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Year 4 Counting, partitioning and calculating - Unit 1

Learning overview

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:

  • Ma1, Communicating
  • Ma2, Numbers and the number system
  • Ma2, Operations and relationships between them
  • Ma2, Mental methods.

Children read, write and order numbers with four digits. They partition them into multiples of 1000, 100, 10 and 1 and understand the importance of zero as a place-holder in numbers such as 2036. They use their understanding of place value to add or subtract 1, 10, 100 or 1000 to or from whole numbers, responding to questions such as:

What needs to be added/subtracted to change 4782 to 9782? Or 2634 to 2034?
What is 100 ml more/less than 3250 ml? What is 10 m more/less than 5000 m?
Which is less: 4 hundreds or 41 tens?

Assessment focus: Ma2, Numbers and the number system

Look for children who understand the place value of each digit in three and four-digit numbers, for example, those who can say how much to subtract from a four-digit number to reduce a chosen digit to zero and then use a calculator to check their suggestion.

Children recognise and interpret negative numbers on the number line and in practical contexts, and use this knowledge to solve problems. For example, they read positive and negative numbers representing temperatures on a thermometer. They compare temperatures from different places around the world, or from their work in science, and can say which are warmer or colder. They compare and order positive and negative numbers, and position them on a number line, for example, to identify temperatures that are higher than –9degreesC but lower than –6degreesC. They use the < and > signs to record statements such as –3 < –1 or –1 > –3. They solve problems such as:

The temperature is –2degreesC. How much must it rise to reach 3degreesC?

Children count forwards and backwards in steps of equal sizes, starting from a positive or negative number. They count back in fours from 40 and discuss what happens when they reach 0. They predict numbers that will occur in the sequence, using their counting skills to answer questions such as: If I keep on subtracting 3 from 10, will –13 be in my sequence? They use a calculator to check, recognising how negative numbers appear in the display.

Children multiply and divide numbers up to 1000 by 10 and then 100. They understand and can explain that when a number is divided by 100 the digits of the number move two places to the right and when a number is multiplied by 100 the digits move two digits to the left. They use a calculator to investigate whether dividing by 10 and then 10 again has the same effect as dividing by 100. They apply their knowledge of multiplying and dividing by 10 and 100 to solve problems involving scaling, such as: A giant is 100 times bigger than you. How wide is the giant's hand span? How long is the giant's foot? They extend their knowledge of multiplication and division facts to 10 × 10, and use this knowledge and their understanding of place value to begin to multiply and divide multiples of 10 such as 50 × 6, 90 × 3, 80 ÷ 4, 150 ÷ 3.

Assessment focus: Ma2, Mental calculation

Look for evidence of children using mental recall of the 2, 5 and 10 multiplication tables and their understanding of place value to calculate the value of some coins, for example, to find the value of eight 50p coins or nine 20p coins. Look for children who know facts in the 2, 3, 4, 5 and 10 multiplication tables and are beginning to derive and recall multiplication facts for other tables up to 10 × 10.

Children add and subtract pairs of two-digit numbers by drawing on their knowledge of place value and number facts. They identify when to use mental strategies such as partitioning or rounding and adjusting. They recognise that 49 plus 37 is equivalent to 50 plus 37 - 1, or that 98 minus 43 can be calculated as 98 minus 40 minus 3. They record the steps of a mental calculation, for example on an empty number line, and compare their approach with the approaches used by others.

Children solve problems, including those involving money. They identify what calculations to do, when to calculate mentally (with or without jottings) and when to use a calculator. They learn how to clear a calculator display before starting a calculation and how to correct an accidental wrong entry with the clear-entry key. They learn also how to enter money and how to interpret the display in the context of the question. For example, to calculate £4.35 plus £3.85, they key in 4.35 [plus] 3.85 [=] and interpret the outcome of 8.2 as £8.20. They write down the keys pressed as a record of their method.

Children solve puzzles involving addition and subtraction. For example, they use numbers 37, 52, 77 and 87 to satisfy statements such as Square - circle = 35, or Square plus circle = 114.

