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In this learning overview are suggested assessment opportunities linked to the assessment focuses within the Assessing Pupils’ Progress (APP) guidelines. As you plan your teaching for this unit, draw on these suggestions and on 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:
Children create sequences by counting on and back from any start number in equal steps such as 19 or 25. They record sequences on number lines. They describe and explain the patterns in a sequence. For example, when subtracting 19 to generate the sequence 285, 266, 247, ..., they explain that subtracting 19 is equivalent to subtracting 20 then adding 1, so the tens digit gets smaller by 2 each time and the units digit increases by 1. They use patterns to predict the next number (228) and explore what happens when the hundreds boundary is crossed.
Children explore sequences using the ITP 'Twenty cards' or the Flash program 'Counter'.
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They identify the rule for a given sequence. They use this to continue the sequence or identify missing numbers, e.g. they find the missing numbers in the sequence 89, 
, 71, 62, , recognising that the rule is 'subtract 9'. They explore sequences involving negative numbers using a number line. For example, they continue the sequence –35, –31, –27, ... by recognising that the rule is 'add 4'.
Assessment focus: Ma1, Reasoning
Look for evidence of children identifying patterns. For example, as they work with sequences that increase or decrease in steps of a regular size, they might work out that the difference is always 5. Look for children who are beginning to predict whether particular numbers will be in the sequence or not. For example, they might notice that each of the numbers in a sequence is 2 more than a multiple of 5, and use this to reason that 47 will be in the sequence.
Children read and write large whole numbers. For example, they work in pairs using a set of cards containing six- and seven-digit numbers: one child takes a card and reads the number in words; their partner keys the number they hear into a calculator; they check that the calculator display and the number card match. Children recognise the value of each digit and they use this to compare and order numbers, for example, they explain which has the greater value, the 5 in 3215067 or the 5 in 856207. They compare two numbers and explain which is bigger and how they know. They solve problems such as:
Use a single subtraction to change 207070 to 205070 on your calculator.
Children use calculators (possibly by setting a constant function) or the ITP 'Moving digits' to explore the effect of repeatedly multiplying/dividing numbers by 10.
They compare the effect of multiplying a number by 1000 with that of multiplying the number by 10 then 10 then 10 again (and similarly for division). They use digit cards and a place value grid to practise multiplying and dividing whole numbers by 10, 100 or 1000 and answer questions such as:
32 500 ÷
= 325
How many £10 notes would you need to make £12 000?
Assessment focus: Ma2, Numbers and the number system
Look for evidence of children understanding place value in four-digit numbers, and those who can begin to say what each digit represents in a five- or six-digit number. Look for children who can use their knowledge of place value to explain the effect of multiplying and dividing whole numbers by 10. Identify children who can extend this understanding to multiplying and dividing whole numbers by 100 and 1000.
Children rehearse multiplication facts and use these to derive division facts, to find factors of two-digit numbers and to multiply multiples of 10 and 100, e.g. 40 × 50. They use and discuss mental strategies for special cases of harder types of calculations, for example to work out 274 
96,
8006 - 2993, 35 × 11, 72 ÷ 3, 50 × 900. They use factors to work out a calculation such as 16 × 6 by thinking of it as 16 × 2 × 3. They record their methods using diagrams (such as number lines) or jottings, and explain their methods to each other. They compare alternative methods for the same calculation and discuss any merits and disadvantages. They record the method they use to solve problems such as:
How many 25p fruit bars can I buy with £5?
Find three consecutive numbers that total 171.
Assessment focus: Ma2, mental methods
Look for evidence of the mental calculations that children perform, and the strategies they choose to use. Look for children who can add and subtract two-digit numbers mentally and can apply this to calculations with larger numbers. Look for children who can recall multiplication facts, noting which facts they can remember, and for those who can use their knowledge of multiplication facts and place value to solve calculations involving multiples of 10, e.g. children who use knowledge of 5 × 7 to solve 50 × 7 and 50 × 70.
