Maths Lesson Template

Section
3

Year 8 intervention lessons and resources

These lessons are designed to support teachers working with Year 8 pupils who need to secure level 5 at the end of Year 9. They are not appropriate for those pupils in Year 8 who are working on the main Year 8 teaching programme. When using the lessons, teachers need to take into account pupils’ prior knowledge and experience of the topics.

Most of the lessons are drawn from existing Key Stage 3 Strategy materials that support the main Year 7 mathematics teaching programme. The lessons focus on teaching strategies to address the stated learning objectives.

The lessons are linked to units of work corresponding to the sample medium-term plan: Year 8 intervention(see section 2). The order of the units is designed to ensure progression. Maintaining the order will help to ensure progression and continuity, building up pupils’ understanding systematically during the year.

Lesson starters provide opportunities to recall previously learned facts and to practise skills. Some of the starters introduce ideas that are then followed up in the main part of the lesson.

You can also base the teaching in a lesson on a single test question. This helps pupils realise the level of difficulty expected of them as well as helping them gain familiarity with the style of test questions.

You could complete the main part of a lesson by:

•extending your questioning of pupils;

•increasing the number of examples that you demonstrate.

It is important that while pupils are working on a task you continue to teach by rectifying any misconceptions and explaining key points.

Use the final plenary to check pupils’ learning against the lesson objectives. These define the standard required – what pupils need to know and be able to do in order to reach level 5 in mathematics at the end of Key Stage 3.

When you are preparing to use the lessons, read them through using a highlighter pen to mark key teaching points and questions. You can then refer to these quickly while you are teaching. Annotate the lesson plan to fit the needs of your pupils.

You will need to prepare overhead projector transparencies (OHTs) and occasional handouts. You also will need to select and prepare resources, matched to pupils’ needs, to provide practice and consolidation during the lesson and for homework.

From level 4 to level 5 in mathematics: Year 8 intervention

Lesson
8N1.1

Solving number problems 1

Objectives

•Understand and use decimal notation and place value.

•Understand negative numbers as positions on a number line; order and add positive and negative numbers.

•Consolidate the rapid recall of number facts, including multiplication facts to 10×10, and quickly derive associated division facts.

•Solve word problems and investigate in the context of number; compare and evaluate solutions.

Starter

5 minutes

Resources

Counting stick

Number fans or mini-whiteboards

Practise counting on and back from different starting numbers in steps of different sizes, including decimals.

Establish that pupils are familiar with negative numbers and can continue patterns below 0,using a counting stick or an empty number line.For example:

•Count back from 20 in steps of 3, 7, 11, …

•Count on from –11 in steps of 5, 20, 13, …

•Count back from 10 in steps of 0.2, 0.7, …

Main activity

50 minutes

Resources

Two large double-sided cards, with 7 and –2 on one card and 5 and –3 on the other

Sets of small double-sided cards, numbered as above; one set per pair

Framework examples, pages 36, 40, 48, 88

Introduce the main activity by asking the class to imagine that the Government has decided to issue only 3p and 5p coins. Practise quick calculations involving 3s and 5s by asking pupils questions such as:

QI have seven 3p coins. How much is that?

QI have 60p. How many 5p coins is that?

QI have 6000p. How many 3p coins is that?

Now pose the following problems.

QUsing only 3p and 5p coins, you can pay for goods of any price.
Is this true or false?

QWhat other sets of coins could the Government introduce? What about 7p and 10p?

Discuss with pupils how they could approach the problems, reminding them that they could receive change.

Ask pupils, in pairs, to consider then answer these questions:

QHow do you pay for an item costing 39p? Is there more than one way of paying 39p?

QWhat about 7p and 10p coins?

Model some possible solutions and approaches to the problems, establishing the important steps in finding the answers and whether pupils are able to produce convincing arguments.

Highlight some important things to think about when solving problems, for example:

•being systematic;

•keeping a careful record of their findings as they go along;

•identifying patterns in their findings and drawing on these to come to some conclusions that they can explain and justify.

Explain that these are important skills that pupils will be expected to use.

Explore with pupils what would happen if they had to give an ‘exact amount’ and could not receive any change.

QCould you still make every value?

Ask them to discuss this quickly, in pairs, considering either 3p and 5p coins or 7p and 10p coins. Draw out some responses, asking pupils to explain their answers. Summarise which values are not possible, and why.

Extend the problem to considering double-sided cards with positive and negative integers. Use some large cards, some with 7 on one side and –2 on the other, and others with 5 on one side and –3 on the other. Demonstrate the different values you can make. For example, using one of each card you can make:

7+–3=4

Confirm that, using one of each card, these values are possible:12, 4, 3, –5.

