Year 2 band
Jubilee Mathematical Calculation and Progression Policy – June 2016
Band 2: Addition For Success: Star Words: : +, add, addition, more, plus, and, Key Statements • Solve problems with addition and subtraction. • Recall and use addition and subtraction facts to 20 fluently, and make, sum, total, altogether, equal to, equals, derive and use related facts up to 100. most, count on, tens, units, partition, column, • Recognise place value in two- digit numbers. Compare and order numbers to 100 using and = signs. tens boundary, score, double, near double, one • Recall bonds to 20 and bonds of tens to 100 (20 + 80 etc.) • Count in steps of 2, 3 and 5 and count in tens from any number. more, two more... ten more... one hundred • Show that addition of two numbers can be done in any order more…how many more to make…? how many (commutative) and subtraction of one number from another cannot. more is… than…? how much more is…? • Add and subtract numbers using concrete objects, pictorial
•
representations, and mentally, including: a two-digit number and ones, a two-digit number and tens, two two-digit numbers and adding three one-digit numbers. Recognise and use the inverse relationship between addition and subtraction and use this to check calculations and solve missing number problems.
Children will begin to use ‘empty number lines’ themselves starting with the larger number and counting on. First counting on in tens and ones using concrete objects and pictorial representations.
•
Then helping children to become more efficient by adding the units in one jump (by using the known fact 4 + 3 = 7).
Followed by adding the tens in one jump and the units in one jump.
Bridging through ten can help children become more efficient.
To model partitioning and place value using resources such as numicon, base 10 and arrow cards. 14 = 10 + 4 10 +10 + 4 = 24 Missing number problems e.g. 15+5= 10+ 38+ + = 100 30= 1 + +5 Demonstrate the commutative law of addition + 20 = 20 + 25 Key Resources: Mastery: Concrete objects: See Year 2 Maths Mastery Document. Counters Captain Conjecture says, Numicon ‘An odd number + an odd number = an even number’. Bead Strings Is this sometimes, always or never true? Base Ten Explain your reasoning. Number Lines Concrete resources might help pupils to explain their Everyday objects (cereal, smarties, pencils etc.) reasoning.
Jubilee Mathematical Calculation and Progression Policy – June 2016
Band 2: Subtraction Star Words: - , subtract, subtraction, take Key Statements For Success: • Solve problems with addition and subtraction. away, minus, leave, how many are left/ left • Recall and use addition and subtraction facts to 20 fluently, and derive and use related facts up to 100. over? one less, two less… ten less… • Add and subtract numbers using concrete objects, pictorial representations, and mentally, including: a two-digit number and difference, half, halve, how many fewer is… ones, a two-digit number and tens, two two-digit numbers and than…? How much less is…? count on, number adding three one-digit numbers. • Recognise and use the inverse relationship between addition and line, tens, units, partition, column, tens subtraction and use this to check calculations and solve missing number problems. boundary • • •
Count backwards in 2s, 3s, 5s, and 10s from any number. Recall and use subtraction facts to 20 fluently. Derive and use subtraction facts to 100.
Children will begin to use concrete objects and pictorial representations to support calculations. Counting back: First counting back in tens and ones using a normal number line then moving on to using an empty number line. 47-23=24
Then helping children to become more efficient by subtracting the units in one jump (by using the known fact 7 – 3 = 4).
Subtracting the tens in one jump and the units in one jump.
Bridging through ten can help children become more efficient.
Counting on: The number line should still show 0 so children can cross out the section from 0 to the smallest number. They then associate this method with ‘taking away’. Use Dienes or Numicon to aid practical subtraction. Can be learned alongside number line methods.
Key Resources: Concrete objects: Counters Numicon Bead Strings Base Ten Number Lines Everyday objects (cereal, smarties, pencils etc.)
