Maths. Using numbers to carry out calculations and solve problems.


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1 Maths Using numbers to carry out calculations and solve problems.
2 We want children to be confident manipulating numbers based on their visualisation of quantities. Which group has 30? Children often muddled the teen numbers and the multiples of ten because they are not familiar with what each group looks like.
3 23 represents 23 items (ones). To make it easier to count we group these items. Our number system is based on grouping into tens then representing the number of groups using a digit, recognised by its position in the number. Therefore children need to start seeing numbers as these tens and ones. Cubes in tens frame Beads on bar or string
4 We then start representing the group of ten using one item with practical equipment which can be manipulated tens rods and ones cubes coins
5 or pictorials lines to represent the tens rod and squares to represent the ones cubes brackets to represent the groups of beads
6 Partitioning Children need to show their understanding of numbers. Partition twodigit numbers into different combinations of tens and ones. This may include using apparatus (e.g. 23 is the same as 2 tens and 3 ones which is the same as 1 ten and 13 ones).
7 Make 32p or
8 = = = = = = = = = 56
9 They need to be able to talk about and answer questions about numbers What number has 3 tens and 5 units? How many tens are there in 67? What number is made of 3 tens and 14 units? My number has 2 tens and 24 units. What is my number?
10 Size of numbers Children need to understand how these numbers fit into our number system. They need to be able to place numbers within the number system using their knowledge of size Roughly where would 23 fit on this number line? What number would come straight after / just before 23? So what is / 23 1? Think of a number: Bigger / greater than / more than 18 Smaller / less than / fewer than 12 A number between 14 and 24 An even or an odd number for each of the above
11 Addition and subtraction strategies To enable them to add and subtract comfortably, children must have a secure understanding of: How numbers partition and recombine into tens and ones How to count on and back in ones and tens from any given number ie add one at a time, add ten at a time Numbers to recognise whether the answer is realistic should the answer be bigger or smaller? Should the ones digit be the same or different?
12 We want the children to use mental methods at this stage and start seeing how the numbers work together. We therefore start with practical equipment, move onto pictorial representation of the equipment then jottings to support their thinking.
13 Add 2 twodigit numbers within 100 (e.g ) and can demonstrate their method using concrete apparatus or pictorial representations.
14 2 bananas 32p + 32p
15 (with practical equipment then picture representations) + = = 62
16 or
17 or = = 62 Or = 62
18 Subtract mentally a twodigit number from another twodigit number when there is no regrouping required (e.g ). The pupil was able to complete a mental calculation of 4817, by partitioning 17 into 10 and 7. They then subtracted in stages from 48, stating that 48 subtract 10 is 38, 38 subtract 7 is 31. I can partition 24 into 20 and subtract 20 is 46, then subtract 4 is 42.
19 68 25 or = = 43
20 Recognise the inverse relationships between addition and subtraction and use this to check calculations and work out missing number problems (e.g. Δ 14 = 28). As a different number was missing from each calculation, the pupil demonstrated a thorough understanding of the concept.
21 The pupil was able to explain what they were doing and how they knew the following: If I know 6+4=10, I also know that 4+6=10 because you can add in any order. The pupil also knew that 60+40=100 because each digit has moved in to the tens and there is a zero in the ones.
22 Identify 1/3, ¼, ½, 2/4,¾ and knows that all parts must be equal parts of the whole.
23
24 ¼ ¼ ¼ ¼ ¾ ¼ of 12 = 3 ¾ of 12 = 9
25 Use different coins to make the same amount (e.g. pupil uses coins to make 50p in different ways; pupil can work out how many 2 coins are needed to exchange for a 20 note). How could you make 80p using only silver coins? I used 3 coins to pay for a 20p banana. What coins did I use?
26 Read the time on the clock to the nearest 15 minutes.
27 Describe properties of 2D and 3D shapes (e.g. the pupil describes a triangle: it has 3 sides, 3 vertices and 1 line of symmetry; the pupil describes a pyramid: it has 8 edges, 5 faces, 4 of which are triangles and one is a square). 2D shapes circle square rectangle triangle hexagon pentagon
28 3D shapes cube cuboid sphere pyramid prism cone
29 Properties of shapes 2D 3D vertices side corner face edge
30 Practise helps, but this does not have to be pages of written, recorded calculations. Maths is based on mental skills which are developed and maintained through constant rehearsing. We all need to have a concept and visualisation of the size of numbers to enable us to estimate and to recognise if our calculations are roughly correct. This comes from looking at and counting real things then relating to the number: How many people are in this room? How many coins are in your purse? How many strawberries are in the punnet? Can be 31? Which is more 46 or 64? Why?
31 Talking about maths, showing it practically and making drawings and jottings helps us all to embed and maintain skills and to gain a deeper understanding. Encourage your child to explain how they calculate and how they know the answer. Listen for them explaining that they counted on or back / used known number facts / make connections with previous calculation? What did you do? Why did you do that? How did you know that? How many tens did you count on? What can you tell me about that number? Why is that number bigger than that number? Could that be correct? Why? Why not?
32 Although we show the children efficient strategies to use, there is no one correct way to solve problems. Children will often develop their own methods and refine these as they become more secure to enable them to be more efficient. As long as they can show and explain what they have done, so that misconceptions, gaps and errors can be corrected, we are happy. We work with numbers up to 100, which can be managed mentally. Therefore any recording is to support the memory of where in the process the child is up to. It is perfectly acceptable, and sensible, to use fingers to keep track of counting that is how the decimal number system originated after all! Encourage your child to show this if that is what they are doing.
33 We need to be able to count on and back in different size numbers, especially 10s and 100s, to support us to carry out calculations efficiently. This comes from chanting number patterns and counting groups: Crossing 10s boundaries/multiples of 10 (10, 20, 30, 40 etc), especially going backwards, can be difficult for children so as you are walking or driving to school, recite numbers together. Try starting from different numbers and every time you see a specific item, eg a red car, change counting direction or the size of number you are chanting in. Try counting different items as you are walking along eg the number of feet you see by counting in 2s, the number of fingers by counting in 10s. Count pairs of socks to count the socks 2, 4, 6 etc Count how much money you have in 5p pieces. When counting loose change put in piles of 10p then count up.
34 Games What number am I? I am greater than 20 but less than 30, I am a multiple of 5. How many facts can you think of about the number 36? It is a 2digit number, it has 3 tens and 6 unit, it is an even number, it is a multiple of 3. Keep the score generate a series of small numbers adding them along the way  5 and 6 is 11 and 3 is 14 and 2 is 16 and 4 is 20. Use dice, playing cards, numbers seen in the street. You could set a number to reach or start at a number and subtract along the way.
35
36 Signs and symbols + add / plus / more  subtract / take away / minus / less = equals / is equal to / is the same as / balances with x times by / lots of divided by / shared with > is greater / more than (8 > 3) < is less / fewer than (3 < 8)
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