Key Progressions for Multiplication and Division

Stage Progression / Key Outcomes / Key Knowledge / Key Materials / Problem Progressions
Advanced 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