Lesson Summary: The teacher begins by leading a discussion about commonalities between addition and multiplication. Students work in pairs to deduce that the associative and commutative properties apply to addition and multiplication, but not subtraction or division. The teacher then shows students how to define and apply the distributive property. Students then answer multiple-choice questions for independent practice. Advanced learners will sort problems according to the number property they display. Struggling learners make flashcards to help them learn the definitions of the different number properties.
Lesson Objectives:
The students will know…
- How to define the associative, commutative, and distributive properties.
- How to use the associative, commutative, and distributive properties to find equivalent number sentences.
- Define the associative, commutative, and distributive properties.
- Use the associative, commutative, and distributive properties to find equivalent number sentences.
Learning Styles Targeted:
Visual / Auditory / Kinesthetic/Tactile
Pre-Assessment: Ask students, “Do you know anything that addition and multiplication have in common?” Elicit responses from students, leading the discussion about the two operations’ similarities. Don’t lead students in one direction or another; just assess what they already know.
Whole-Class Instruction
Materials Needed:Example Chart Paper* for teacher reference, 3 pieces of chart paper, writing utensils, scratch paper, 1 copy of the Independent Practice* per student
Procedure:
Prior to the lesson, prepare 3 pieces of chart paper to look like the Example Chart Paper.
1)Tell students they are going to learn about some special number properties as you post the piece of chart paper for the associative property.Explain to students that the associative property states that in certain types of problems, the grouping of numbers does not matter and does not affect the answer. Put students in pairs, and write all of the problems in the “Examples” and “Non-Examples” out of order on the board. Don’t include the ≠ symbol for the subtraction and division problems. Ask students to work together to solve each of the problems, classifying the problems into problem in which the grouping does not matter and those in which the grouping does matter. For the problems in which the grouping does matter, you may want to show students how to change the equal sign (=) into a not equal (≠) sign to show that the two sides of the equation are not equal. If necessary, explain to students that the problems within the parenthesis should be solved first. Walk around as students are working to make sure they are solving the problems correctly. When all pairs finish, discuss with students in which problems the grouping matters (division and subtraction) and in which problems the grouping does matter (addition and multiplication). Ask students, “Which types of problems display the associative property?” Elicit responses, leading students to see that the addition and multiplication problems show the associative property. Record the definition of the associative property in the “states…” box. See the answer key, if necessary.
2)Post the piece of chart paper for the commutative property. Repeat the exact same procedure as you did for the associative property. Allow students to discover that the commutative property applies to addition and multiplication, but not subtraction or division.
3)Post the piece of chart paper for the distributive property. Tell students the definition of the distributive property, and record it in the “states…” box. Write the first problem from the “Examples” box on the answer key on the board. You may want to draw an arrow from the 2 to the 10 and to the 3 to show how the number is distributed. Model for students how to solve either side of the equation to prove that both sides are equal. Repeat this for the remaining problems from the “Examples” box.
4)Give each student a copy of the Independent Practice, explain the directions, and allow students to work independently.
Advanced Learner
Materials Needed:1 piece of construction paper per student, writing utensils, 1 copy of the Advanced Learner Independent Practice* per student, 1 pair of scissors per student, 1 bottle of glue or glue stick per student
Procedure:
1)Give each student a piece of construction paper, and have them divide it into three sections. Have students title each of the sections with one number property—associative property, commutative property, and distributive property. Give each student a copy of the Advanced Learner Independent Practice, a pair of scissors, and glue. Tell students that they should cut out the problems and sort them according to the number property shown on the card. Make sure students understand that some cards demonstrate none of the number properties. These cards should be discarded. The other cards should be glued in the appropriate section of the construction paper.
Struggling Learner
Materials Needed:3 index cards per student, writing utensils
Procedure:
1)Give each student 3 index cards. Have students write the name of each number property on the front of each card. Remind students what the associative property states, and have students write the definition of it on the back of the index card labeled “associative property.” Remind students that it applies to addition and multiplication only. You may want students to draw a large addition and multiplication symbol on the front of the card to remind them. Ask students to brainstorm problems in which the grouping of numbers does not affect the answer. Elicit responses, correcting them as needed. Have students record a few of these problems on the index card. Repeat this process for the commutative and distributive properties. Students should take the flashcards home to study.
*see supplemental resources
Copyright © 2011 Study Island - All rights reserved.