Key Progressions for Multiplication and Division
Stage Progression / Key Outcomes / Key Knowledge / Key Materials / Problem ProgressionsAdvanced Counting to
Early Additive / · Solve multiplication as repeated addition / · Skip counting sequences for 2’s, 5’s, 10’s only
· Doubles to twenty,
4 + 4 = 8, 9 + 9 = 18 / Animal strips
Slavonic abacus
[Ref: Book 6 Pages 6-7] / · 2 × 6 = ? so 3 × 6 = ?
· 4 × 5 = ? (using skip counting or doubles) so 5 × 5 = ?, 6 × 5 = ?
· 5 × 8 = ? so 6 × 8 = ? and 7 × 8 = ?
· 10 × 4 = ? so 11 × 4 = ? and 12 × 4 = ?
· Solve five times tables by doubling and halving (and learn them) / · ‘-Ty’ numbers place value, e.g. 6 tens is sixty
· Doubles to twenty,
4 + 4 = 8, 9 + 9 = 18 / Fly Flip Cards
Slavonic Abacus
Unifix cubes
[Ref: Book 6 Pages 9-11] / · 2 × 10 = ? (using ty code) so 4 × 5 = ? (using doubling and halving)
· 4 × 10 = ? so 8 × 5 = ?, 6 × 5 = ?
· 3 × 10 = ? so 6 × 5 = ? and 7 × 5 = ?
· 4 × 5 = ? so 5 × 5 = ?
· 8 × 5 = ? so 9 × 5 = ?
· Use the commutative property, e.g. 4 × 6 = 6 × 4 / · Multiplication facts for two times, ten times, five times / Counters or unifix cubes
[Ref: Book 6 Pages 17-18] / · 5 × 6 = ? as 6 × 5 = ?
· 9 × 2 = ? as 2 × 9 = ?
· 10 × 7 = ? as 7 ×10 =?
· 100 × 6 = ? as 6 × 100 = ?
· 50 × 2 = ? as 2 × 50 = ?
· Dividing by sharing using addition to predict / · Multiplication facts for two times, ten times, five times / Counters or unifix cubes
[Ref: Book 6 Pages 7-8] / · 10 ÷ 2 = ? so 20 ÷ 4 = ?
· 12 ÷ 2= ? so 12 ÷ 4 = ?
· 16 ÷ 2 = ? so 16 ÷ 4 so 16 ÷ 8
· 100 ÷ 2 = ? so 100 ÷ 4 = ?
· Dividing by making equal sets / · Multiplication facts for two times, ten times, five times / Unifix cubes
[Ref: Book 6 Pages 8-9] / · Twos in 20 so fours in 20
· Tens in 30 so fives in 30
· Twos in 16 so fours in 16
· Fives in 30 so fives in 60
· Fours in 16 so eights in 16
· Fours in 12 so fours in 24
Stage Progression / Key Outcomes / Key Knowledge / Key Materials / Problem Progressions
Early Additive to Advanced Additive / · Use five times facts to work out six and seven times facts (using the distributive property) / · Multiplication facts for two times, ten times, five times / Slavonic abacus
Unifix cubes
Fly Flip cards
Animal Cards
[Ref: Book 6 Pages 12-14] / · 2 × 5 = ? so 2 × 6 = ? so 2 × 7 = ?
· 4 × 5 = ? so 4 × 6 = ? so 4 × 7 = ?
· 6 × 5 = ? so 6 × 6 = ? so 6 × 7 = ?
· 9 × 5 = ? so 9 × 6 = ? so 9 × 7 = ?
· 20 × 5 = ? so 20 × 6 = ? so 20 × 7 = ?
· Use ten times facts to work out nine times facts (using the distributive property) / · Multiplication facts for two times, ten times, five times / Slavonic abacus
Unifix cubes
Animal Cards
[Ref: Book 6 Pages 15-17] / · 2 × 10 = ? so 2 × 9 = ?
· 9 × 10 = ? so 9 × 9 = ?
