BUILD-UP/BUILD DOWN

Array card for Inverse relationship between Multiplication and Division

Designed for Grade 2

EDX1280 S3 2014Student no: 0031010900

A Language Model for MathematicsJamieson-Proctor, R. & Larkin, K. (2014).

Student LanguageFamiliar objects

Materials LanguageSubstituted objects

Mathematical LanguageMultiply, divide, equal, inverse

Photographs

Symbolic Language

VerbalConcrete/visual

Symbolic

Division is ‘inverse’ multiplication

Mathematics LanguageHow 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’

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

Step 2 – Division

15 divide by 3

equals 5

‘Mathematics Language’How many fish are there altogether? (15) 15 divide by 3?Think multiplicationWe know 5 by 3 equals 15 so 15 divide by 3 must be 5

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)

CONCLUSION

3 groups of 5 equals 15

INVERSE

15 divide by 3 must be 5