Mult-e-Maths



Calculating with fractions 4NUM23

National curriculum objective

Pupils should be taught to:

• add and subtract fractions with the same denominator.

Prior knowledge and skills

• Add and subtract fractions with the same denominator within one whole [for example, 5/7 + 1/7 = 6/7].

Vocabulary

denominator, numerator, equivalent, add, subtract, improper fraction, mixed number

Resources

• small whiteboards and pens

• counting stick (or metre rule)

• Resource sheet 1 (fraction strips laminated and cut out), one per pair

• Resource sheet 2

Oral and mental starter

Rehearse counting in steps of different sizes using the counting stick. Tell pupils that zero is at one end of the counting stick and 250 is at the other. Establish that they need to count in 25s to get from zero to 250. Together, count in 25s from zero to 250 and back again. Repeat this but jump your finger around so that the pupils have to think about how many 25s there are in random numbers. Ask pupils to tell you which division you should touch to show 125, 200 etc. Repeat this for zero to 1 and zero to 0.1

Q What do we need to count in steps of to get from zero to 0.1? (Hundredths) How do you know?

Main teaching activity

Whole class

(Screen 1: Activity 1, Question 1)

Q What fractions can you see here? (Halves, quarters and eighths.) How do you know? (Halves are one whole divided into two equal parts; quarters are one whole divided into four equal parts; eighths are one whole divided into eight equal parts.)

Ask pupils to talk with a partner about the equivalent fractions that they can see on the board. After a few minutes take feedback. Agree these equivalences: 8/8 = 1; 4/8 = 1/2; 2/8 = 1/4; 6/8 = 3/4; 4/4 = 1; 2/4 = 1/2; and 1/2 + 1/4 = 3/4.

Q How do we add fractions with the same denominator? (Add the numerators.) … with a different denominator?

Elicit that if they are adding two fractions with a different denominator, they can use a fraction wall (or strips) to help them. Remove The hide panel. For example, 1/2 + 2/8. Using the fraction wall on the board, they can see that 1/2 + 2/8 = 3/4 by lining up 1/2 and 2/8 side by side up against the three of the quarter strips. Alternatively, pupils might see that 1/2 is equivalent to 2/4 and that 2/8 is equivalent to 1/4. So, 1/2 + 2/8 is equivalent to 2/4 + 1/4 = 3/4. This is demonstrated in the bottom right-hand of the screen.

Using this new idea, return to equivalences. Can they tell you any other ways to make one whole, this time using a mixture of fractions with different denominators? E.g., 1/2 + 1/4 + 2/8. What about making 3/4?

Pairs

Give pairs a set of fraction strips from Resource sheet 1, for halves, quarters and eighths. Ask them to explore different ways to make half, three quarters and one whole. They could record their ideas on their small whiteboards. After about five minutes take feedback, inviting pairs to show their ideas on the board as fraction number statements e.g., 4/8 + 2/8 = 6/8 = 3/4; 4/8 + 1/4 = 3/4.

Groups of 4

Ask pupils to work in fours to make up some addition number sentences using two sets of fraction strips. Their answers need to be greater than one whole. Remind them that 8/8 = 1; 4/4 = 1; 2/2 = 1. So, 4/4 + 1/2 = 1 + 1/2 = 11/2.

Q What would 1/4 + 1/4 + 1/4 + 1/4 + 1/4 + 1/4 (six quarters) equal? (12/4, or 11/2)

Ask groups to prove this by laying out six quarter strips and putting one whole strip and one half strip above or below it.

Encourage pupils to create their number sentences using fractions with the same denominator initially, and then to add fractions with different denominators using the fraction strips to help them find equivalent fractions e.g., replacing 2/4 + 1/4 + 1/4 + 1/4 = 11/4 with 1/2 + 2/8 + 2/4 = 11/4.

Whole class

Take feedback from the group activity, writing appropriate fraction number statements on the board. For example, 1/2 + 1/2 + 1/2 = 11/2; 1/4 + 1/4 + 1/4 + 1/4 + 1/4 = 11/4.

