No 7

Transition: Advanced Additive to Advanced Multiplicative Achievement Objectives

Domain: Addition and Subtraction

E

Mathematical Processes: Level Two and Three

Number and Algebra: Level Two and Three

Problem Solving: Devise and use problem solving strategies to  explore situations mathematically. Use equipment appropriately when exploring mathematical  ideas. Logic and Reasoning: Classify objects. Communicating Mathematical Ideas: Devise and follow a set of  instructions to carry out a mathematical activity.   Record and talk about the results of mathematical exploration.

Explain the meaning of the digits in any whole number. Explain the meaning of the digits in decimal numbers with up to 3  decimal places. Order decimals with up to 3 decimal places. Explain the meaning of negative numbers. Express a fraction as a decimal and vice versa. Make sensible estimates and check the reasonableness of  answers. Mentally perform calculations that involve addition and  subtraction.  Write and solve story problems that involve whole numbers using  addition, subtraction, multiplication, or division. Explain satisfactory algorithms for addition, subtraction, and  multiplication.

Strategies being developed

Problem progression

References

Knowledge being developed

Resources

Use multiplication to solve addition and subtraction problems where common factors can be found, e.g. 24 + 27 + 22 + 28 = 4 × 25

36 + 45 =  as 4 × 9 + 5 × 9 = 9 × 9 =  77 - 28 =  as 11 × 7 - 4 × 7 = 7 × 7 =  24 + 48 + 64 + 32 as (3 + 6 + 8 + 4) × 8 = 21 × 8 =  29 + 30 + 28 + 33 + 32 + 27 + 31 + 30 =  as 8 × 30 = 

Teaching Addition and Subtraction (Book 5) Average Ability (53) Multiple Ways to Add  and Subtract (54) Teaching Algebraic   Thinking and Number   Sense (Book 8) Adding Sequences (34) Figure It Out NS&AT3.1 Crafty

Say the forwards and backwards decimal  word sequences by thousandths,  hundredths, tenths, ones, tens, etc, starting  at any whole number..

Teaching Number knowledge (Book 4) Number fans (4) Place value houses (5) Number hangman (5) Skip counting on the number line (11) Hundreds Boards  and thousands  board (16) Figure It Out N 3­4 Changes, 

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Numeracy Development Projects

1

CA AC EA AA AM AP

99 – 36 – 27 =  as (11 - 4 – 3) × 9 = 

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Combinations (16)

Numeracy Development Projects

highs and lows  (6)

2

Transition: Advanced Additive to Advanced Multiplicative Strategies being developed

Problem progression

References

Add and subtract fractions that have related denominators using a range of mental and written strategies..

See AA to AM for Ratios and Proportions

Domain: Addition and Subtraction Knowledge being developed

E

Resources

CA AC EA AA

Add and subtract decimals using a range of mental and written strategies.

Solve addition and subtraction problems with integers (positive and negative numbers).

© 2006 Crown Copyright

See AA to AM for Ratios and Proportions

+

2 + +3 =  4 + -1 =  + 4 + -5 =  2 + -8 =  + 6 - +5 =  7 - -3 =  + 5 - -2 =  3 - +7 = 

Teaching Addition and Subtraction (Book 5) Dollars and Bills (50) Hills and Dales (50) Teaching Algebraic Thinking   and Number  Sense (Book 8) 6 Minus 8 Does Work (31) Figure It Out N3-4.1 Walking the Plank (23) N3-4.3 The Volcanoes Erupt (20) N3-4.3 Chilly Heights (22) N7/8 4.4 It’s a Try (8) N7/8 4.4 Lifting Weights (9) N7/8 4.4 Integer Zap (10) N7/8 4.4 Shifty Subtraction (15) N7/8 4.6 Judo Competition (14)

Numeracy Development Projects

Say the number one-thousandth, onehundredth, one-tenth, one, and ten, etc, before and after any given whole number. Order decimals to three places.

Teaching Number knowledge (Book 4) Number fans (4) Skip counting on the number line (11), Lucky dip (13) Teaching Number knowledge (Book 4) Reading decimal fractions (8) Card ordering (12) Arrow Cards (13) Rocket- Where will it fit? (15) Squeeze- Guess my number (15) Bead strings (17) Who wins? (20) Figure It Out N 7/8 4.3 Going for gold (12) L7/8 L.1 Up the Ladder (15)

3

AM AP

Transition: Advanced Additive to Advanced Multiplicative

Domain: Addition and Subtraction

E

Strategies being developed

Problem progression

References

Knowledge being developed

Resources

Use a range of mental and written strategies to solve multi-step problems that involve a combination of addition, subtraction, multiplication, and division with whole numbers.

Julie bought three tops for $16 each and four pairs of shorts for $13 each. How much did her clothes cost altogether? Tame bought 204 cans of softdrink for the disco. They used 13 six-packs. How many cans were left over? Three girls did jobs for their neighbours. For each job they got paid $43, $56, $21, and $33. They split the money evenly between them. How much did each girl get?

Figure It Out BF3 Paths and Pairs (9) BF3 Calculator Golf (18) N3.2 Stepping Out (2) N3.3 Strategy Strut (6) N3.3 Worth the Work (10) N3-4.1 Head Cases (13) N3-4.1 Kapa Haka (14) NS&AT3.2 Maths Detective (2)

Recall the number of groupings of tens, hundred, and thousands that can be made from a number of up to seven digits.

Teaching Number knowledge (Book 4) Number hangman (5) Tens in hundreds and more (27) Estimating (25) Figure It Out N 7/8 4.2 A million grains of rice (4)

CA

Knowledge being developed

Resources

Round whole numbers and decimals, with up to two places, to the nearest whole number, or  tenth.

Teaching Number knowledge (Book 4) Swedish Rounding (28), Sensible rounding (28) Figure It Out NS 7/8 Number scavenge (6), NS 7/8 2 Time versus money (7) Figure It Out NS 7/8 2 Same answer every time (11)

Carry out column addition and subtraction for whole numbers and decimals.

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Numeracy Development Projects

4

AC EA AA AM AP