Mastery: See Year 2 Maths Mastery Document. Dan needs 80 g of sugar for his recipe. There are 45 g left in the bag. How much more does he need to get? The temperature was 26 degrees in the morning and 11 degrees colder in the evening. What was the temperature in the evening? A tub contains 24 coins. Saj takes 5 coins. Joss takes 10 coins. How many coins are left in the tub?
Jubilee Mathematical Calculation and Progression Policy – June 2016 Band 2: Multiplication Star Words: X, groups of, lots of, times, Key Statements For Success: • Recall and use multiplication and division facts for the 2, 5 and 10 array, altogether, multiply, count, multiplied multiplication tables, including recognising odd and even numbers. • Calculate mathematical statements for multiplication and division by, multiple of, once, twice, three times… ten within the multiplication tables and write them using the multiplication (×), division (÷) and equals (=) signs. times, repeated addition, array, column, row, • Show that multiplication of two numbers can be done in any order double, sets of, equal groups, commutative (commutative) and division of one number by another cannot. •
•
Solve problems involving multiplication and division, using materials, arrays, repeated addition, mental methods, and multiplication and division facts, including problems in contexts. Pupils use a variety of language to discuss and describe multiplication.
Children will develop their understanding of multiplication and use jottings to support calculation. Numicon to show repeated addition: Repeated addition 3 times 5 is 5 + 5 + 5 = 15
or 3 lots of 5 or 5 x3
Arrays Children should be able to model a multiplication calculation using an array. This knowledge will support with the development of the grid method.
Repeated addition can be shown easily on a number line:
And on a bead string:
Commutativity Children should know that 3 x 5 has the same answer as 5 x 3. This can also be shown on the number line.
Key Resources: Concrete objects: Counters Numicon Bead Strings Base Ten Number Lines Everyday objects (cereal, smarties, pencils etc.)
Mastery: See Year 2 Maths Mastery Document. Write these addition sentences as multiplication sentences. The first one has been completed. 5+5+5+5+5=5×5 2+2+2+2+2= 2+2+2= 10 + 10 + 10 + 10 =
Jubilee Mathematical Calculation and Progression Policy – June 2016 Year 2: Division Star Words: ÷, divide, divided, division, Key Statements For Success: • Recall and use multiplication and division facts for the 2, 5 and 10 share, share equally, half, halve, quarter, multiplication tables, including recognising odd and even numbers. • Calculate mathematical statements for multiplication and division groups, groups of, array within the multiplication tables and write them using the • •
•
multiplication (×), division (÷) and equals (=) signs. Show that multiplication of two numbers can be done in any order (commutative) and division of one number by another cannot. Solve problems involving multiplication and division, using materials, arrays, repeated addition, mental methods, and multiplication and division facts, including problems in contexts. Pupils use a variety of language to discuss and describe division.
Children will develop their understanding of division and use jottings to support calculation Sharing equally 6 sweets shared between 2 people, how many do they each get?
Sharing is covered but the emphasis in Year 2 should be on grouping. Grouping or repeated subtraction There are 6 sweets, how many people can have 2 sweets each?
Arrays Children should be able to model a division calculation using an array: This represents 12÷3, posed as ‘how many groups of 3 are in 12? Pupils should also show that the same array can represent 12÷4=3 if grouped horizontally. Represent arrays in books using dots.
Repeated subtraction using a number line or bead bar: 12 ÷ 3 = 4
When drawing their own blank number lines they could be vertical. Using symbols to stand for unknown numbers to complete equations using inverse operations ÷ 2 = 4 20 ÷ = 4 ÷=4 Key Resources: Mastery: See Year 2 Maths Mastery Document. Concrete objects: Two friends share 12 sweets equally between them. How Counters many do they each get? Write this as a division number Numicon sentence. Make up two more sharing stories like this one. Bead Strings Chocolate biscuits come in packs (groups) of 5. Sally wants Base Ten to buy 20 biscuits in total. How many packs will she need to Number Lines buy? Write this as a division number sentence. Everyday objects (cereal, smarties, pencils etc.) Make up two more grouping stories like this one.
