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Common Core Learning StandardsGRADE 3 Mathematics

OPERATIONS & ALGEBRAIC THINKING

Common Core Learning Standards Concepts Embedded Skills Vocabulary

Represent and solve problems involving multiplication and division.

Multiplication Describe whole number products in terms of factors products whole

numbers multiplication array equal groups digit solve factor(s)

Draw a model to represent a given product

3.OA.1Interpret 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.

Create a manipulative model to represent a multiplication equationState/ list the factors of a given product

Translate word form in a multiplication context to numeric form and vice versa

SAMPLE TASKS

I.

a. Write a multiplication sentence for the array above. __________________________________________

Copyright (c) 2011 by Erie 1 BOCES- Deep Curriculum Alignment Project for Mathematics-- Permission to use (not alter) and reproduce for educational purposes only.

b. Explain why you chose the above two factors and describe how you determined the product.

II. Draw a model to represent the number sentence 5 x 3 = 15.

III. Sophia puts seven books on six shelves. How many books does Sophia have?

IV. There are twelve cupcakes on a tray. Write two different multiplication sentences to represent how the cupcakes could be arranged.


V.

Write a multiplication sentence to represent the total number of marbles above.

VI. Write a multiplication story to represent the number sentence 8 x 3 = 24.




Division Describe whole number division in terms of equal groups/ partitions

equal groups/ parts

division dividend quotient divisor digit

Translate word form in a division context to numeric form and vice versa

3.OA.2Interpret 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.

Draw a model to represent a given division equation.Create a manipulative model to represent a division equation

State/list the factors of a given product

SAMPLE TASKSI. There are twenty students in a class sitting in groups of four. How many students are in each group?

A. Draw a model to represent your answer.

B. Write a number sentence to represent your answer.


II.

A. Write a division number sentence to represent the above model.

B. Describe the steps you took to create your number sentence.

C. Explain how multiplication can help you solve this problem.


III. Write a number that would make both number sentences true. 40 ÷ ___ = 4 4 x ___ = 40

IV.

Robert rolled the dice above.

A. Write two division facts for the picture.

B. Write two multiplication facts for the picture.




Multiplication & Division

Solve multiplication and division word problems within 100

multiplication division solve area model digit equation

Write an equation to represent a multiplication or division word problem with a symbol for the unknown

3.OA.3Use 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.

Draw a visual representation (array, drawing, area model, etc.) for a given multiplication or division word problemChoose the appropriate operation based on context clues in text

SAMPLE TASKSI.

Sally buys five white t-shirts. Each shirt costs six dollars.

A. Write a multiplication sentence to show how much she spent.


II. Sarah spent forty-two dollars on packages of silly bands. A. If she bought seven packages, how much does each package cost?

B. Write a division sentence to represent your work.

III. Landon hiked the trail for two hours. His father hiked twice as long.

A. Write a multiplication sentence to show how long his father hiked.

IV. Ken, Tim, and Dennis have one box of candy bars with twenty-four candy bars inside. They want to split the box among them equally. How many will each boy receive?

A. Draw a model of the problem.

B. Write a division sentence for the problem using for the quotient.

C. How many candy bars did each boy receive?


V. Joey earns $14 a week for his allowance. How much does he earn per day?

VI. What multiplication-division fact family does this picture show?

A. How many equal groups of hats are there?

B. How many hats are in each group?

C. How many hats are there in all?

D. Write two multiplication facts for this picture.

E. Write two division facts for this picture.




Multiplication & Division

Solve for a missing factor of a given product (divisor, dividend or quotient) with a symbol for the unknown

equal groups/ parts

division dividend quotient divisor factor(s) solve product

Evaluate the truth value of a product for a given factor

3.OA.4Determine 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 = ?

SAMPLE TASKSI. Below is a chart representing how many books Jeffery read each week.

Number of Weeks Number of Books

1 43 125 20

289

A. How many weeks did it take Jeffery to read 20 books?

B. Explain the rule that is used to complete the chart.


C. How many weeks did it take Jeffery to complete 28 books?

D. How many books did he read in 9 weeks?

E. If this pattern continues how many weeks would it take him to read 44 books?

II. A.. Create an array to represent 15 circles in 3 rows.

B. Complete the number sentence.

15÷3= ____

C. Write two multiplication sentences related to the above number sentence.

III. 4 x ________= 8 x 2


IV. Kim brought home 32 oranges. She wants to put them in 4 baskets to give to each of her neighbors. Complete the chart below to show how many oranges each neighbor will receive.

______________________32______________________

4 ?

Write the fact family to represent the above diagram.



Understand properties of multiplication and the relationship between multiplication & division.

