National curriculum content

• Multiply multi-digit numbers up to 4 digits by a two-digit whole number using the formal written method of long multiplication
• Divide numbers up to 4 digits by a two-digit whole number using the formal written method of long division, and interpret remainders as whole number remainders, fractions, or by rounding, as appropriate for the context
• Divide numbers up to 4 digits by a two-digit number using the formal written method of short division where appropriate, interpreting remainders according to the context
• Perform mental calculations, including with mixed operations and large numbers
• Solve addition and subtraction multi-step problems in contexts, deciding which operations and methods to use and why
• Solve problems involving addition, subtraction, multiplication and division
• Use estimation to check answers to calculations and determine, in the context of a problem, an appropriate degree of accuracy.
• Solve problems involving the relative sizes of two quantities where missing values can be found by using integer multiplication and division facts
• Solve problems involving the calculation and conversion of units of measure, using decimal notation up to three decimal places where appropriate
• Use, read, write and convert between standard units, converting measurements of length, mass, volume and time from a smaller unit of measure to a larger unit, and vice versa, using decimal notation to up to three decimal places
• Calculate, estimate and compare volume of cubes and cuboids using standard units, including cubic centimetres (cm³) and cubic metres (m³), and extending to other units [for example, mm³ and km³].
• Recognise when it is possible to use formulae for area and volume of shapes
• Recognise, describe and build simple 3-D shapes, including making nets

Lesson objectives

1. Activity 1: Ratio and proportion (Calculating quantities of ingredients)
2. Activity 2: Four operations (Costing the ingredients)
3. Activity 3: Converting units of measurement (Finding the best value for money of ingredients packaged in different ways)
4. Activity 4: Money (Profit and loss)
5. Activity 5: Nets of 3D shapes (Creating packaging for our products)
6. Activity 6: Area, perimeter and volume (Calculating appropriate sizes for our packaging)
7. Activity 7: Word problems with time relating  to our cakes
8. Activity 8: Word problems with number and fractions relating to our cakes
9. Activity 9: To apply knowledge and understanding of all of the aspects covered to bake and package our own cakes

What we want children to know

• Pupils practise addition, subtraction, multiplication and division for larger numbers, using the formal written methods of columnar addition and subtraction, short and long multiplication, and short and long division
• To develop their skills of rounding and estimating as a means of predicting and checking the order of magnitude of their answers to decimal calculations. This includes rounding answers to a specified degree of accuracy and checking the reasonableness of their answers.
• Pupils recognise proportionality in contexts when the relations between quantities are in the same ratio (for example, similar shapes and recipes).
• Solve problems involving unequal quantities, for example, ‘for every egg, you need three spoonfuls of flour’
• To consolidate their understanding of ratio when comparing quantities, sizes and scale drawings by solving a variety of problems. They might use the notation a:b to record their work.
• Know approximate conversions and are able to tell if an answer is sensible
• Draw shapes and nets accurately, using measuring tools and conventional markings and labels for lines and angles.
• Describe the properties of shapes and explain how unknown angles and lengths can be derived from known measurements.
• Using the number line, pupils use, add and subtract positive and negative integers for measures such as time.

What skills we want children to develop

Use knowledge to solve reasoning and problem solving questions such as:

What’s the same, what’s different?

What is the same and what is different about the nets of a triangular prism and a square based pyramid?

Other possibilities

A cuboid has a volume between 200 and 250 cm cubed.

Each edge is at least 4cm long. List four possibilities for the dimensions of the cuboid.

Undoing

A film lasting 200 minutes finished at 17:45. At what time did it start?

Write more statements

Chen, Megan and Sam have parcels. Megan’s parcel weighs 1.2kg and Chen’s parcel is 1500g and Sam’s parcel is half the weight of Megan’s parcel. Write down some other statements about the parcels. How much heavier is Megan’s parcel than Chen’s parcel?

Unpicking

A recipe needs to include three times as much apple than peach. The total weight of apples and peaches in a recipe is 700 grams. How much apple do I need?

Use the inverse

Use the inverse to check if the following calculations are correct:

£23.46 x 46 = £3327.96

£27.74 ÷ 19 = 1.46

Vocabulary/Mathematical Talk

• Explain the value of each digit in your calculation
• Which is the most appropriate unit to use to measure the object? Explain your answer.
• Why do you think _____ is not an appropriate estimate?
• What’s the same and what’s different between 1.5 kg and 1.500 kg? Are the zeroes needed? Why or why not?
• What do you think would be the most efficient method for converting the units of time?
• How can we represent this ratio using a bar model? What does each part represent? What will each part be worth?
• If we know what one part is worth, can we calculate the other parts?
• What is a net? What shape will this net make? How do you know? What shape won’t it make?
•  If you make this net, what would happen if you were not accurate with your measuring?