Year 3 Block E – Securing number facts, relationships and calculating
- 1 Year 3 Block E – Securing number facts, relationships and calculating
- 2 Building on previous learning
- 3 Key aspects of learning
- 4 Unit 1
- 5 Unit 2
- 6 Unit 3
- 7 Unit 1 - ICT Resources
- 8 Unit 2 - ICT Resources
- 9 Unit 3 - ICT Resources
- 10 Speaking and listening
- 11 Vocabulary
- 12 Opportunities to apply mathematics in science
Unit 3
Learning overview
In this learning overview are suggested assessment opportunities linked to the assessment focuses within the Assessing Pupils' Progress (APP): Assessment guidelines. As you plan your teaching for this unit, draw on these suggestions and alternative methods to help you to gather evidence of attainment or to identify barriers to progress that will inform your planning to meet the needs of particular groups of children. When you make a periodic assessment of children's learning, this accumulating evidence will help you to determine the level at which they are working.
To gather evidence related to the three Ma1 assessment focuses (problem solving, reasoning and communicating), it is important to give children space and time to develop their own approaches and strategies throughout the mathematics curriculum, as well as through the application of skills across the curriculum.
In this unit the illustrated assessment focuses are:
- Ma1, Communicating
- Ma2, Numbers and the number system
- Ma2, Operations and relationships between them
- Ma2, Fractions and decimals
Children partition two and three-digit numbers in different ways. For example, they continue the patterns:
72 = 70 + 2
72 = 60 + 12
72 = 50 + 22
853 = 800 + 53
853 = 700 + 153
853 = 600 + 253
Assessment focus: Ma2, Numbers and the number system
Look for evidence of children demonstrating their knowledge of numbers, using a range of models and images. Look for children using base-10 materials, place-value cards and number lines to demonstrate how two and three-digit numbers can be partitioned in different ways. Look for children who can use more than one type of practical material to demonstrate their understanding.
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:
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?
Assessment focus: Ma1, Communicating
Look for evidence of the ways in which children represent their work, for example, using pictures, diagrams, symbols and number sentences. Look out for children who use lists and tables to collect results and for children who are beginning to order results to reveal patterns and help them check that they have all possible results.
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.
Assessment focus: Ma2, Operations and relationships between them
Look for evidence that children understand division as sharing and as grouping. Look for children making a connection between grouping and the multiplication facts they know.
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 1/3 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:
| X | 10 | 3 |
| 3 | 30 | 9 |
30 + 9 = 39
Children find 1/2, 1/4, 1/10, 1/3 or 1/5 of numbers by using known multiplication and division facts. They read and write proper fractions such as 2/3 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.
Children use diagrams to identify pairs of fractions that make a whole, such as 1/4 and 3/4, 1/5 and 4/5, 3/10 and 7/10.
Assessment focus: Ma2, Fractions and decimals
Look for evidence of children using a wider range of unit fractions and some fractions that are several parts of a whole. Look for those children who recognise and record fractions such as 3/4 or 2/3 in a range of contexts. They might recognise, for example, that a container is about 3/4 full or that by the end of Thursday they are 4/5 of the way through the school week.
| 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. |
|
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? |
|
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 |
|
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. |
|
Read and write proper fractions (e.g. 3/7, 9/10), 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 1/2 is shaded. Describe the shaded part in another way. |
|
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? |
|
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. |
|
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? |
|
Find unit fractions of numbers and quantities (e.g. 1/2, 1/3, 1/4 and 1/6 of 12 litres) I can find fractions of numbers |
Would you rather have 1/3 of 30 sweets or 1/5 of 40 sweets? Why? |
|
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? |
Resource links to existing published material
| Activities | Resources |
|---|---|
| Activity 38 – Maisie the mouse | Puzzles and problems for Year 3 and 4 |
| Springboard unit | Resources |
|---|---|
| None currently available | |
| Diagnostic focus | Resources |
|---|---|
| Makes unequal groups and is unable to compare the groups | 3 YR ×/÷ Wave 3 (3 YR ×/÷) Teaching activities to help children make and compare equal groups |
| When sharing, can sometimes make equal groups but has no strategies to deal with any left over | 4 YR ×/÷ Wave 3 (4 YR ×/÷) Teaching activities to help children understand making equal groups |
| 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 ×/÷ Wave 3 (1 Y2 ×/÷) Teaching activities to help children count in equal groups |
| Does not link counting up in equal steps to the operation of multiplication; does not use the vocabulary associated with multiplication | 2 Y2 ×/÷ Wave 3 (2 Y2 ×/÷) Teaching activities to help children understand multiplication |
| 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 ×/÷ Wave 3 (6 Y2 ×/÷) Teaching activities to help children share objects systematically |
| Does not understand that 'sets of' or 'groups of' need to be subtracted to solve the problem | 7 Y2 ×/÷ Wave 3 (7 Y2 ×/÷) Teaching activities to help children understand division as repeated subtraction |
| Does not recognise when a remainder is significant in the decision about whether to round up or down | 6c Y4 ×/÷ Wave 3 (6c Y4 ×/÷) Teaching activities to help children round up or down after division |
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- Next:Unit 1 - ICT Resources
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