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# Ma2 Number

## Number sequences

At the top of the page are the instructions 'Work out these missing numbers'. The first line reads '23 26 29 32 35 38 and the 32 and 38 have been handwritten. The second line reads '33 32 31 30 29 28' and the 29 and 28 have been handwritten. The third line reads '18 14 10 6 2 minus 2' and the 6 and 2 have been handwritten. All the numbers in between two digits have been written lightly so the complete line reads '18 17 16 15 14 13 12 11 10 9 8 7 6 5 4 3 2 1 0 minus 1 minus 2'. The fourth line reads '6 12 18 24 30 36' and the 24 and 36 have been handwritten. Again all the numbers in between the digits have been filled in lightly so the complete line reads '6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36'.

### Teacher’s notes

• Counts forward and backwards in small steps to find missing numbers in sequences.
• Uses jottings to support counting on or back in larger steps.
• Recognises negative numbers, counting backwards in ones, from 2 to 2.

### Next steps

Find the rule for the sequence, for example, ‘adding three each time’, then calculate with fewer jottings.

## Inverse operations

### Teacher’s notes

• Finds the missing numbers in two-digit addition sentences.
• When modelled, shows the related subtraction sentence, ordering the numbers correctly.
• Independently applies knowledge to final subtraction calculation.

## Fraction dominoes

Each card has a line drawn down the middle. On the left hand side of each card is a diagram representing a fraction and on the right hand side is a fraction which does not match the diagram. The cards have been arranged in a rectangle so that each fraction lies alongside its matching diagram. Starting with the card in the the top left hand corner and moving clockwise, the first card's diagram is of a rectangle divided into five equal parts. Two of the five parts have been coloured in. The written fraction is of a half. The next card's diagram is of a square divided into four, with two of the parts coloured in. The written fraction is of three quarters. The next card's diagram is of a circle divided into four, with three of the parts coloured in. The written fraction is a half. The next card's diagram is of a parallelogram, divided into two, with one part coloured in. The written fraction is a quarter. The next card's diagram is of a rectangle, divided into eight, with two parts coloured in. The written fraction is a half. The final card's diagram is of a rectangle, divided into twelve, with six parts coloured in. The written fraction is of two fifths, which matches up with the diagam of the first card.

### Teacher’s notes

• Recognises halves and quarters of given shapes, including those divided into more than four squares.
• Independently matches a fraction to a diagram, in a game of dominoes.
• Creates his own domino fraction game, using 1/2, 1/4, 3/4 and 2/5.

### Next steps

Recognise 3/4 represented in different ways, for example when a rectangle is showing 6/8.

## What the teacher knows about David’s attainment in Ma2

David can count sets of objects reliably and is beginning to understand the place value of each digit in a three-digit number. He can recognise and continue number sequences which increase in steps of equal size, forwards and backwards, for example 12, 18, 24, 30, 36. He recognises odd and even numbers, and multiples of 2, 5 and 10. He can multiply two-digit whole numbers by 10 and single digits by 100. David represents multiplication as an array of dots and understands it as repeated addition.

He understands simple fractions such as 1/2, 1/4, 1/3, and can find those fractions of shapes. When a shape is divided into small squares or rectangles, he is able to find half and a quarter; however, he is unable to find 3/4 of a shape that is split up into 8 or 12 parts. David can solve simple problems involving fractions; he can find small unitary fractions of whole numbers, using diagrams or apparatus to help him, for example 1/3 of 9 = 3, 1/5 of 10 = 2.

He understands that subtraction is the inverse of addition and sometimes uses this knowledge to check his work. Mentally, he can double and halve two-digit numbers, knowing that halving is the inverse of doubling. He also demonstrates knowledge of inverse in multiplication and division, for example 3 × 7 = 21 so 21 ÷ 7 = 3.

Using mental recall of addition and subtraction facts to 10, he adds and subtracts two-digit numbers, for example 89 + 11 or 35 + 65.

He uses knowledge of place value when adding and subtracting multiples of 10: for example, he uses 5 – 3 to work out 50 – 30. David knows multiplication facts for the ×2 and ×10 tables and can find the related division facts with support. He multiplies by 3, 4 and 5, but does not yet have a quick recall of these tables facts.

He solves problems involving money and measures, using a number line and/or jottings to support his thinking. He can highlight the key words in a problem and uses this knowledge to select the appropriate operation. His preferred method for solving multiplication problems is repeated addition. He is beginning to solve division problems with support.

David consistently uses informal jottings such as a number line, where he jumps in large steps using multiples of 10 as ‘stepping stones’. He divides small numbers by sharing, using apparatus or marks on a page, and is beginning to divide two-digit numbers by 2, mentally. His written method for addition and subtraction of two-digit numbers involves partitioning the tens and units.