Assessment focus: Ma2, Operations and relationships between them

Look for evidence of children’s understanding of inverses. Look out for children who understand addition and subtraction as inverse operations and use this to find missing numbers, for example, Square – 35 = 56. Look for children who understand multiplication and division as inverse operations and use this to check their results when they divide.

Children contribute to paired, grouped and whole-class discussions about their calculation strategies. They listen to others' explanations and ask questions if they need clarification. They explain their solutions in writing, recording the stages in the problem in a systematic way. Children contribute to paired, grouped and whole-class discussions about their calculation strategies. They listen to others' explanations and ask questions if they need clarification. They explain their solutions in writing, recording the stages in the problem in a systematic way.

Assessment focus: Ma1, Communicating

Look for children who appreciate the value of recording their work so that they can review their approach and check their calculations. Look for children who present their work clearly and in an organised way.

Objectives

Children's learning outcomes are emphasised 		Assessment for learning
  • Report solutions to puzzles and problems, giving explanations and reasoning orally and in writing, using diagrams and symbols

    I can explain to someone else how I solve problems and puzzles

How did you solve this problem?
If you had to solve it again would you do anything differently? Why?
Suppose the problem had these numbers. Would that change the way you would solve the problem?
What diagram did you draw to help you to solve the problem? Did anyone use a different diagram? Which diagram is more helpful? Why?

  • Partition, round and order four-digit whole numbers; use positive and negative numbers in context and position them on a number line; state inequalities using the symbols < and > (e.g. –3 > –5, –1 < plus1)

    I can read, write and put in order four-digit numbers and positive and negative numbers
    I can use the < and > signs with positive and negative numbers (e.g. –3 < 1)

What is the biggest whole number that you can make with these four digits: 3, 0, 6, 5? What is the smallest whole number that you can make with the digits?
Look at this number sentence: Square + Diamond = 1249. What could the missing numbers be?
What tips would you give someone who is learning how to round numbers to the nearest 10, or 1000?
I rounded a number to the nearest 10. The answer is 340. What number could I have started with?
The local newspaper said that 800 people attended the summer fair. The newspaper gave the number to the nearest 100. What is the smallest number of people that could have attended? What is the largest number?
I measured the temperature in the morning. By the evening it had fallen by 8 degrees and was below freezing point. What could the morning and evening temperatures be?
Tell me two temperatures that lie between 0 degrees and –10 degrees. Which of the two temperatures is the warmer?
What number can you put in the box to make this statement true? Square < –2

  • Use knowledge of addition and subtraction facts and place value to derive sums and differences of pairs of multiples of 10, 100 or 1000

    I can work out sums and differences of multiples of 100 or 1000

Add or subtract these numbers. Tell me how you did it.
30 + 80, 70 - 50
800 + 500, 900 - 400
5000 + 3000, 8000 - 6000

  • Add or subtract mentally pairs of two-digit whole numbers
    (e.g. 47 + 58, 91 - 35)

    I can add and subtract two-digit numbers in my head (e.g. 26 + 47, 43 - 16)

Work out 37 + 58 (or 91 - 35) in your head. Tell me how you did it. Did anyone do it a different way? How could we record the method that you used?
What number do you need to add to 46 to make 92? How did you work it out? Is there a different way to do it?

  • Recognise and continue number sequences formed by counting on or back in steps of constant size

    I can count on and back in eights

Count on in eights from zero. Now count back to zero. This time, count on seven eights from zero.
Show me seven hops of eight from zero on the number line.

  • Derive and recall multiplication facts up to 10 × 10, the corresponding division facts and multiples of numbers to 10 up to the tenth multiple

    I know my 8 times-table and my 9 times-table

How can you work out the 8 times-table from the 4 times-table? Or the 9 times-table from the 3 times-table?
If you know that 9 × 8 = 72, what is 72 ÷ 9? What is 720 ÷ 9?
What is the relationship between 8 × 7 = 56, 6 × 7 = 42 and 14 × 7 = 98?

