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Year 3 Block E - Securing number facts, relationships and calculating Unit 3

Objectives Children's learning outcomes are emphasised	Assessment for learning
Solve one-step and two-step problems involving numbers, money or measures, including time, choosing and carrying out appropriate calculations I know that a division problem can involve sharing or grouping	Look at this problem. 15 grapes are shared equally onto 3 plates. How many grapes are there on each plate? What calculation would you do to answer it? Draw a picture to represent the problem. Now look at this problem. How many bunches of 3 grapes can you get from 15 grapes? What calculation would you do to answer it? Draw a picture of this problem. Write your own word problem that involves sharing. Write the calculation that you need to do to solve it.
Follow a line of enquiry by deciding what information is important; make and use lists, tables and graphs to organise and interpret the information I can test examples to follow an enquiry about numbers	What is the biggest remainder you can have when you divide a number by 3? How did you collect information to answer this question? How did you record your findings? Think of a time recently when you used a list. Why was it helpful?
Identify patterns and relationships involving numbers or shapes, and use these to solve problems I can recognise and continue a pattern	What is the next calculation in this pattern? Explain how you know 853 = 800 53 853 = 700 153 853 = 600 253 How many £1 coins do you need to make £2? How many 10p coins? What is the relationship between the answers? How many 1p coins do you need to make £2?
Partition three-digit numbers into multiples of 100, 10 and 1 in different ways I can partition numbers in different ways	What number is equal to 200 110 7? Partition the number in a different way. To work out half of 34, Winston partitions it into 20 and 14 then halves each part. What answer does he get? Why do you think he partitioned 34 like this?
Read and write proper fractions (e.g. , ), interpreting the denominator as the parts of a whole and the numerator as the number of parts; identify and estimate fractions of shapes; use diagrams to compare fractions and establish equivalents I can recognise what fraction of a shape is shaded, and say and write it	Complete the shading on this diagram so that is shaded. Describe the shaded part in another way. Leah says that this rectangle is divided into thirds because it is divided into three parts. Is she right? Explain your answer. What fraction of this shape is shaded? Use a fraction wall to find a fraction that is the same size as .
Derive and recall multiplication facts for the 2, 3, 4, 5, 6 and 10 times-tables and the corresponding division facts; recognise multiples of 2, 5 or 10 up to 1000 I can use my knowledge of multiplication tables to find division facts	What multiplication fact can you use to find the answer to 28 ÷ 4? Find some division calculations that have the answer 6. How did you do this? What tips would you give to someone who cannot remember the 6 times-table? Is 354 a multiple of 10, 5 or 2? Explain how you know.
Develop and use written methods to record, support or explain addition and subtraction of two-digit and three-digit numbers I can add and subtract two-digit and three-digit numbers by writing them down	Find the sum and the difference of 164 and 136 by writing your calculations down. Explain each step. Molly drew a number line to find the answer to 43 32. What number is hidden under the card?
Use practical and informal written methods to multiply and divide two-digit numbers (e.g. 13 × 3, 50 ÷ 4); round remainders up or down, depending on the context I can multiply and divide a two-digit number by a one-digit number	Meg drew this number line. What calculation did she work out? 10 × 4 = 40 and 3 × 4 = 12. What is 13 × 4? How many 3p lollies can you buy with 45p? Show me how you worked this out. Harry saves 20p coins. He has saved £3.20. How many coins has he saved? Show how you work it out.
Find unit fractions of numbers and quantities (e.g. , , and of 12 litres) I can find fractions of numbers	Would you rather have of 30 sweets or of 40 sweets? Why? 15 grapes are shared equally onto five plates. What fraction of the grapes is on each plate?
Sustain conversation, explaining or giving reasons for their views or choices I can discuss how to solve a problem. I can explain how I solved it and why I chose that method	Explain your method for solving a problem to your friend. Compare their method with yours. Discuss what you did that was the same. Did you make any different choices? What would you do if you were solving a similar problem in the future? Why?

Learning overview

Children partition two- and three-digit numbers in different ways. For example, they continue the patterns:

72 = 70 2	853 = 800 53
72 = 60 12	853 = 700 153
72 = 50 22	853 = 600 253

They use partitioning to add and subtract two- and three-digit numbers using written methods. For example, they find the sum and the difference of 85 and 46 using expanded column methods:

An addition sum using partitioning to calculate; 85 is partitioned horizontally with 46 partitioned underneath and the total below A subtraction sum using partitioning to calculate; 85 is partitioned horizontally with 46 partitioned underneath and the total below

Children recall multiplication and division facts for the 2, 3, 4, 5, 6 and 10 times-tables. They use them to solve problems involving multiplication and division. They represent the information in the problem using images or number calculations and use these to find a solution. They work methodically, making lists of the multiplication facts they may need to solve problems such as:

Tables have 4 legs and stools have 3 legs. I see 25 legs. How many tables and stools do I see?
Pentagons have 5 sides and rectangles have 4 sides. I have 28 straws to use to make some of each shape. How many of each can I make?