Jubilee Mathematical Calculation and Progression Policy – June 2016
Band 2: Addition For Success: Star Words: : +, add, addition, more, plus, and, Key Statements • Solve problems with addition and subtraction. • Recall and use addition and subtraction facts to 20 fluently, and make, sum, total, altogether, equal to, equals, derive and use related facts up to 100. most, count on, tens, units, partition, column, • Recognise place value in two- digit numbers. Compare and order numbers to 100 using and = signs. tens boundary, score, double, near double, one • Recall bonds to 20 and bonds of tens to 100 (20 + 80 etc.) • Count in steps of 2, 3 and 5 and count in tens from any number. more, two more... ten more... one hundred • Show that addition of two numbers can be done in any order more…how many more to make…? how many (commutative) and subtraction of one number from another cannot. more is… than…? how much more is…? • Add and subtract numbers using concrete objects, pictorial
•
representations, and mentally, including: a two-digit number and ones, a two-digit number and tens, two two-digit numbers and adding three one-digit numbers. Recognise and use the inverse relationship between addition and subtraction and use this to check calculations and solve missing number problems.
Children will begin to use ‘empty number lines’ themselves starting with the larger number and counting on. First counting on in tens and ones using concrete objects and pictorial representations.
•
Then helping children to become more efficient by adding the units in one jump (by using the known fact 4 + 3 = 7).
Followed by adding the tens in one jump and the units in one jump.
Bridging through ten can help children become more efficient.
To model partitioning and place value using resources such as numicon, base 10 and arrow cards. 14 = 10 + 4 10 +10 + 4 = 24 Missing number problems e.g. 15+5= 10+ 38+ + = 100 30= 1 + +5 Demonstrate the commutative law of addition + 20 = 20 + 25 Key Resources: Mastery: Concrete objects: See Year 2 Maths Mastery Document. Counters Captain Conjecture says, Numicon ‘An odd number + an odd number = an even number’. Bead Strings Is this sometimes, always or never true? Base Ten Explain your reasoning. Number Lines Concrete resources might help pupils to explain their Everyday objects (cereal, smarties, pencils etc.) reasoning.
Jubilee Mathematical Calculation and Progression Policy – June 2016
Band 2: Subtraction Star Words: - , subtract, subtraction, take Key Statements For Success: • Solve problems with addition and subtraction. away, minus, leave, how many are left/ left • Recall and use addition and subtraction facts to 20 fluently, and derive and use related facts up to 100. over? one less, two less… ten less… • Add and subtract numbers using concrete objects, pictorial representations, and mentally, including: a two-digit number and difference, half, halve, how many fewer is… ones, a two-digit number and tens, two two-digit numbers and than…? How much less is…? count on, number adding three one-digit numbers. • Recognise and use the inverse relationship between addition and line, tens, units, partition, column, tens subtraction and use this to check calculations and solve missing number problems. boundary • • •
Count backwards in 2s, 3s, 5s, and 10s from any number. Recall and use subtraction facts to 20 fluently. Derive and use subtraction facts to 100.
Children will begin to use concrete objects and pictorial representations to support calculations. Counting back: First counting back in tens and ones using a normal number line then moving on to using an empty number line. 47-23=24
Then helping children to become more efficient by subtracting the units in one jump (by using the known fact 7 – 3 = 4).
Subtracting the tens in one jump and the units in one jump.
Bridging through ten can help children become more efficient.
Counting on: The number line should still show 0 so children can cross out the section from 0 to the smallest number. They then associate this method with ‘taking away’. Use Dienes or Numicon to aid practical subtraction. Can be learned alongside number line methods.
Key Resources: Concrete objects: Counters Numicon Bead Strings Base Ten Number Lines Everyday objects (cereal, smarties, pencils etc.)
Mastery: See Year 2 Maths Mastery Document. Dan needs 80 g of sugar for his recipe. There are 45 g left in the bag. How much more does he need to get? The temperature was 26 degrees in the morning and 11 degrees colder in the evening. What was the temperature in the evening? A tub contains 24 coins. Saj takes 5 coins. Joss takes 10 coins. How many coins are left in the tub?