· 6 × 10 = ? so 6 × 9 = ?
· 3 × 9 = 30 - ? = ?
· 8 × 9 = 80 - ? = ?
· 5 × 9 = 50 - ? = ?
· 2 × 20 = ? so 2 × 19 = ?
· 4 × 100 = ? so 4 × 99 = ?
· Use two times facts to work out three and four times facts (using doubling and the distributive property) / · Multiplication facts for two times, ten times, five times / Slavonic abacus
Unifix cubes
Animal Cards / · 5 × 2 = ? so 5 × 3 = ? so 5 × 4 = ?
· 6 × 2 = ? so 6 × 3 = ? so 6 × 4 = ?
· 8 × 2 = ? so 8 × 3 = ? so 8 × 4 = ?
· 25 × 2 = ? so 25 × 3 = ? so 25 × 4 = ?
Stage Progression / Key Outcomes / Key Knowledge / Key Materials / Problem Progressions
Early Additive to Advanced Additive / · Multiply by tens, hundreds and thousands / · Multiplication facts for two, three, four, five, nine, ten times / Tens frames with BeaNZ and canisters or Place value blocks
[Ref: Book 6 Pages 14-15] / · 5 × 10 = ? so 5 × 20 = ? so 5 × 40 = ?
· 8 × 10 = ? so 8 × 20 = ? so 8 × 30 = ?
· 6 × 10 = ? so 6 × 30 = ? so 6 × 60 = ?
· 4 × 100 = ? so 4 × 200 = ? so 4 × 400 = ?
· 3 × 100 = ? so 3 × 400 = ? so 3 × 900 = ?
· Use three and four times facts to work out six and eight times facts (using doubling) / · Multiplication facts for two, three, four, five, nine, ten times / Slavonic abacus or Unifix cubes / · 3 × 5 = ? so 6 × 5 = ?
· 4 × 5 = ? so 8 × 5 = ?
· 3 × 9 = ? so 6 × 9 = ?
· 4 × 9 = ? so 8 × 9 = ?
· 3 × 6 = ? so 6 × 6 = ?
· 4 × 7 = ? so 8 × 7 = ?
· 3 × 25 =? so 6 × 25 =?
· 4 × 50 =? so 8 × 50 =?
· Solve sharing problems by reversing multiplication facts / · Multiplication facts for two, three, four, five, six, seven, eight, nine, ten times / Unifix cubes or counters
Animal strips
[Ref: Book 6 Pages 20-22] / · 4 × 9 = ? so 36 shared among 4?, among 2?
· 6 × 10 = ? so 60 shared among 10?, among 5?, among 20?
· 3 × 8 = ? so 24 shared among 3?, among 6?
· 8 × 8 = ? so 64 shared among 8?, among 4, among 16?
· 9 × 8 = ? so 72 shared among 3?, among 18?
Stage Progression / Key Outcomes / Key Knowledge / Key Materials / Problem Progressions
Early Additive to Advanced Additive / · Solve “How many equal sets of ?” problems by reversing multiplication facts / · Multiplication facts for two, three, four, five, six, seven, eight, nine, ten times / Unifix cubes or counters
Animal strips
[Ref: Book 6 Pages 19-20] / · 5 × 8 = ? so 40 can be made into ? sets of 4, of 2, of 8
· 6 × 7 = ? so 42 can be made into ? sets of 6, of 7, of 3, of 14?
