capacity Real Situations
Connect capacity to real life situations
Lesson 6
Mass
Measure and estimate masses of objects using standard units of gram (s), kilograms, (kg),
Lesson 7
Mass Real Situations
Connect Mass to real life situations
Lesson1
Pictographs
Draw a scaled picture graph to represent a data set with several categories
Lesson 2
Bar Graphs
Draw a scaled bar graph to represent a data set with several categories
Lesson 3
Measuring To The Nearest Length
Generate measurement data by measuring lengths using rules marked with halves and fourths of an inch
half inch, quarter inch, nearest
line plot, length
Material
CCSS
Mathematical Practice
fraction, whole, part, numerator, fraction stripes denominator
3.NF.1
MP.2, MP.3, MP.6, MP.7
fraction stripes
3.NF.1
MP.2, MP.3, MP.6, MP.7
3.NF.1
MP.2, MP.3, MP.6, MP.7
3.NF.2
MP.2, MP.3, MP.6, MP.7
3.NF.3
MP.2, MP.3, MP.6, MP.7
fraction stripes
3.NF.3a, b
MP.2, MP.3, MP.6, MP.7
compare, like fractions, common denominator
fraction stripes
3.NF.3d
MP.2, MP.3, MP.6, MP.7
common numerator, unit fractions
fraction stripes
3.NF.3d
MP.2, MP.3, MP.6, MP.7
3.NF.1, 3.NF.2, 3.NF.3
MP.2, MP.3, MP.6, MP.7
analog clock
3.MD.1
MP.2, MP.4, MP.6, MP.7
analog clock, number line
3.MD.1
MP.2, MP.4, MP.6, MP.7
time situation, a.m, p.m
3.MD.1
MP.2, MP.4, MP.6, MP.7
capacity, liter, milliliter, metric units
3.MD.2
MP.2, MP.4, MP.6, MP.7
3.MD.2
MP.2, MP.4, MP.6, MP.7
3.MD.2
MP.2, MP.4, MP.6, MP.7
3.MD.2
MP.2, MP.4, MP.6, MP.7
3.MD.3
MP.2, MP.5, MP.6, MP.7
3.MD.3
MP.2, MP.5, MP.6, MP.7
3.MD.4
MP.2, MP.5, MP.6, MP.7
number line
mass, matter, kilogram, gram
pictograph, key vote
Lesson 4
Line Plots
Show the data by making a line plot
Lesson 5
Problem Solving Strategy
Use the problem solving strategy to Solve word problem concerning Data
3.MD.4
MP.2, MP.5, MP.6, MP.7
3.MD.3, 3.MD.4
MP.2, MP.5, MP.6, MP.7
Lesson 1
Understanding Perimeter
Understanding the meaning of perimeter, Finding the perimeter of some simple shapes
Lesson 2
Perimeter
Finding the Perimeter by finding the sum of the sides of the figure
3.MD.8
MP.2, MP.3, MP.6, MP.7, MP.8
3.MD.8
MP.2, MP.3, MP.6, MP.7, MP.8
Lesson 3
Understanding Area
Understanding the meaning of area, Finding the area r of some simple shapes
area, graph paper, square unit
3.MD.5a, b
MP.2, MP.3, MP.6, MP.7, MP.8
Lesson 4
Measuring Area
Measure areas by counting unit square using different units
square cm, square inch, square foot, square meter
3.MD.5a, b
MP.2, MP.3, MP.6, MP.7, MP.8
Lesson 5
Area Of Rectangles
Understanding and calculating the formula of area of rectangle
length, width
3.MD.7a, b
MP.2, MP.3, MP.6, MP.7, MP.8
Lesson 6
Properties Application
Applying commutative and distributive properties in measuring area of rectangles
commutative property, distributive property
3.MD.7c
MP.2, MP.3, MP.6, MP.7, MP.8
Lesson 7
Area Of Composite Shapes
Understanding and calculating the area through decomposing figures
composite shapes, polygon
3.MD.7d
MP.2, MP.3, MP.6, MP.7, MP.8
Lesson 8
Area And Perimeter
Exhibiting rectangles with the same perimeter and, different areas or with the same area and different perimeters
3.MD.8
MP.2, MP.3, MP.6, MP.7, MP.8
Lesson 9
Problem Solving Strategy
Use the problem solving strategy to Solve word problem concerning Perimeter and Area.
3.MD.8
MP.2, MP.3, MP.6, MP.7, MP.8
Lesson 1
Angles
Knowing and Find angles around us, right angle, angle less than right angle and angle greater than right angle
angle, line, vertex, side, point, right angle
Lesson 2
Polygons
Name, Draw and Classify polygons according to their attributes
polygon, triangle, quadrilateral, pentagon, hexagon, geometric stripes heptagon, octagon
3.G.1
MP.1, MP.2, MP.3, MP.5, MP.6, MP.7, MP.8
Lesson 3
Quadrilaterals
Identifying quadrilaterals according to their attributes
trapezoid, parallelogram, kite, rectangle, square, rhombus, parallel
geometric stripes
3.G.1
MP.1, MP.2, MP.3, MP.5, MP.6, MP.7, MP.8
Lesson 4
Special Kinds Of Parallelograms
Understand that shapes in different categories may share attributes and that the shared attributes can define a larger category
attributes
geometric stripes
3.G.1
MP.1, MP.2, MP.3, MP.5, MP.6, MP.7, MP.8
Lesson 5
Partition Figures
Partition shapes into parts with equal areas. And express the area of each part as a unit fraction of the whole
partition, unit fraction
geometric stripes
3.G.2
MP.1, MP.2, MP.3, MP.5, MP.6, MP.7, MP.8
Lesson 6
Problem Solving
Use the problem solving strategy to Solve word problem concerning, Understanding that shapes in different categories may share attributes.
3.G.1, 3.G.2
MP.1, MP.2, MP.3, MP.5, MP.6, MP.7, MP.8
perimeter, side, outside, edge
graph paper
geometric stripes
SCOPE SEQUENCE
Chapter 6
Chapter
MP.1, MP.2, MP.3, MP.5, MP.6, MP.7, MP.8
11
12