The document outlines a teaching strategy for Grade 2 students to understand the inverse relationship between multiplication and division using a build-up and build-down approach. It emphasizes the use of familiar objects and mathematical language to facilitate learning, showing how repeated addition relates to multiplication and separation relates to division. The document provides steps for both multiplication and division, concluding that understanding this relationship is key to mastering both operations.

1. BUILD-UP/BUILD
DOWN
Array card for Inverse relationship between
Multiplication and Division
Designed for Grade 2
EDX1280 S3 2014
Student no: 0031010900

2. A Language Model for Mathematics
Jamieson-Proctor, R. & Larkin, K. (2014).
Student LanguageFamiliar objects
Materials LanguageSubstituted objects
Mathematical Language
Multiply, divide, equal,
inverse
Photographs
Symbolic Language
VerbalConcrete/visual
Symbolic

3. Division is ‘inverse’ multiplication
Mathematics Language
How many fish are there altogether? (15) How
many groups of 3? How do we work it out? Build-
up by 3, 3 add 3 equals 6, add 3 equals 9, add 3
equals 12, add 3 equals 15. We know there are 5
groups of 3, so we can say 5 multiply by 3 equals
15.
Multiply - Build-up
Inverse – Opposite
Divide – Build-down
 Multiplication is repeated addition of equal
groups or sets
 Example 5 by 3 involves build-up
 Division is separating groups into equal parts
 Example 15 divide by 3 involves build-down
 We call this the ‘inverse relationship’

4. Step 1 – Build-up
 ‘Mathematics’ Language
 We know 3 by 5 equals 15
 How do we know? Build-up, 3
add 3 (6) add 3 (9) add 3 (12)
add 3 (15)
 3 multiply by 5 equals 15

5. Step 2 – Division
15
divide
by 3
equals 5
‘Mathematics Language’
How many fish are there altogether?
(15)
15 divide by 3?
Think multiplication
We know 5 by 3 equals 15 so 15 divide
by 3 must be 5

6. Step 3 – Build-down
‘Mathematics’
Language
Build-down
 Division is the inverse
(opposite) of multiplication
 So 15 divide by 3 must be 5
 How do we know? Build-
down, 15 minus or take-away
3 (12) minus 3 (9) minus 3 (6)
minus 3 (3)

7. CONCLUSION
3 groups of 5 equals 15
INVERSE
15 divide by 3 must be 5