Ask pupils to work in pairs to establish how many different values they can find if they use two of each of these cards.

Plenary

5 minutes

Question pupils about what they have found, asking them to explain what they recorded, what conclusions they came to, and how.

Pose questions such as:

QHow did you know you had found all the possible values?

QHow could you convince someone else that you had found all the possible values?

QWere there any values you couldn’t make? Can you explain why?

Summarise.

Set the following problem for homework:

QI have two double-sided cards. Using both cards, I can make the values7,10,–1,–4. What integers are on each side of the two cards?(2,–1; 8,–3)

Key ideas for pupils

When solving problems, remember to:

•be systematic;

•keep a careful record of your findings as you go along;

•identify patterns in your findings and draw on these to come to some conclusions that you can explain and justify.

Lesson
8N1.2

Solving number problems 2

Objectives

•Understand negative numbers as positions on a number line; order, add and subtract negative numbers.

•Solve word problems and investigate in the context of number; compare and evaluate solutions.

Starter

10 minutes

Resources

Resource 8N1.2a– number cards printed back to back and cut out as cards; one set per pair

Framework examples, pages 40, 48

Draw a blank number line and write a number at each end. Put a mark or a cross halfway along the line and ask pupils what number will be at the mid-point. For example:

Ask pupils how they found the mid-point. Discuss their methods, using the number line to model their thinking.

Quickly model another two examples, such as the mid-point between –11 and 5, and between –3.5 and –1.

Ask pupils if their strategies change when they are dealing with different types of number, or when the end numbers are close or far apart.

Ask pairs of pupils to practise finding mid-points, using a set of number cards (resource 8N1.2a). Pupils each choose a card and then they find the number halfway between the numbers they have chosen, using a blank number line if they wish.

Main activity

45 minutes

Resources

Resource 8N1.2a

Framework examples, pages 48, 92, 94

Using blank number lines (horizontal and vertical) or by extending number patterns (Framework examples, page 48), model addition and subtraction of positive and negative integers.Ensure that pupils can record their number statements consistently.

Pose the problem:

QUsing any number of double-sided cards, some with 7 on one side and –2 on the other and others with 5 on one side and –3 on the other, what values could you find?

Discuss some of the possible values using both addition and subtraction.

5+–2+–2+–2 =–1

7+–3–5 = –1

–3––2 = –1

Ask pupils:

QCan you find every value from –5 to 5?

Discuss responses, acknowledging different ways of obtaining the same value.

Support:Use only positive values, by allowing the use of any number of cards or by using addition only.

As an extension, ask pupils to consider whether values areimpossible to find.

QCan you find integers that produce all the values from –25 to 25?

QDoes this mean that any value could be found?

QHow can you justify your answer?

Plenary

5 minutes

Discuss results and strategies, for example by asking pairs:

QIs it possible to make –6?

QHow many different ways are there to make –6?

QIs it possible to make every value from –10 to 10?

QHow can you convince someone that this is true?

Summarise the results and, if possible, get a pupil to demonstrate a systematic way of recording them.

Set the following problem for homework.

QFill in the missing numbers so that each row, each column and each diagonal adds up to 3.

Key ideas for pupils

When solving problems, remember to:

•be systematic;

•keep a careful record of your findings as you go along;

•identify patterns in your findings and draw on these to come to some conclusions that you can explain and justify.

Resource
8N1.2a

Number cards

Resource
8N1.2a

Number cards (cont.)

Lesson
8N2.1

Exploring calculation methods

Objectives

•Understand and use decimal notation and place value; multiply and divide integers and decimals by 10, 100, 1000, and explain the effect.

•Enter numbers in a calculator and interpret the display in different contexts (decimals, money, metric measures).

•Solve word problems and investigate in the context of number; compare and evaluate solutions.

Starter

10 minutes

Resources

Framework examples,
page 6

Remind pupils that previously they have solved puzzles where they had to put numbers into boxes.

Ask pupils to work as quickly as they can, using the digits 2, 3, 7 and 8 as often as they like, to make these number sentences correct.

 +  = 54

155 –  = 

Discuss the different strategies used by pupils and clarify key points such as the difference between a digit (numeral) and a number (made up of digits or numerals), the need to have a sense of place value, and the need to have a sense of the number as a whole.

Set the following examples.

 +  = 69 105 –  = 

 +  = 99  +  = 110

Main activity

45 minutes

Resources

Resource 8N2.1a, one per pair

Framework examples, pages 6, 36

Give pairs of pupils one minute to discuss the following problem and to decide how they would tackle it.