· 9 × 4 = ? so 36 can be made into ? sets of 8, of 3, of 12
Stage Progression / Key Outcomes / Key Knowledge / Key Materials / Problem Progressions
Advanced Additive to Advanced Multiplicative / · Use standard place value to solve multiplication problems (distributive property) / · Basic multiplication facts, e.g. 4 7 = 28
· Nested whole number place value, e.g. 240 is 24 tens / Tens frames with BeaNZ and canisters or Place value blocks
[Ref: Book 6 Pages 34-36] / · 3 × 44 = ? as 3 × 40 + 3 × 4
· 7 × 27 = ? as 7 × 20 + 7 × 7
· 9 × 53 = ? as 9 × 50 + 9 × 3
· 8 × 36 = ? as 8 × 30 + 8 × 6
· 4 × 217 = ? as 4 × 200 + 4 × 10 + 4 × 7
· Use tidy numbers to solve multiplication problems (distributive property) / · Basic multiplication facts, e.g. 4 7 = 28
· Nested whole number place value, e.g. 240 is 24 tens / Tens frames with BeaNZ and canisters or Place value blocks
[Ref: Book 6 Pages 34-36] / · 4 × 26 = ? as 4 × 25 + 4 × 1
· 6 × 99 = ? as 6 × 100 - 6 × 1
· 7 × 48 = ? as 7 × 50 - 7 × 2
· 8 × 47 = ? as 8 × 50 - 8 × 3
· 6 × 248 = ? as 6 × 250 - 6 × 2
· Use proportional adjustment like doubling and halving, thirding and trebling, to solve multiplication problems / · Basic multiplication facts, e.g. 4 7 = 28 / Unifix cubes
[Ref: Book 6 Pages 25-26] / · 4 × 6 = ? so 2 × ? = 24 and 8 × 3 = 24
· 12 × 10 = ? so ? × 5 = 120 and 6 × ? = 120
· 9 × 8 = ? so 3 × ? = 72 and ? × 4 = 72
· 4 × 16 = ? from 8 × 8
· 468 × 5 =? from 234 ×10
· 18 × 33 =? from 6 ×99
Stage Progression / Key Outcomes / Key Knowledge / Key Materials / Problem Progressions
Advanced Additive to Advanced Multiplicative / · Use standard place value to solve division problems, including written forms, e.g. 8 / · Basic multiplication and division facts, e.g. 4 7 = 28, 49 ÷ 7 = 7 / Tens frames with BeaNZ and canisters or Place value blocks
[Ref: Book 6 Pages 34-36] / · 96 ÷ 4 = ? as 80 ÷ 4 = 20 and 16 ÷ 4 = 4
· 135 ÷ 5 = ? as 100 ÷ 5 = 20 and 35 ÷ 5 = 7
· 189 ÷ 3 = ? as 180 ÷ 3 = 60 and 9 ÷ 3 = 3
· 414 ÷ 9 = ? as 360 ÷ 9 = 40 and 54 ÷ 4 = 6
· 296 ÷ 8 = ? as 240 ÷ 8 = 30 and 56 ÷ 8 = 7
· 318 ÷ 6 = ? as 300 ÷ 6 = 50 and 18 ÷ 6 = 3
· Use standard place value with tidy numbers to solve division problems / · Basic multiplication and division facts, e.g. 4 7 = 28, 49 ÷ 7 = 7 / Tens frames with BeaNZ and canisters or Place value blocks
[Ref: Book 6 Pages 34-36] / · 96 ÷ 4 = ? from 100 ÷ 4 = 25
· 162 ÷ 3 = ? from 180 ÷ 3 = 60
· 476 ÷ 7 = ? from 490 ÷ 7 = 70
· 616 ÷ 8 = ? from 640 ÷ 8 = 80
· 792 ÷ 9 = ? from 810 ÷ 9 = 90
Stage Progression / Key Outcomes / Key Knowledge / Key Materials / Problem Progressions
Advanced Additive to Advanced Multiplicative / · Use splitting by factors to solve multiplication and division problems / · Basic multiplication and division facts, e.g. 4 7 = 28, 49 ÷ 7 = 7 / Animal Strips
Paper Strips
[Ref: Book 6 Pages 42-43] / · 4 × 44 = ? as 2 × 2 × 44
· 8 × 57 = ? as 2 × 2 × 2 × 57
· 12 × 23 = ? as 2 × 2 × 3 × 23
· 72 ÷ 4 = ? as 72 ÷ 2 ÷ 2 = ?
