Progress from objects/ Numicon to bead string to number track to number line.

Transcription

1 Year 1 Read, write and interpret mathematical statements involving subtraction (-) and equals (=) signs Vocabulary: Number bonds, number line Inverse Half, halve Equals, is the same as (including equals sign) Difference between Subtract, take away, minus How many fewer is than..?, how much less is..? Number Zero, one, two, three to twenty, and beyond None Count (on/up/to/from/down ) Before, after Given a number, identify one less Progress from objects/ Numicon to bead string to number track to number line. Count back in ones from any given number Children need to be able to confidently count back from any given number. Counting practice needed. Use mental oral starters. Progression: Given a number, identify one less Count back on ones from any given number Read, write and interpret mathematical statements involving subtraction (-) and the equals (=) sign -concrete objects -number track -marked number line -empty number line (only if children are secure) Counting on to find the diiference. Page 1 of 19

2 More, less, many, few, fewer, least, fewest, smallest, greater, lesser Equal to, the same as Odd, even Pair Units, ones, tens One less, two less/ three less/ Ten less Digit Numeral Figure(s) Value Between, halfway between Above, below Read, write and interpret mathematical statements involving subtraction (-) and the equals (=) sign Make sure that children understand that subtraction cannot be done in any order. Revision from foundation stage: Initially use the number track to count back for subtraction Subtract onedigit and twodigit numbers within 20, including zero Solve missing number problems eg 20 - = 15 Page 2 of 19

3 Progress onto marked number line: Children must be confident using a marked number line before moving onto an empty number line (see year two guidance) Page 3 of 19

4 Counting onto find the difference (complementary addition). The use of models is extremely important. This should only be used for small differences. Count up from the smallest number to find the difference. Use resources such as Numicon, cubes, bead strings, number tracks and number lines. Solve missing number problems eg 20 - = 15 Year 2 Subtract numbers using concrete objects, pictorial representations, and mentally, including: A two digit number and ones Subtract any single digit number to or from a multiple of 10. Progression: Subtract any single digit number to or from a multiple of 10 (80 7). Subtract a single-digit number to or Page 4 of 19

5 A two digit number and tens Two two-digit numbers Vocabulary: Number bonds, number line Inverse Half, halve Equals, is the same as (including equals sign) Difference between Subtract, take away, minus, find the difference, How many fewer is than..?, how much less is..? Hundred less, counting back, Number Zero, one, two, three to twenty, and beyond None Count (on/up/to/from/down ) Before, after More, less, many, few, fewer, least, fewest, Subtract a single-digit number from a two-digit number, including crossing the tens boundary Marked number line Progressing to counting back using an empty number line (within 100) in ones. from a twodigit number, including crossing the tens boundary (57 3 progressing to 52 7) marked number line progressing to empty number line. Subtract a multiple of 10 from any 2- digit number ( , 72 50) Subtract two 2- digit numbers (68 35) Counting on to find differences. Further develop with subtraction Page 5 of 19

6 smallest, greater, lesser Equal to, the same as Odd, even Pair Units, ones, tens One less, two less/ three less/ Ten less Digit Numeral Figure(s) Value Between, halfway between Above, below Subtract a multiple of 10 from any 2-digit number Subtract two 2-digit numbers that bridges 100. Subtraction using partitioning on an empty number line (used marked number line initially if children need to): Page 6 of 19

7 Encourage children to begin to use more efficient jumps: Counting on to find differences children may be more successful at this than taking away on the number line. Consolidate complementary addition by counting on from the smallest number to the largest (small differences). Page 7 of 19

8 If children are confident, further develop this method Further develop subtraction with numbers that bridge 100 Year 3 Subtract numbers with up to three digits, using formal written methods of columnar subtraction Vocabulary: Expanded written method, partition, Ensure children are confident in previous year s guidance before moving on. Develop the use of the empty number line Bridging 100 Progression: Develop the use of the empty number line -bridging 100 -making more efficient jumps -extend onto larger numbers by counting back -find the difference by counting on. Page 8 of 19

9 Column subtraction, Number bonds, number line Inverse Half, halve Equals, is the same as (including equals sign) Difference between Subtract, take away, minus, find the difference, How many fewer is than..?, how much less is..? Hundred less, counting back, Number Zero, one, two, three to twenty, and beyond None, efficient jumps, Count (on/up/to/from/down ) Before, after More, less, many, few, fewer, least, fewest, smallest, greater, lesser Equal to, the same as Odd, even Pair, Units, ones, tens One less, two less/ three less/ Ten less Digit Making more efficient jumps Extend onto larger numbers by counting back Counting on to find the difference -Expanded written method leading to formal written method two digits (no decomposition ) -Expanded written method leading to formal written method two digits (with decomposition ) -Expanded written method numbers over 100. Page 9 of 19