QUsing each of the digits 1, 2, 3, 4, 5 only once, what is the largest addition calculation you can make?

 + 

Take feedback and establish that they will use what they know about place value and addition to make a decision. Which digit would they place first? Which one next? …

Acknowledge that addition is relatively easy. What if they used a different operation, while still looking for the highest result? For subtraction, for example, would they approach the problem in the same way? What about multiplication and division?

Give out resource 8N2.1afor pupils to work on, in pairs. Ask them to think carefully about how they will tackle the problem and how they can draw on what they already know about numbers and number operations.

Take feedback on answers, the ways pupils have thought about the problem and the prior knowledge and understanding that they have used.

Ask how the problem could be extended. For example:

QWhat if …

•you could use any five digits from 1 to 9?

•you could group the digits in different ways, for example:

 × 

or ×  ×  ?

•you could use a decimal point?

•you were trying to find the smallest result?

Ask each pair to decide upon the question they will pursue and give them 5 minutes to get started. Bring the class together to share their thinking so far and to establish their lines of investigation.

Plenary

5 minutes

Resources

Dice

Resource 8N2.1b; one per pair in lesson, one each for homework

To emphasise the importance of place value, play this game.

   ×  

Explain that the aim is for each pupil to make the largest possible product.

Roll a dice, call out the number (say, 3) and allow 10 seconds for pupils to decide what they think is the most advantageous position for the digit represented by the number on the dice. Play continues until everyone has placed all five digits. What is the largest product?

Ask pairs to play the same game, using resource 8N2.1b.

For homework, ask pupils to play this game with someone at home.

Key ideas for pupils

When solving problems, remember to:

•be systematic;

•keep a record of your findings;

•explain your answer.

Resource
8N2.1a

Largest calculations

Using each of the digits 1, 2, 3, 4 and 5 only once, what is the largest result you can find for each calculation?

 + 

 – 

 × 

 ÷ 

Resource
8N2.1b

Largest product

Rules

The aim of the game is to make the largest product.

Each player takes it in turn to roll a dice and decide where to place the number in their calculation.

After each player completes their calculation, the player with the largest product wins.

Try a few games and see if you can improve your strategy.

Lesson
8N3.1

Fraction operators

Objectives

•Use fraction notation to describe parts of shapes and to express a smaller whole number as a fraction of a larger one; identify equivalent fractions.

•Calculate simple fractions of quantities (whole-number answers); multiply a fraction by an integer.

Starter

15 minutes

Vocabulary

decimal

equal

equivalent

fraction

of

percentage

Resources

Mini-whiteboards

Large sheets of plain paper

OHP or flipchart

Display the six key words in the vocabulary list.

QWhich key words do you recognise?

QCan you give me a fact or expression related to one or more of the key words?

For example, 5/10 is equivalent to 1/2;1/10 is the same as 10%.

Take responses from pupils, perhaps using whiteboards. Encourage them to use words, numbers, symbols and pictures. Discuss some of their examples.

QCan you give me another example, to include a statement with the equals sign?

QCan you give me an example with a labelled diagram?

QCan you use the same example for a different key word?

Ask pupils in pairs to record on blank paper particular things they know, related to the familiar words. Encourage a variety of expressions: equivalences, labelled diagrams, number lines, statements in words, etc. For example:

Circulate during this work and note examples that will be useful to share.

Next, invite pupils to the front of the class to write up an example chosen from their collection, preferably on an OHT or flipchart. Encourage a variety of responses:

QIs there another way to write this?

QIs there another diagram to show this?

Spend a few minutes discussing the collected examples, making links between them where appropriate. Conclude by explaining that in this lesson pupils will be linking their ideas together, meeting some new ideas and using fractions in practical contexts.

Main activity

35 minutes

Vocabulary

decrease

improper fraction

increase

mixed number

operator (‘of’)

Resources

Two copies each of OHTs 8N3.1a and 8N3.1b

Further copies of OHT 8N3.1b shaded to show 5×1/3 and 1/3 of 5

(If repeating for quarters, copies of OHTs 8N3.1a and 8N3.1c)

Lead into the main activity by saying that you will show some diagrams to help pupils illustrate facts they have noted. The diagrams will also link ideas together and help pupils to see why certain facts are true or certain calculations equivalent. If possible, start with an example from pupils’ contributions, finding a fraction of an amount, such as 1/3 of 15 = 5.

QCan you give me more examples of finding ‘1/3 of’?

Record the examples given by the class.