· 184 ÷ 8 = ? as 184 ÷ 2 ÷ 2 ÷ 2 = ?
· 396 ÷ 6 = ? as 396 ÷ 3 ÷ 2 = ?
· Simplify division problems by changing both numbers / · Basic multiplication and division facts, e.g. 4 7 = 28, 49 ÷ 7 = 7 / Counters or cubes and paper plates
[Ref: Book 6 Pages 30-32] / · 52 ÷ 4 = ? as 26 ÷ 2 = ?
· 208 ÷ 8 = ? as 104 ÷ 4 = ? as 52 ÷ 2 = ?
· 408 ÷ 12 = ? as 204 ÷ 6 = ? as 102 ÷ 3 = ?
· 378 ÷ 27 = ? as 42 ÷ 3 = ?
· Use proportional adjustment to solve division problems / · Basic multiplication and division facts, e.g. 4 7 = 28, 49 ÷ 7 = 7 / Unifix cubes
[Ref: Book 6 Pages 28-30] / · 24 ÷ 4 = 6 so 24 ÷ 8 = ? and 24 ÷ 2 = ?
· 40 ÷ 10 = 4 from 40 ÷ 5 = ? and 40 ÷ 20 = ?
· 72 ÷ 9 = 8 so 72 ÷ 3 = ? and 72 ÷ 18 = ?
· 56 ÷ 8 = 7 so 56 ÷ 16 = ? and 56 ÷ 4 = ?
· 1000 ÷ 2 = 500 so 1000 ÷ 4 = ? and 1000 ÷ 8 = ?
Stage Progression / Key Outcomes / Key Knowledge / Key Materials / Problem Progressions
Advanced Additive to Advanced Multiplicative / · Use place value units to solve multiplication and division problems, including written multiplication algorithms, e.g. 34
× 26
/ · Basic multiplication and division facts, e.g. 4 7 = 28, 49 ÷ 7 = 7
· Nested place value, e.g. 4350 has 435 tens / Dotty arrays
[Ref: Book 6 Pages 37] / · 10 × 20 = 200 so 14 × 23 = ?
· 20 × 40 = 800 so 23 × 47 = ?
· 50 × 40 = 2000 so 53 × 46 = ?
· 900 ÷ 30 = 30 so 1080 ÷ 30 = ?
· 4000 ÷ 80 = 50 so 3840 ÷ 80 = ?
· 10 000 ÷ 100 = 100 so 10 000 ÷ 25 = ?
· Solve division problems that involve remainders expressing the remainders as whole numbers, fractions or decimals depending on the context, e.g. 38 ÷ 4 = 9 r2 or 9.5 or 9½ / · Basic multiplication and division facts, e.g. 4 7 = 28, 49 ÷ 7 = 7
· Nested place value, e.g. 4350 has 435 tens / Tens frames with BeaNZ and canisters or Place value blocks
Calculators
[Ref: Book 6 Pages 32-33] / · 35 ÷ 2 = ? from 34 ÷ 2 = 17
· 78 ÷ 5 = ? from 75 ÷ 5 = 15
· 67 ÷ 4 = ? from 64 ÷ 4 = 16
· 53 ÷ 3 = ? from 51 ÷ 3 = 17
· 205 ÷ 8 = ? from 200 ÷ 8 = 25
· 486 ÷ 24 = ? from 480 ÷ 24 = 20
· Use divisibility rules for 2, 3, 4, 5, 6, 8, 9 / · Basic multiplication and division facts, e.g. 4 7 = 28, 49 ÷ 7 = 7
· Nested place value, e.g. 4350 has 435 tens / Tens frames with BeaNZ and canisters or Place value blocks
Calculators
[Ref: Book 6 Pages 38-39] / · Divisible by 4 and 8? 132, 248, 481, 925, 2412, 6664
· Divisible by 3 and 9? 72, 144, 267, 496, 1002
· Divisible by 6? 108, 243, 522, 963
Stage Progression / Key Outcomes / Key Knowledge / Key Materials / Problem Progressions