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Learning objectives and AfL

You can use this breakdown of learning objectives, possible learning outcomes and Assessment for Learning (AfL) prompts to support your planning and assessment of children's learning across this unit.

Objectives Children's learning outcomes 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 record the calculations needed to solve a problem and check that my working is correct
• How do you know you have identified the maximum number of intersections for five streets?
• Explain how making a table could help you to solve this problem.
• Parveen has the same number of 20 p and 50 p coins. She has £7.00. How many of each coin does she have?
Explain reasoning and conclusions, using words, symbols or diagrams as appropriate I can talk about how I solve problems

[Give children a completed table, e.g. for the number of handshakes made between a given number of people.]

• What does this table represent?
• How would you explain this table to other children?
Solve multi-step problems, and problems involving fractions, decimals and percentages; choose and use appropriate calculation strategies at each stage, including calculator use I can work out problems involving fractions, decimals and percentages using a range of methods
• Find another way of expressing: 175% $33\frac{1}{3}$% $1\frac{1}{4}$
• Explain how you would solve these problems. Would you use a calculator? Why or why not?
• 185 people go to the school concert. They pay £1.35 each.
• How much ticket money is collected?
• Programmes cost 15 p each. Selling programmes raises £12.30. How many programmes are sold?
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 place value and my tables to work out multiplication and division facts for decimals What multiplication table does this image represent?
• How do you know?
• What other numbers will you see in the boxes outside?
Use efficient written methods to add and subtract integers and decimals, to multiply and divide integers and decimals by a one-digit integer, and to multiply two-digit and three-digit integers by a two-digit integer I can use efficient written methods to add, subtract, multiply and divide whole numbers and decimals
• What do you expect the mean length to be? Why?
• Make up an example of a calculation involving decimals that you would do in your head, and one that you would do on paper.
• Write in the missing digit. The answer does not have a remainder.

$\begin{array}{c}\hfill 2\phantom{\rule{0.1cm}{0ex}}6\\ \hfill 3\overline{)\square \phantom{\rule{0.1cm}{0ex}}8}\end{array}$

Use a calculator to solve problems involving multi-step calculations I can, when needed, use a calculator to solve problems
• Here is a set of instructions on cards for using a calculator to solve a problem. Put the cards in the correct order.
• What is the answer to the problem?
• Is it a sensible answer?
• Write in the missing number: $50÷\square =2.5$
Express a larger whole number as a fraction of a smaller one (e.g. recognise that 8 slices of a 5-slice pizza represents $\frac{8}{5}$ or 1 $\frac{3}{5}$ pizzas); simplify fractions by cancelling common factors; order a set of fractions by converting them to fractions with a common denominator I can write a large whole number as a fraction of a smaller one, simplify fractions and put them in order of size
• What clues did you look for to cancel these fractions to their simplest form?
• How do you know when you have the simplest form of a fraction?
• Karen makes a fraction using two number cards. She says, 'My fraction is equivalent to $\frac{1}{2}$. One of the number cards is 6'
• What could Karen's fraction be?
Relate fractions to multiplication and division (e.g. $6÷2=\frac{1}{2}$ of $6=6×\frac{1}{2}$); express a quotient as a fraction or decimal (e.g. $67÷5=13.4$ or $13\frac{2}{5}$); find fractions and percentages of whole-number quantities (e.g. $\frac{5}{8}$ of 96, 65% of £260) I can find fractions and percentages of whole numbers
• Harry said: 'To calculate 10% of a quantity you divide it by 10, so to find 20% of a quantity you must divide by 20.' What is wrong with Harry's statement?
• Explain how you would solve this problem: 'There are 24 coloured cubes in a box. Three quarters of the cubes are red, four of the cubes are blue and the rest are green.'
• How many green cubes are in the box?
• One more blue cube is put into the box.
• What fraction of the cubes in the box is blue now?
Solve simple problems involving direct proportion by scaling quantities up or down I can scale up or down to solve problems
• Two rulers cost 80 pence. How much do three rulers cost?
• Here is a recipe for pasta sauce.
• 300 g tomatoes
• 120 g onions
• 75 g mushrooms
• Josh makes the pasta sauce using 900 g of tomatoes. What weight of onions should he use? What weight of mushrooms?
• A recipe for 3 portions requires 150 g flour and 120 g sugar. Desi's solution to a problem says that for 2 portions he needs 80 g flour and 100 g sugar.
• What might Desi have done wrong?
• Work out the correct answer.
Participate in a whole-class debate using the conventions and language of debate, including Standard English (speaking and listening objective) I can take part in a debate
• How might we set about solving this problem on percentages?
• What ideas do you have?
• What are the advantages and disadvantages of multiplying the two numbers like this?
• Could you use a more efficient method?