Jubilee Mathematical Calculation and Progression Policy – June 2016 Band 2: Multiplication Star Words: X, groups of, lots of, times, Key Statements For Success: • Recall and use multiplication and division facts for the 2, 5 and 10 array, altogether, multiply, count, multiplied multiplication tables, including recognising odd and even numbers. • Calculate mathematical statements for multiplication and division by, multiple of, once, twice, three times… ten within the multiplication tables and write them using the multiplication (×), division (÷) and equals (=) signs. times, repeated addition, array, column, row, • Show that multiplication of two numbers can be done in any order double, sets of, equal groups, commutative (commutative) and division of one number by another cannot. •
•
Solve problems involving multiplication and division, using materials, arrays, repeated addition, mental methods, and multiplication and division facts, including problems in contexts. Pupils use a variety of language to discuss and describe multiplication.
Children will develop their understanding of multiplication and use jottings to support calculation. Numicon to show repeated addition: Repeated addition 3 times 5 is 5 + 5 + 5 = 15
or 3 lots of 5 or 5 x3
Arrays Children should be able to model a multiplication calculation using an array. This knowledge will support with the development of the grid method.
Repeated addition can be shown easily on a number line:
And on a bead string:
Commutativity Children should know that 3 x 5 has the same answer as 5 x 3. This can also be shown on the number line.
Key Resources: Concrete objects: Counters Numicon Bead Strings Base Ten Number Lines Everyday objects (cereal, smarties, pencils etc.)
Mastery: See Year 2 Maths Mastery Document. Write these addition sentences as multiplication sentences. The first one has been completed. 5+5+5+5+5=5×5 2+2+2+2+2= 2+2+2= 10 + 10 + 10 + 10 =
Jubilee Mathematical Calculation and Progression Policy – June 2016 Year 2: Division Star Words: ÷, divide, divided, division, Key Statements For Success: • Recall and use multiplication and division facts for the 2, 5 and 10 share, share equally, half, halve, quarter, multiplication tables, including recognising odd and even numbers. • Calculate mathematical statements for multiplication and division groups, groups of, array within the multiplication tables and write them using the • •
•
multiplication (×), division (÷) and equals (=) signs. Show that multiplication of two numbers can be done in any order (commutative) and division of one number by another cannot. Solve problems involving multiplication and division, using materials, arrays, repeated addition, mental methods, and multiplication and division facts, including problems in contexts. Pupils use a variety of language to discuss and describe division.
Children will develop their understanding of division and use jottings to support calculation Sharing equally 6 sweets shared between 2 people, how many do they each get?
Sharing is covered but the emphasis in Year 2 should be on grouping. Grouping or repeated subtraction There are 6 sweets, how many people can have 2 sweets each?
Arrays Children should be able to model a division calculation using an array: This represents 12÷3, posed as ‘how many groups of 3 are in 12? Pupils should also show that the same array can represent 12÷4=3 if grouped horizontally. Represent arrays in books using dots.
Repeated subtraction using a number line or bead bar: 12 ÷ 3 = 4
When drawing their own blank number lines they could be vertical. Using symbols to stand for unknown numbers to complete equations using inverse operations ÷ 2 = 4 20 ÷ = 4 ÷=4 Key Resources: Mastery: See Year 2 Maths Mastery Document. Concrete objects: Two friends share 12 sweets equally between them. How Counters many do they each get? Write this as a division number Numicon sentence. Make up two more sharing stories like this one. Bead Strings Chocolate biscuits come in packs (groups) of 5. Sally wants Base Ten to buy 20 biscuits in total. How many packs will she need to Number Lines buy? Write this as a division number sentence. Everyday objects (cereal, smarties, pencils etc.) Make up two more grouping stories like this one.
Jubilee Mathematical Calculation and Progression Policy – June 2016