  • Multiply and divide numbers to 1000 by 10 and then 100 (whole-number answers), understanding the effect; relate to scaling up or down

    I can multiply and divide by 10 and 100. I can explain what happens to the digits when I do this

Why do 6 × 100 and 60 × 10 give the same answer?
I have 37 on my calculator display. How can I change it to 3700 in one operation? Is there another way to do it?
What number is 10 times smaller than 2450? What number is 100 times bigger than 36?
I divide a four-digit number by 100. The answer is between 70 and 75. What could the four-digit number be?
Change 4527 pence into pounds. Change £10.39 to pence.
Write a price ticket for four pounds and six pence.

  • Identify the doubles of two-digit numbers; use these to calculate doubles of multiples of 10 and 100 and derive the corresponding halves

    I can double two-digit numbers

Work out double 47 in your head. Tell me how you did it. Is there a different way to do it? What is double 470? Double 4700?
What is half of 72? How did you work it out? Is there a different way to do it? What is half of 720? Half of 7200? How do you know?

  • Use a calculator to carry out one-step and two-step calculations involving all four operations; recognise negative numbers in the display, correct mistaken entries and interpret the display correctly in the context of money

    I can use a calculator to help me solve one-step and two-step problems
    I know how to enter prices such as £1.29 and £2.30 into a calculator
    I know that –7 on a calculator means negative 7

What can go wrong when you are doing a calculation on a calculator? How would you put it right?
I typed in 124 on my calculator. I meant to type in 125. What keys should I press to correct my mistake?
Add these prices on your calculator. I will read them one at a time for you to enter: six pounds and seventy-six pence; nine pounds and ten pence; seven pounds and six pence. What is the total? Did you get £22.92? What do you need to add to get £23?

  • Use knowledge of rounding, number operations and inverses to estimate and check calculations

    I can estimate and check the result of a calculation

Roughly, what will the answer to this calculation be?
How do you know that this calculation is probably right?

  • Use and reflect on some ground rules for dialogue (e.g. making structured, extended contributions, speaking audibly, making meaning explicit and listening actively)

    I can explain how I add and subtract two-digit numbers in my head

Tell everyone about the method you used. Explain to the group why you chose that method.
Listen carefully while Mai tells you about her method. Now use Mai's method to work out this calculation.

Resource links to existing published material

Mathematical challenges for able pupils Key Stages 1 and 2

Activities

 

None currently available

Intervention programmes

Objectives for Springboard intervention unit

Springboard unit

Read and write whole numbers to at least 1000
Know what each digit represents and partition three-digit numbers into a multiple of 100, a multiple of ten and ones
Order whole numbers to at least 1000, and position them on a number line

Springboard 4 Unit 1 (PDF 169KB)

Partition into tens and ones, then recombine

Springboard 4 Unit 3 (PDF 173KB)

Count on or back in twos and recognise odd/even numbers
Count in steps of 3 or 4
Count on or back in tens or hundreds
Say the number that is 1, 10, 100 more or less than any given two- or three-digit number

Springboard 4 Unit 4 (PDF 157KB)

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

Diagnostic focus

Resource

Is not confident when recalling multiplication facts

1 Y4 ×/÷
DfES 1150-2005 (PDF 104KB)

Describes the operation of multiplying by ten as 'adding a nought'

3 Y4 ×/÷
DfES 1152-2005 (PDF 68KB)

Has difficulty in partitioning

2 Y4 plus/-
DfES 1129-2005 (PDF 108KB)

Has insecure understanding of the structure of the number system

1 Y4 plus/-
DfES 1128-2005 (PDF 101KB)

Click here for information on different file formats and their usage.

Year 4 Counting, partitioning and calculating - Unit 1

PDF 49KB RTF 122KB Word 64KB

Wave 3 addition and subtraction tracking children's learning charts

PDF 161KB RTF 930KB Word 315KB

Wave 3 multiplication and division tracking children's learning charts

PDF 195KB RTF 1.3MB Word 430KB

Wave 3 Resource sheets and index of games booklet

PDF 500KB
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