Children consolidate written methods for addition and subtraction. They explain how they work out calculations, showing understanding of the place value that underpins written methods. They continue to move towards more efficient recording, from expanded methods to compact layouts.
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Addition examples:
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Carry digits are recorded below the line, using the words 'carry ten' or 'carry one hundred', not 'carry one'. |
Subtraction, illustrating 'difference', is complementary addition or counting up:
The decomposition method, illustrating the 'take away' model of subtraction, begins like this:
Children use written methods to solve problems and puzzles such as
| Choose any four numbers from the grid and add them. Find as many ways as possible of making 1000. |  |
Place the digits 0 to 9 to make this calculation correct: - =
Two numbers have a total of 1000 and a difference of 246. What are the two numbers?
| Objectives Children's learning outcomes are emphasised |
Assessment for learning |
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Tell me how you solved this problem. |
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Create a sequence that includes the number –5. Describe your sequence to the class. |
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What is the value of the 7 in 3 274 105? |
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Look at these calculations with two-digit decimals. Tell me how you could work them out in your head. |
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[Point to a 'carry digit' 1.] What is the value of this 1? Why is it there? |
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If someone had forgotten the 8 times-table, what tips would you give them to help them to work it out? |
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Here are four number cards.
Which two number cards are factors of 42? Put a ring around the numbers which are factors of 30. 4 5 6 20 60 90 How can you use factors to multiply 15 by 12? |
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This calculator display shows 0.1. Tell me what will happen when I
multiply by 100. What will the display show? What number is ten times
as big as 0.01? How do you know that it is ten times 0.01? |
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Which of these subtractions can you do without writing anything down? Why is it possible to solve this one mentally? What clues did you look for? What is the answer to the one that can be solved mentally? How did you find the difference? Talk me through your method. [If the child explains a method of counting backwards, ask:] Is it possible to count up as well? Why will this give the same result? Which is easier? If 2003 is the answer to a similar question, what could the question be? |
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Roughly, what will the answer to this calculation be? How do you know that this calculation is probably right? Could you check it a different way? |
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These cards describe the steps in adding £4.65, 98p and £3.07. Arrange the cards in order. Write a list of the steps you would take to solve this problem: A pack of plums costs 68p. Mark bought three packs of plums. How much change did he get from a £5 note? Explain to the class why you solved the problem in that way. |
| Activities | PDF 1MB |
| Activity 60 - Three digits | |
| Activity 54 - Joins | |
| Activity 65 - Age old problems | |
| Activity 61 - Make five numbers | |
| Activity 66 - Zids and Zods | |
| Activity 62 Maze |
| Objectives for Springboard intervention unit | Springboard unit |
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Read, write and order whole numbers to at least 1000 |
Springboard 5 Unit 2 (PDF 305KB) |
| Springboard 5 Unit 2 supplementary (PDF 86KB) | |
| Multiply and divide whole numbers by 10 and 100 and understand the effect | Springboard 5 Unit 6 (PDF 305KB) |
| Springboard 5 Unit 6 supplementary (PDF 57KB) | |
| Calculate a difference mentally by counting up from the smaller to the larger number | Springboard 5 Unit 7 (PDF 305KB) |
| Springboard 5 Unit 7 supplementary (PDF 77KB) | |
| Develop and refine written methods for subtraction, building on mental methods. Reinforce the fact that subtraction is the inverse of addition |
Springboard 5 Unit 8 (PDF 245KB) |
| Springboard 5 Unit 8a Part 1 supplementary (PDF 77KB) | |
| Springboard 5 Unit 8a Part 2 supplementary (PDF 75KB) | |
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Know the three- and four-times tables |
Springboard 5 Unit 9 (PDF 269KB) |
| Springboard 5 Unit 9 supplementary (PDF 110KB) |
| Diagnostic focus | Resource |
| None currently available |
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, –9, –5, –1, 
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