Children understand that a division sentence could describe a situation involving either grouping or sharing. For example, the calculation 30 ÷ 6 = 5 could represent either:

30 children are organised into teams of 6. How many teams are there?
or:
30 crayons are put equally into six pots. How many crayons are in each pot?

Children solve a variety of division problems, some involving sharing and some involving grouping. They use the inverse operation to check answers. For example, they solve:

How many teams of four can be made from 32 children?
27 apples are arranged equally in three bowls. How many apples are in each bowl?
I have £2 in my money box. All the coins are the same. How many coins could there be? Describe all the possibilities.

Children investigate remainders in division calculations. They research the question:

What is the biggest remainder you can have when you divide a number by 3? What if you divide by 4 or by 5?

Children work as a group on this enquiry. They decide what examples they should try and how they will work. They discuss how they can record their findings so that it is easy to identify patterns. Children use their results to explain their answer to the question.

Children decide whether to round up or down to answer word problems such as:

We have 21 building block wheels. How many four-wheeled cars can we make?
Peaches come in packs of six. I want 20 peaches. How many packs do I need to buy?
How many 30 cm lengths of ribbon can I cut from a ribbon measuring 2 metres?

Children model such problems with objects or draw a sketch to help them. They discuss their answers and give reasons why they decided to round up or down.
Children use multiplication facts and place value to multiply a two-digit multiple of 10 by 2, 3, 4, 5, 6 and 10, calculating for example 70 × 3 or 4 × 60. They respond to problems such as:

Find 20 multiplied by 3.
What is of 60?
Paul has saved seven 50p coins and six 20p coins. How much is this altogether?

Children use partitioning to multiply two-digit numbers by one-digit numbers. For example, they work out 13 × 3 by finding 10 × 3 and adding 3 × 3. They record their working using informal methods:

A number line showing 0, 30, 39 along the bottom with 10 by 3 and 3 by 3 in the spaces between above

A multiplication grid with 10 and 3 across the top and 3 along the left, completed

Children find One half , One quarter , One tenth , One third or of numbers by using known multiplication and division facts. They read and write proper fractions such as Two thirds and understand the denominator as the number of parts of the whole and the numerator as the number of parts. They count in fractions along a number line from 0 to 1, for example 'zero, one fifth, two fifths, three fifths, four fifths, one'. They use such number lines to compare simple fractions and begin to find equivalent fractions.

Three number lines; 1st divided into ten parts from 0 to 1 with a half marked in the middle, 2nd divided into ten parts from 0 to 1, with 1, 2, 3 and 4 fifths marked and the 3rd is divided into ten parts from 0 to 1 each tenth marked accordingly

Children use diagrams to identify pairs of fractions that make a whole, such as One quarter and Three quarters , One fifth and Four fifths , Three tenths and Seven tenths .

Resource links to existing published ma

Springboard unit

None currently available

terial

Mathematical challenges for able pupils Key Stages 1 and 2

Activities	PDF 923KB
Activity 38 - Maisie the mouse

Intervention programmes

Supporting children with gaps in their mathematical understanding (Wave 3)

Diagnostic focus	Resource
Makes unequal groups and is unable to compare the groups	3 YR×/÷ DfES 1139-2005 (PDF 69KB)
When sharing, can sometimes make equal groups but has no strategies to deal with any left over	4 YR×/÷ DfES 1140-2005 (PDF 77KB)
Still counts in ones to find how many there are in a collection of equal groups; does not understand vocabulary, for example, 'groups of', 'multiplied by'	1 Y2×/÷ DfES 1143-2005 (PDF 73KB)
Does not link counting up in equal steps to the operation of multiplication; does not use the vocabulary associated with multiplication	2 Y2×/÷ DfES 1144-2005 (PDF 71KB)
Is not systematic when sharing into equal groups using a 'one for you' approach; does not use the language of division to describe the process	6 Y2×/÷ DfES 1148-2005 (PDF 96KB)
Does not understand that 'sets of' or 'groups of' need to be subtracted to solve the problem	7 Y2×/÷ DfES 1149-2005 (PDF 104KB)
Does not recognise when a remainder is significant in the decision about whether to round up or down	6c Y4×/÷ DfES 1157-2005 (PDF 65KB)

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