Download Distributive Property Lesson Ideas

Distributive Property Lessons Ideas
1. Have students explore the following distributive property scenarios with manipulatives:
a. Scenario 1
Lay out manipulatives as 7 groups of 3 to give a total of 21. Ask students to
express this as a multiplication problem. (7 ´ 3). Separate the 7 groups so that
there are two distinct groups (5 groups and 2 groups). Ask students if this
changes the number of total blocks/cubes. Ask students to represent this situation
given the two distinct groups.
(5 ´ 3) + (2 ´ 3). Have them calculate to show that they are both equal.
15 + 6 = 21
Write 7 ´ 3 and ask what was changed when they split up the group of 7? (It
wasn’t exactly 7 whole groups, but it was 5 groups + 2 groups). Therefore, it can
be stated that we rewrote 7 into (5 + 2). Hence, (5 + 2) ´ 3 = 7 ´ 3.
Next, with (5 ´ 3) + (2 ´ 3), ask students if they believe this is the same as (5 +
2) ´ 3. Calculating it will produce the same answer, so these two expressions are
equivalent. Ask students to point out anything they notice between these two
expressions. Do they see any patterns? The multiplication of 3 is shared or
distributed to the 5 and the 2. Arrows from the 3 to the 5 and the 2 will help
illustrate this.
Ask students if they find any common factors in both 15 and 6. (Answer: 3)
b. Scenario 2
Lay out manipulatives as 5 groups of 4 to give a total of 20 (5 ´ 4). Ask
students to break up the 5 groups into 2 distinct groups. *Preferably a group of 3
and 2
Repeat the same steps with the previous problem showing how
(3 ´ 4) + (2 ´ 4) = (3 + 2) ´ 4.
c. Scenario 3
Lay out a group of 12 and a group of 8 manipulatives. Ask students to organize
each set of groups so that there is an EQUAL NUMBER of clusters in each group
(clusters in this context are also groups but just to differentiate).
Example: 2 clusters of 6
and 2 clusters of 4 → (2 ´ 6) + (2 ´ 4)
Example: 4 clusters of 3
and 4 clusters of 2
Example: 1 ´ 12 and 1 ´ 8
Ask what is common between both groups (clusters of 2). Ask what 2 represents
(think factors and multiples). Students should answer “common factor.”
Write on the board 12 + 8. Underneath it, take examples of common factors that
students used (2, for example) and ask them to represent it as a multiplication
problem (2 ´ 6) + (2 ´ 4). Then, ask students if they can rewrite this problem
using the patterns and algorithms previously looked at in the previous two
scenarios. Ask if there is a common factor in both amounts (Answer: 2). Hence,
students can write 2 (6 + 4). If they combine the clusters of 6 and 4, then there
are 2 clusters of 10 or 2 ´ 10 = 2 (6 + 4). Students’ goal should be to recognize
how (2 ´ 6) + (2 ´ 4) = 2(6+4) and how the 2 is shared or distributed with the 6
and the 4.
d. Scenario 4
Write down 16 + 24 on the board. Ask students if they can rewrite this using
common factors and the distributive property, 4 is a common factor of both.
Hence, 16 + 24
(4 ´ 4) + (4 ´ 6) = 4(4 + 6) since 4 is the common factor of both
Repeat with 18 + 21.
2. Group students in pairs or trios. Students will be completing a “Pass it On!” game. With
a whiteboard for each group, have students write down an addition problem that has a
GCF greater than 1. (Example: 15 + 25)
 Student 1 will write down the GCF of both numbers. (5)
 Student 1 pass it to the next student
 Student 2 will rewrite the problem using the GCF (5 ´ 3 + 5 ´ 5)
 Student 2 will pass it to the next student.
 The next student will write the equivalent expression using the distributive
property 5(3+5)
 The students will continue to pass accordingly.
3. For each problem, each student will rotate jobs. Complete approximately 6 - 9 rounds or
as time permits. Collect student work and review as a formative assessment.
Sample problems:
15+ 25
36+48
21+35
60+90
22+44
30+42
8+10
28+36
72+27
95+65