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Year 6 Block B - Securing number facts, understanding shape Unit 3

Objectives

Children's learning outcomes are emphasised 		Assessment for learning
  • Tabulate systematically the information in a problem or puzzle; identify and record the steps or calculations needed to solve it, using symbols where appropriate; interpret solutions in the original context and check their accuracy

    I can use a table to help me solve a problem
    I can identify and record what I need to do to solve the problem, checking that my answer makes sense and is accurate

Imagine you have 25 beads. You have to make a three-digit number on an abacus. You must use all 25 beads for each number you make.

How many different three-digit numbers can you make? How can you be sure that you have counted them all?

How will you organise the information in this problem?
Two boys and two girls can play tennis.
Yasir said: 'I will only play if Holly plays.'
Holly said: 'I won't play if Ben is playing.'
Ben said: 'I won't play if Luke or Laura plays.'
Luke said: 'I will only play if Zoe plays.'
Zoe said: 'I don't mind who I play with.'
Which two boys and which two girls play tennis?

  • Represent and interpret sequences, patterns and relationships involving numbers and shapes; suggest and test hypotheses; construct and use simple expressions and formulae in words then symbols (e.g. the cost of c pens at 15 pence each is 15c pence)

    I can describe and explain sequences, patterns and relationships
    I can suggest hypotheses and test them
    I can write and use simple expressions in words and formulae

Draw the next two terms in this sequence:

A grid 5 squares by 13 squares; one square is shaded followed by 1 with 3 above in a 'T' shape, followed by the same with 5 above

Describe this sequence to a friend using words. Describe it using numbers.
How many small squares would there be in the 10th picture?
I want to know the 100th term in the sequence. Will I have to work out the first 99 terms to be able to do it? Is there a quicker way? How?
How would you change an amount of money from pounds sterling to euros? Record it for me using symbols.

  • Use knowledge of multiplication facts to derive quickly squares of numbers to 12 × 12 and the corresponding squares of multiples of 10

    I can say the squares of numbers to 12 × 12 and work out the squares of multiples of 10

How many squares of multiples of 10 lie between 1000 and 2000? How many lie between 1000 and 10 000?

  • Use knowledge of place value and multiplication facts to 10 × 10 to derive related multiplication and division facts involving decimals (e.g. 0.8 × 7, 4.8 ÷ 6)

    I can use my tables to work out decimal facts like 0.4 × 8 and 5.6 ÷ 7

Which of these are incorrect?
56 × 0.7 = 8
56 ÷ 0.7 = 80
0.7 × 0.8 = 6.6
Explain how you know using words or diagrams.

  • Recognise that prime numbers have only two factors and identify prime numbers less than 100; find the prime factors of two-digit numbers

    I can tell you all the prime numbers up to 100 and find the prime factors of other numbers

Investigate which numbers to 30 have only one distinct prime factor (prime numbers, squares of prime numbers, cubes of prime numbers). Predict what numbers to 60 will have only one distinct prime factor when you test them.

  • Use a calculator to solve problems involving multi-step calculations

    I can use a calculator to solve problems with more than one step

Which part of your problem will you solve mentally? Which part will you solve using a calculator?
My calculator shows:

A calculator screen displaying 0.35

My question was about pounds. Complete this:
0.35 means ... pence.
My question was about litres. Complete this:
0.35 means ... millilitres.
My question was about metres. Complete this:
0.35 means ... centimetres.

  • Use approximations, inverse operations and tests of divisibility to estimate and check results

    I can estimate and check the result of a calculation

Is this calculation correct? How do you know?
What inverse operation could you use to check this result?
I multiplied two odd numbers and my answer was 186. Explain why I cannot be correct.
Should the answer be a multiple of 6? How could you check?
This sequence of numbers goes up by 40 each time.
40 80 120 160 200 ...
This sequence continues. Will the number 2140 be in the sequence? Explain how you know.

  • Describe, identify and visualise parallel and perpendicular edges or faces; use these properties to classify 2-D shapes and 3-D solids

    I can identify 3-D shapes with perpendicular or parallel edges or faces

Imagine a triangular prism. How many faces does it have? Are any of the faces parallel to each other?
How many pairs of parallel edges has a square-based pyramid? How many perpendicular edges?
Look at these 3-D shapes (e.g. a cuboid, tetrahedron, square-based pyramid and octahedron). Show me a face that is parallel to this one. Which face is perpendicular to this one?
What can you tell me about the faces of a cuboid? Why are so many packing boxes made in the shape of a cuboid?
Which of these shapes is incorrectly placed on this Carroll diagram? Change the criteria so the shapes are correctly sorted according to their properties.

