This is a short 7 slide presentation demonstrating the use of an array card for inverse relationship between multiplication and division. It has been designed for Grade 2.

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