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Multiplication and Order of Operations


Common Core, Math  


4, 5  


Common Core State Standard

CCSS.3.OA.B.5 Apply properties of operations (commutative property of multiplication, associative property of multiplication, distributive property) as strategies to multiply and divide.




Students will identify and define the properties of operations and be able to apply them to equations.



Triangles cut out of construction paper


Introduction: Math Language (5 minutes)

Write the terms factor, product, sum, order, and difference on the board. Tell the students to write their own definitions for each of the terms and create a picture that shows what each word means in math. If students are struggling to identify these terms, provide them definitions and have the students create the visual.



Math definition


A number that you use to multiply


The answer of a multiplication problem (2 factors multiplied together)


The answer to an addition problem


Put in sequence (i. e. 1, 2, 3)


The answer to a subtraction problem



Math Rules Mini-Lesson (10 minutes)

Explain to the students that mathematicians have rules for how numbers work. Math rules are things that are always true in math. Ask students to think about some rules that we already have for how numbers work (numbers always show amounts, addition increases the amount, subtraction decreases the amount, and fractions are equal parts of a whole). Record these rules on an anchor chart for students to refer to throughout the year.



What it means


In My Own Words

Commutative Property of Multiplication

The order of the numbers doesn’t change the product (answer)

4 x 5 = 5 x 4


Associative Property of Multiplication

How factors (numbers) are grouped doesn’t matter in multiplication

(2 x 7) x 3 = 2 x (3 x 7)


Distributive Property

Multiplying the sum or difference of a number is the same as multiplying the sum or difference by the number and adding (or subtracting) the product.

3(5 + 2) = (3×5) + (3×2)


3(5-2) = (3×5) – (3×2)





Prove the Rule (15 minutes)

Pass out papers cut into triangles. The triangles should have numbers students could use for multiplication problems written on the corners of the triangles. Model how to use the three numbers to prove each of the three properties. For example, with a triangle with numbers 3, 4, and 2 on the points, you can create:

  • Commutative Property: 3 x 2 = 2 x 3
  • Associative Property: (3 x 2) x 4 = 3 x (2 x 4)
  • Distributive Property: 3 x (2 + 4) = (3 x 2) + (3 x 4)

Have students work independently or in pairs. They should work through as many triangles as possible in the allowed time. One way to differentiate this activity and provide additional choice and challenge for students is to color code the triangles with numbers that are more challenging or less challenging on triangles of different colors (green triangles have easier problems, red triangles have harder problems).



Reverse It (15 minutes)

This time, tell students that you are going to give them a number and ask them to create equations that could get them to that number. For example, if you give students the number 24, they could create equations: 3 x 8, 8 x 3, (2 x 4) x 3, or (4 x 2) + (3 x 1). Have students create equations for as many numbers as possible.


Math Talk (5 minutes)

As you conclude, ask students to reflect and share:

  • What did you learn about numbers during this lesson?
  • How will you use these properties during the year?
  • How can you help yourself remember these rules for numbers?



Extension Activity

Give students number cards and cards with math symbols on them (parenthesis, x, +, etc.). have students stand in front of the room and rearrange themselves to show equations that represent each rule.


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