National curriculum content

• Interpret and construct pie charts and line graphs and use these to solve problems
• 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
• Convert between miles and kilometres
• 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
• Solve addition and subtraction multi-step problems in contexts, deciding which operations and methods to use and why
• Multiply one-digit numbers with up to two decimal places by whole numbers
• Use written division methods in cases where the answer has up to two decimal places
• Solve problems which require answers to be rounded to specified degrees of accuracy
• Recall and use equivalences between simple fractions, decimals and percentages, including in different contexts.
• Solve problems involving the calculation of percentages [for example, of measures, and such as 15% of 360] and the use of percentages for comparison

Lesson objectives

1. Activity 1: Statistics (Reading and interpreting climate graphs)
2. Activity 2: Statistics (Creating a climate graph to show temperature and rainfall in your chosen area)
3. Activity 3: Converting units of measurement – miles to kilometres; time (Calculating flight length to chosen destination)
4. Activity 4: Word problems using the four operations (Researching and choosing the best airport to fly from)
5. Activity 5: Word problems with money and percentages (Researching accommodation costs – including those with discounts)
6. Activity 6: Decimals (Choose activities to do on holiday and budget for these accordingly)
7. Activity 7: Time (Calculating time differences from chosen holiday destinations)  
8. Activity 8: Use prior learning to calculate how much the whole holiday will cost including: journey, accommodation and budget per day.

What we want children to know

• Encounter and draw graphs relating two variables, arising from their own enquiry and in other subjects.
• Connect conversion from kilometres to miles in measurement to its graphical representation.
• To know approximate conversions and are able to tell if an answer is sensible.
• Using the number line, pupils use, add and subtract positive and negative integers for measures.
• Be introduced to compound units for speed, such as miles per hour, and apply their knowledge in science or other subjects as appropriate.
• Multiply and divide numbers with up to two decimal places by one-digit and two-digit whole numbers
• Multiply decimals by whole numbers, starting with the simplest cases, such as 0.4 × 2 = 0.8, and in practical contexts, such as measures and money.
• Pupils are introduced to the division of decimal numbers by one-digit whole number, initially, in practical contexts involving measures and money
• Recognise division calculations as the inverse of multiplication.
• 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.
• When recurring decimal equivalents are found, pupils learn about rounding the decimal to two decimal places, or other appropriate approximations depending on the context.

What skills we want children to develop

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

True or false?

• (Looking at a line graph/bar chart/pie chart) “More than twice the number of people say their favourite type of T.V. programme is soaps than any other”.

Is this true or false? Convince me.

Make up your own ‘true/false’ statement about the chart.

• 25% of 23km is longer than 0.2 of 20km.

              Convince me.

What’s the same, what’s different?

Pupils identify similarities and differences between different representations and explain them to each other.

What do you notice?

One thousandth of my money is 31p. How much do I have?

Undoing

I multiply a number with three decimal places by a multiple of 10. The answer is approximately 3.21

What was my number and what did I multiply buy?

Making an estimate

Circle the number that is the best estimate to  932.6  - 931.05

1.3     1.5    1.7   1.9

Vocabulary/Mathematical Talk

• What do the x and y axis represent?
• Why is it useful to have both sets of data on one graph?
• How will you make it clear which line represents which set of data?
• Why would this information be placed on a line graph and not a different type of graph?
• If we know 5 miles ≈ 8 km, how can we work out 15 miles converted to km?
• Give an example of a length you would measure in miles or km.
• If we know a percentage, can we work out the whole?
• Is dividing by 10 and multiplying by 9 the most efficient way to find 90%? Explain why.
• Why do we divide a quantity by 2 in order to find 50%?