build up array/build down 1
TRANSCRIPT
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