10 Numeral Figure(s) Value Between, halfway between Above, below, exchange, decomposition, Expanded written method leading to formal written method 2 digit numbers (no decomposition) Introduce the expanded written method showing the children the calculation written horizontally and then laid out in columns vertically. Use two-digit numbers when initially introducing this method. This will lead to the formal written method: Page 10 of 19

11 Expanded written method where exchange/ decomposition is required. Use dienes to consolidate children s understanding of this. Only move onto the formal written method when children can confidently use the expanded column method without error. Page 11 of 19

12 Formal written method using numbers over 100. Only if children are confident. It may be necessary to return to the expanded written method first. If at any time the children are making significant errors, return to the previous stage in calculation. Page 12 of 19

13 Year 4 Subtract numbers with up to 4 digits using the formal written methods of columnar addition and subtraction where appropriate Vocabulary: Expanded written method, partition, Column subtraction, Number bonds, number line Inverse Half, halve Equals, is the same as (including equals sign) Difference between Subtract, take away, minus, find the difference, How many fewer is than..?, how much less is..? Hundred less, Continue to use empty number lines to subtract three and four-digit numbers. Revisit the expanded column method first. Extend to the formal method, including decomposition. Subtracting 3-digit numbers from 3 digit numbers. Consider using and instead of + if this confuses the children. Progression: Continue to use the empty number line to subtract three and four-digit numbers. Revisit expanded written method. Extend onto formal written method, including decomposition. Subtracting 3- digit from 3- digit numbers expanded method leading to formal written method. Extend onto 4- digit numbers and decimal numbers. Page 13 of 19

14 counting back, Number Zero, one, two, three to twenty, and beyond None, efficient jumps, Count (on/up/to/from/down ) Before, after More, less, many, few, fewer, least, fewest, smallest, greater, lesser Equal to, the same as Odd, even Pair, Units, ones, tens One less, two less/ three less/ Ten less Digit Numeral Figure(s) Value Between, halfway between Above, below, exchange, decomposition, decimial numbers, Extend onto 4-digit numbers and decimal numbers. Only if the children are confident. Use a number line where appropriate with money. Page 14 of 19

15 Page 15 of 19

16 Year 5 Subtract whole numbers with more than 4 digits, including using formal written method (columnar subtraction) Vocabulary: Expanded written method, partition, Column subtraction, Number bonds, number line Inverse Half, halve Equals, is the same as (including equals sign) Difference between Subtract, take away, minus, find the difference, How many fewer is than..?, how much less is..? Hundred less, counting back, Number Zero, one, two, three to twenty, and beyond Continue to use empty number lines with larger numbers and decimals Consider appropriate numbers i.e. when finding change it may be easier to use the number line. Develop the formal written method for subtraction with three or four-digit numbers Return to the expanded method if necessary (use year 4 guidance). This leads to the formal written method. Take care. There is potential for error in this example and children must have a secure understanding of place value. Progression: Continue to use empty number lines with larger numbers and decimals as appropriate. Develop formal written method for subtraction with three or four digit numbers. (discuss where the number line might be more appropriate) Extend onto larger numbers, including decimals. Page 16 of 19

17 None, efficient jumps, Count (on/up/to/from/down ) Before, after More, less, many, few, fewer, least, fewest, smallest, greater, lesser Equal to, the same as Odd, even Pair, Units, ones, tens One less, two less/ three less/ Ten less Digit Numeral Figure(s) Value Between, halfway between Above, below, exchange, decomposition, decimial numbers, Ensure that discussions are had about the efficiency of the method would an empty number line be a more efficient method with these numbers? Extend onto larger numbers, including decimals. Only if the children are confident. Introduce subtraction of decimals, initially in the context of money and measures Ensure that the decimal points line up. Page 17 of 19

18 Year 6 Vocabulary: Expanded written method, partition, Column subtraction, Number bonds, number line Inverse Half, halve Equals, is the same as (including equals sign) Difference between Subtract, take away, minus, find the difference, How many fewer is than..?, how much less is..? Hundred less, counting back, Number Zero, one, two, three to twenty, and beyond None, efficient jumps, Count (on/up/to/from/down ) Before, after More, less, many, few, fewer, least, fewest, No objectives have been included in the programmes of study explicitly related to written methods for subtraction in Y6. However, there is an expectation that children will continue to practice and use the formal written method for larger numbers and decimals and use these methods when solving problems, when appropriate (see previous years guidance for methods). Our aim is that by the end of Y6 children use mental methods (with jottings) when appropriate, but for calculations that they cannot do in their heads, they use an efficient formal written method accurately and with confidence. Page 18 of 19

19 smallest, greater, lesser Equal to, the same as Odd, even Pair, Units, ones, tens One less, two less/ three less/ Ten less Digit Numeral Figure(s) Value Between, halfway between Above, below, exchange, decomposition, decimial numbers, Page 19 of 19