(Screen 2: Activity 2, Question 1)

Q What fractions can you see on this page? (Thirds, sixths and twelfths.) How do you know? (Thirds are one whole divided into three equal parts; sixths are one whole divided into six equal parts; and twelfths are one whole divided into 12 equal parts.)

Ask pupils to write fraction equivalences on their whiteboards, for example, 3/3 = 1; 2/6 = 1/3; 4/12 = 1/3; 1/6 = 2/12. Ask them to tell you which fractions are equivalent to one half: 3/6 and 6/12. You can invite some pupils to demonstrate their equivalences on the board using the fraction bars (once placed together these will stick together, so only a few examples can be displayed at one time).

Q How many twelfths are the same as 1 and a half? (18) How do you know? (12 twelfths is equivalent to 1, and 6 twelfths are equivalent to half, and 12 + 6 = 18)

Write 18/12 on the board and tell pupils that fractions with numerators that are the same as or more than the denominator are called improper fractions. Improper fractions will make mixed numbers, in this case 16/12 or 11/2.

Pairs

Give pairs of a set of fraction strips from Resource sheet 1 for thirds, sixths and twelfths. Ask them to explore different ways to make thirds, sixths, twelfths and one whole. After about five minutes take feedback, inviting pairs to show their ideas on the board as fraction number statements.

Groups of 4

Ask pupils to work in fours to make up some addition and subtraction number sentences using two sets of fraction strips. Their answers need to be given as improper fractions and then mixed numbers as appropriate. For example, 5/6 + 3/6 = 8/6 = 12/6 or 11/3; 110/12 – 5/12 = 15/12. Encourage them to use fractions with the same denominator initially and then to explore mixing them using their fraction strips (e.g., replacing 5/6 + 3/6 = 12/6 with 5/6 + 6/12 = 12/6).

Q What would 4/3 equal? (11/3)

Ask groups to prove this by laying out four third strips and putting one whole strip and one third strip above or below it.

Whole class

Take feedback from the group activity, writing appropriate improper fractions and their mixed number equivalents on the board. For example, 5/6 + 2/6 = 7/6 = 11/6; 11/12 + 11/12 = 22/12 = 110/12.

Individuals

Pupils complete Resource sheet 2. You might need to select questions depending on the level of your class. They make up some addition and subtraction fraction number statements, converting improper fractions to mixed numbers. Let pupils use their fraction strips as visual representations to help them.

Other tasks

You could ask pupils to:

• explore adding fractions with different denominators. For example, halves, quarters and eighths; thirds, sixths and twelfths.

• convert improper fractions to mixed numbers and vice versa.

• explore adding and subtracting fractions within the context of measures. For example, time, length, kilograms and litres.

Review

Take feedback from Resource sheet 2. Work through question 1 together. Invite pupils to draw fraction strips to show each addition and subtraction.

Invite pupils to share the addition and subtractions that they made up and together check that these are correct. Did anyone add and subtract a mixture of fractions, for example 1/5 + 9/10 = 11/10? You could finish the lesson by asking the pupils to add and subtract different numbers of halves, fifths and tenths. For example 1/2 + 1/2 + 1/2; 3/5 + 1/5; 3/10 + 4/10.

Key idea and assessment

To add fractions that have the same denominator, add the numerators together. When fractions add to make a number greater than 1, the fraction can be written as an improper fraction, where the numerator is larger than the denominator, or as a mixed number. You can add fractions with different denominators by using a fraction wall or strips to find equivalent fractions with the same denominators.

Can pupils:

• add and subtract fractions that have the same denominator when the sum is less than or equal to one whole … greater than one whole?

• change improper fractions to mixed numbers?

• change mixed numbers to improper fractions?

Solutions

Resource Sheet 2

1. a. 2/4 or 1/2 b. 2/3 c. 2/4 or 1/2

d. 1 e. 4/6 or 2/3 f. 5/8

2 Opened ended activity. Look out for pupils who are able to use fractions with different denominators when they add and subtract. At this level, being able to use different denominators like this represents an understanding of equivalent fractions e.g., adding 1/2 is the same as adding 4/8.

................
................

In order to avoid copyright disputes, this page is only a partial summary.

Google Online Preview   Download