Properties Explain and give a numeric example commutative, associative & distributive property of multiplication

commutative property

associative property

distributive property

State the property shown in a given multiplication equation

3.OA.5Apply 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.)

SAMPLE TASKS

I. A. Write a multiplication sentence to represent this group of dice.

B. Write a multiplication sentence to represent this group of dice.

C. Explain why the product is the same for both groups of dice.


II. 3 x ____= 9 x 3

III. Is the following number sentence true?

3 x (4 x 2)= (3 x 4) x 2

Explain why or why not.

IV. A. What is the missing number in the following number sentence?___________________

(3 x ) x 5 = 3 x (4 x 5)

B. Explain how you found your answer.

V. Miguel wants to solve (4 x 3) x 2. He needs to change the grouping of the factors in order to help him find the product.

A. Write another way Miguel can group the factors.


B. Find the product of (4 x 3) x 2. Show your work and explain how you found your answer.

VI. 5 x ( 6 + 7)

A. Solve the above number sentence. Be sure to show your work.

B. Explain the steps you used to solve the above number sentence.



Understand properties of multiplication and the relationship between multiplication & division.

Properties Describe division in terms of multiplication (inverse operations)

fact family inverse

operation factor(s) divide multiply

Solve division problems through application of fact families

3.OA.66. Understand division as an unknown-factor problem. For example, find 32 ÷ 8 by finding the number that makes 32 when multiplied by 8.

SAMPLE TASKSI. A. Write a fact family from the following array.

B. Explain how multiplication and division are related.



Multiply & divide within 100. Multiplication & Division

Fluency

Fluently multiply and divide within 100 (know from memory all product of two one-digit numbers)

product operation relationship digit factor(s) divide multiply

Describe the relationship between factors & products in terms of multiplication & division

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.

SAMPLE TASKSI. A. Solve the following:

4 x _______= 8 _______ x 2 = 8

B. Describe a strategy you can use to solve problems with 2 as a factor.

II. A. Solve 42÷7= ___________

B. What multiplication fact can be used to help solve this problem?

III. Describe a strategy you use to remember products of 9.


IV. Sara said that when solving multiplication facts with 5 all the product s should end with 5 or 0. Is she correct? Explain.



Solve problems involving the four operations, and identify and explain patterns in arithmetic.

Two Step Problems

Solve two-step word problems using the four operations (apply order of operations rules: Multiplication & division are first (read left to right) then addition and subtraction are second (read left to right)

equation estimation digit

Write an equation to represent a multiplication or division word problem with a symbol for the unknown

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

Check solutions for a given problem using estimation strategies

SAMPLE TASKSI. A. Malik was shopping at Target. He purchased three video games costing six dollars each. He paid the cashier with a twenty dollar bill. How much change did he receive? Show your work.

B. Briana also went shopping at Target with Malik. She bought two Barbie dolls each costing nine dollars. Brianna thinks she spent more money than Malik. Is she correct? Explain.


II. Gianna and Courtney were selling candy bars. Gianna sold 7candy bars and Courtney sold three times as many. Is it reasonable to say that together they sold ten candy bars? Explain your answer.

III. A. Bob and Sally are buying tickets to the school play. Tickets cost $8 each. Bob needs 4 tickets and Sally needs 8 tickets, how much money do they need all together?

B. Sally thinks she owes twice as much money as Bob. Is she correct? Explain.

C. Sally pays for her tickets with a $100 bill, how much change would she receive?


Solve problems involving the four operations, and identify and explain patterns in arithmetic.

Numeric Patterns

Create a numeric pattern using addition & multiplication

pattern table rule term multiplication addition

Explain a given numeric pattern shown in a table or chart

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.

Conclude a rule from a given table or chart

Solve for a missing number (term) in a given arithmetic pattern

SAMPLE TASKS

I. 6 12 18 24 30 ___ 42 ___

A. Describe the rule being used to number the mailboxes.

B. Fill in the missing numbers in the pattern.

II. Olivia practiced her instrument lessons last week. She practiced for 15 minutes on Sunday, 18 minutes on Monday, 21 on Tuesday, 24 on Wednesday, and 27 on Thursday.


A. If the pattern continues how many minutes will she have practiced on Saturday?

B. At the end of the week, how many total minutes would she have practiced for the week?

III.

Number of Pizzas Number of Slices3 245 407 569 ?

A. Describe the rule for the above chart

B. How many slices would be in nine pizzas?

C. How many slices would be in 6 pizzas?


D. How many pizzas do you need for 64 slices?

E. Karen ordered two pizzas for her sleepover. If five of them each eat 2 slices, how many slices would be left?


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