  • Make and draw shapes with increasing accuracy and apply knowledge of their properties

    I can make and draw shapes accurately

Use your ruler and protractor. Draw the net of a regular tetrahedron with edges of 6 cm.
Use compasses to draw a circle. Use a ruler and protractor to draw a regular pentagon with its vertices on the circumference of the circle.
Tell me an example of a circular object that would have a radius of about 5 cm. What about 50 cm? 500 cm?

  • Use a range of oral techniques to present persuasive arguments and engaging narratives

    I can listen to the ideas of others, making sure that I respond to their ideas when I make my next statement

In your group, consider the sum of five numbers in a straight line on the 100-square. What do you notice? Think about this problem and how to solve it. Take turns to contribute one idea for the group to discuss.

Learning overview

Children use number facts and place value to solve word problems involving whole numbers and decimals. They solve problems such as: A box contains 250 matches and weighs 55 grams. The empty box weighs 12 grams. Calculate the weight of one match. They interpret the decimal answer in the context of the problem.

They identify stages in solving multi-step problems, what calculations to do and the most efficient way to do them. They record their methods clearly, showing each stage. They suggest word problems involving numbers, money or measures to match given calculations, such as 4.2 ÷ 0.7, making sure that the answer will make sense in the context of the problem. They tabulate results systematically so that they know that they have found all possible solutions to a problem. For example, they work systematically through three-digit numbers beginning 99, 98, 97, 96, ... then 89, 88, 87, 86, ..., and so on when they solve this problem:

Imagine you have 25 beads. You have to make a three-digit number on an abacus. You must use all 25 beads for each number you make. How many different three-digit numbers can you make?

They record all their solutions by writing them in order.

Children investigate relationships and patterns in numbers. They write a formula for converting one currency to another, researching the accurate exchange rate and using symbols to express the relationship between the two currencies. They find the digit sum of multiples of 3 and use results to establish a rule for divisibility by 3. They explore multiples of other numbers in a similar way and establish general rules for recognising where a number is a multiple of 2, 3, 4, 5, 6, 8 or 9.

Children approximate and test for divisibility to check results. For example, they give reasons why the calculation 2065 ÷ 3 = 714 cannot be correct, or they find the missing digits in the calculation 3square5 ÷ 9 = square5. They use tests of divisibility to find the prime factors of two-digit whole numbers, writing 60, for example, as 2 × 2 × 3 × 5.

They solve problems and puzzles, testing answers using tests of divisibility and approximation. For example, they investigate the general statement: When you add three consecutive numbers, the sum is a multiple of 3. They predict what will happen when they add four consecutive numbers, and then five. They pose questions of their own, such as: Is the product of two odd numbers always odd? They test their hypotheses for accuracy.

Children use inverse operations to solve problems such as: I think of a number, subtract 15 and then multiply the answer by 4. I get the answer of 130. What number did I start with?

Children extend their explorations of properties of shapes. They identify and visualise shapes. They recognise parallel and perpendicular faces of 3-D shapes practically through, for example, placing one face on a horizontal surface and observing whether any other faces are horizontal (or vertical). They describe the shape generated by cutting through a tetrahedron or a triangular right prism in a plane parallel to a base. They classify 3-D shapes using criteria such as 'has at least one pair of parallel faces'. They investigate the number of edges, faces and vertices in polyhedra, record these in a table and explore the relationship: the number of vertices plus the number of faces equals the number of edges.

Children draw 2-D shapes and make 3-D shapes with increasing accuracy. For example, they program an on-screen turtle to draw regular polygons or specific quadrilaterals. They use compasses to construct circles with a given radius or diameter, suggesting ways to investigate the relationship between the diameters of a set of concentric circles and their radii. They create a set of nesting boxes from card.

Resource links to existing published material

Mathematical challenges for able Key Stages 1 and 2
Activities PDF 1MB
Activity 60 - Three digits
Intervention programmes

Objectives for Springboard intervention unit

Springboard unit

Express a quotient as a fraction or as a decimal when dividing a whole number by 2, 4, 5 or 10
Represent halves, tenths, and fifths as fractions and decimals

Springboard 6 Unit 3 (PDF 1.4MB)
Supporting children with gaps in their mathematical understanding (Wave 3)
Diagnostic focus Resource
None currently available  

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

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
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