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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 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 read and write whole numbers to at least 1000 in figures and words. They identify the position of these numbers on a number line using their understanding of place value to locate the hundreds and tens numbers and to explain their relationships. They know the ordinal numbers to at least 100 and use them in practical contexts, such as describing the position of a team in a league table or the order of quantities or numbers according to size.
Children count on and back in steps of 1, 2, 3, 4, 5, 6 and 10 from zero and then from any given number. They use these sequences to count on or back in steps of 10, 20, 30, 40, 50, 60 or 100. They use their counting skills to answer questions such as:
If I keep subtracting 6 from 49, what is the smallest number I will get?
They recognise the relationships between counting in: 2s and 4s; 3s and 6s; 5s and 10s. Children count a large collection of objects by grouping them, for example into fives, tens or twenties. They recognise how this helps them to find the total number of objects systematically and accurately and gives a method to use to check the result.
Children partition two- and three-digit numbers and use their knowledge of place value to compare and order numbers with up to three digits. They use the vocabulary and symbols associated with comparing and ordering of numbers. They compare two 3-digit numbers, such as 456 and 465, and read and record that 465<456 or 456<465. They give reasons for their choice. Children answer questions such as: What multiples of 10 lie between 256 and 283? In order to identify missing numbers, they pose questions of their own such as:
Does it lie between 50 and 80?
If I count in threes from zero, will it be in my sequence of numbers?
Assessment focus: Ma2, Numbers and the number system
As they become familiar with two- and three-digit numbers, look for those children who can explain the place value of each digit. Look for children who use different models of the number system to represent numbers, for example, using arrow cards to represent numbers or locating numbers quickly on a number line. Look for children who, when given a number, know the multiples of ten between which it lies on the number line and which multiple is nearest. Look for children who know whether a two-digit number is closer to 0 or to 100.
Children say and record numbers that are 1, 10 or 100 more than or less than any number to 1000. They use their knowledge and counting strategies to add or subtract multiples of 10 or 100 . For example, they work out that 167 minus 30 is 137 by counting back in tens from 167 ("157, 147, 137"), keeping track of the count by recording jumps on a number line. They answer one- and two-step word problems , such as: If you add two 20p coins to £1.35, how much money is that altogether? They use notes and diagrams , including number lines, to support and explain their methods.
Children locate and position multiples of 10 or 100 on a number line and recognise the relative position of other numbers. They use their knowledge of place value to establish that 374 is closer to 400 than 300 and closer to 370 than 380. They add or subtract mentally one-digit numbers to or from two-digit numbers , bridging through a multiple of 10 where appropriate. For example, they calculate 72 – 8 by subtracting 2 to give 70 and then subtracting the remaining 6, using a number line to record the steps if necessary. Children use counting on when adding 5 to 36 or counting back when subtracting 5 from 39.
Assessment focus: Ma1, Reasoning
Look for children who identify patterns in results, for example:
6 + 5 = 11
16 + 5 = 21
26 + 5 = 31
Look for children who use the patterns they identify to generate further calculations. As children explain their results, identify the reasoning they use to decide if a particular example will appear later in their list of calculations. Using the pattern above, for example, look for children who can predict and explain which addition will give the first total greater than 50 or greater than 100.
Children solve problems involving counting such as:
How many 5p coins would be needed to pay for an item costing 37p?
How many 3p and 4p stamps might we use for a 19p letter? And a 29p letter?
They also solve number puzzles , such as:
Complete each of these number sentences in as many different ways as possible:
5 + 8 =
Children organise their written responses to problems and puzzles in a systematic way , for example in a list or table. This helps them to recognise and continue patterns, and to reason that all solutions have been found. They talk about their methods and compare solutions. They explain how they organised their work to find all possibilities.
Assessment focus: Ma2, Solving numerical problems
Look for children who can choose the appropriate operation when solving problems. For example, in a problem involving several toy railway carriages of the same length, they might use repeated addition to find the total length of a ‘train’ of carriages placed end to end.
| Objectives Children's learning outcomes are emphasised |
Assessment for learning |
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Tell me how you solved this problem. Why did you decide to subtract these numbers? |
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Here is a number: 472. Read it to me. Write another three-digit number and read it to me. Is it bigger than or smaller than 472? |
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Here are some ways of partitioning 346.
346 = 300 + 46 |
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Look at this number sentence: |
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Look at this calculation: |
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Explain the relationship between adding 3 to 4 and adding 30 to 40 and 300 to 400. |
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Activities |
PDF 923KB |
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Activity 34 - Queen Esmerelda's coins |
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Activity 37 - Stamps |
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Objectives for Springboard intervention unit |
Springboard unit |
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Read and write whole numbers to at least 100 |
Springboard 3 Unit 1 sessions 1 and 2 (PDF 179KB) |
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Read a simple scale to the nearest labelled division |
Springboard 3 Unit 10 sessions 1 and 2 (PDF 171KB) |
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Diagnostic focus |
Resource |
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Can only begin counting at one; inaccurately counts objects when re-arranged; has no consistent recognition of small number of objects; lacks systematic approach |
1 YR |
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Misunderstands meaning of 'one more' and 'one less'; does not consistently identify the number before or after a given number |
2 YR |
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Counts up unreliably; still counting the smaller number to get one too many in the answer |
3 Y2 |
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Has insecure understanding of the structure of the number system, resulting in addition and subtraction errors and difficulty with estimating' - Initial teaching activity and spotlight 1 |
1 Y4 |
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+ 
= 19. What could the two missing numbers be? What else? Can you tell me
all the pairs of numbers that make 19? How do you know you have got
them all?
7, 7
6, 60
/-
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