Martian Fraction Activities: Have Fraction Pieces Cut out Ready Blue Whole Strips (Use

Martian fraction activities: Have fraction pieces cut out ready blue whole strips (Use landscape A4 sheet) for the Martian and other fractions cut using other colours landscape in halves, quarters, eighths, twelfths, thirds, sixths, fifths, tenths. Set the scenario: We all know that Martians are blue (in films anyway) and that they only like to eat blue food. We have some Martian chocolate bars which we are going to use to compare with different chocolate bars we eat which are the same length but can be any colour at all.  Investigate and explore making comparisons. Use same length strips of a set of halves, quarters, eighths, twelfths. 1. Use groups (3-4) and have the children find out how many pieces make one Martian chocolate bar. Reinforce that they need to agree and be able to explain using different ways why for example ‘4 pieces (bits, slices) make one whole’ and ‘4 quarters make one whole’. Emphasise that they are comparing to one whole, and equal parts 2. Have them record on a sheet their different explanations of comparisons. They could also write the fractions as words and as symbols. If they do not use the language of fractions revoice as they say statements like 4 bits. 3. Extend to having them: Make fractions which are bigger than one whole (e.g., 4 halves is the same as 2 whole chocolate bars; 5 quarters is the same as 1 whole chocolate bar and another quarter)

Make fractions which are fractions of the fraction pieces (e.g., 2 quarters equals a half of the one whole chocolate bar)

Make fractions which mix the fractions (e.g., 2 quarters and a half make one whole chocolate bar)

Compare fractions and make statements about which are bigger or smaller (e.g., one half is bigger than one quarter, 7 eighths is bigger than one half)  Introduce fraction strips for thirds, sixths, and fraction strips for fifths and tenths. Use them integrated with the ones used previously to complete the same activities.

1. Extend to having them: Find and make fractions closest to one, a half, bigger than one

Compare fractions and make statements about which are bigger or smaller or the same.

Count in fractions going beyond one whole

Make statements they can validate with the pieces like ‘if the numerator and denominator are the same then the fractional number is the same as one whole’ or ‘if the numerator is one then the bigger the denominator the smaller the fraction’ (piece, bit)  Use problems which confront common misconceptions like those listed below.

1 Mrs Martian has made three cakes which look like this.

She decided to cut them up. First she cut them into halves. Then she cut them into quarters. Then she cut them into eighths.

The Martian children come home from school where they all have been learning about fractions and so Mrs Martian decides to question them about the cakes she cut up.

Baby Martian says that if she cut the 3 cakes into halves she must have 6 had 6 pieces or six halves or /2 Maureen Martian says that if she cut the 3 cakes into quarters she must 12 have had 12 pieces or twelve quarters or /4 Gaylene Martian says that if she cut the 3 cakes into eighths she must 24 have had 24 pieces or twenty four eighths or /8

Baby Martian who is just learning about fractions gets very confused about how they could have the same number and size cakes and yet get all the different fractional pieces. She doesn’t know if her sisters are right. Are all three of her sisters correct? How could you convince Baby Martian? Can you work out different ways to convince her?

2 This little guy from outer space is in your classroom. He is listening to Dylan and Justin and Bradley arguing about sharing a big bar of chocolate. Each one wants to eat the most so…

1 Dylan says he wants /8 of the bar of chocolate 1 Justin says he wants /4 of the bar of chocolate Bradley is laughing and he says he wants ½

Dylan says Bradley doesn’t need to laugh because he is getting more than Bradley? They ask the little guy from out of space if that is true and he explains to them who has the most. What do you think he says? In your group work out a clear explanation that you think that he gave. Can you explain what each person was thinking? They don’t believe him so he has to show them different ways to prove what he says. How many different ways can you help him to show them?

OR He is listening to Dylan and Justin and Bradley arguing about sharing a big bar of chocolate. Each one wants to eat the most so…

4 Dylan says he wants /8 of the bar of chocolate 2 Justin says he wants /4 of the bar of chocolate Bradley is laughing and he says he wants ½

3 This little guy from outer space is in your classroom. He is listening to Annie and Wade and Bradley arguing about sharing a big bar of chocolate.

2 Annie says she could have /8 of the bar of chocolate 1 Wade could have /4 of the bar of chocolate Bradley could have ½

Does that use up all the chocolate? They ask the little guy from out of space if it does and he explains to them what will happen. What do you think he says? In your group work out a clear explanation that you think that he gave. They don’t believe him so he has to show them different ways to prove what he says. How many different ways can you help him to show them? Make sure that you use fractions as one way he shows his thinking

2 Annie says she could have /8 of the bar of chocolate 2 Wade could have /4 of the bar of chocolate 4 Bradley could have /16

4 This little guy from outer space is in your room. He is listening to Annie, Wade, Ruby and Justin arguing about sharing a big bar of chocolate.

Annie says that you can only share the bar of chocolate by dividing it into halves or quarters Wade says he knows one more way of sharing the bar of chocolate Ruby and Justin say that they knows lots of ways of sharing the bar of chocolate and they can find a pattern as well

The little guy from out of space is really interested in what they say so they start to explain all the different ways to him. What do you think they say? In your group work out a clear explanation that you think they gave. He needs lots of convincing so how many different ways can you use to prove what you think they were thinking. Make sure that you use fractions as one way to show him because he likes using numbers. Can you find their pattern? OR

He is listening to Annie, Wade, Ruby and Justin arguing about sharing 3 big bars of chocolate.

Annie says that you can only share the bars by dividing it into halves or quarters Wade says he knows one more way of sharing the bars Ruby and Justin say that they knows lots of ways of sharing the bars and they can find a pattern as well The little guy from out of space is really interested in what they say so they start to explain all the different ways to him. What do you think they say? In your group work out a clear explanation that you think they gave. He needs lots of convincing so how many different ways can you use to prove what you think they were thinking. Make sure that you use fractions as one way to show him because he likes using numbers. Can you find their pattern?

5 Peter and Jack are having an argument over their homework. They have been asked if ⅝ is bigger than ¾.

Peter is arguing that because the numbers are bigger in ⅝ then ⅝ must be bigger than ¾.

Is he right or wrong? Can you work out some different ways to explain how you would solve their argument? You need to work together to convince either Peter or Jack using a range of ways including drawings, diagrams and symbols. Discuss the mathematics argument you would use and the different challenges Peter or Jack might make to your argument.

Peter and Jack are having an argument over their homework. They have 8 2 been asked if /16 is bigger than /4

8 8 Peter is arguing that because the numbers are bigger in /16 then /16 must 2 be bigger than /4

Peter and Jack are having an argument over their homework. They have 45 100 been asked if /90 is bigger than /200

100 100 Peter is arguing that because the numbers are bigger in /200 then /200 45 must be bigger than /90

6 use and the different challenges Peter or Jack might make to your argument.

Try some informal problems which will lead to adding and subtracting fractions.

Mrs Martian had just baked 2 chocolate cakes and suddenly she heard a knock on the door. Guess what? 4 friends had come to visit in their flash car! They were really hungry so she cut up the cakes and they shared them between them. She didn’t eat any because she had already had lunch. If they each ate the same amount how much did each person eat? What fraction of the three cakes did each person eat?

Mrs Martian had just baked 3 chocolate cakes and suddenly she heard a knock on the door. Guess what? 4 friends had come to visit in their flash car! They were really hungry so she cut up the cakes and they shared them between them. She didn’t eat any because she had already had lunch. If they each ate the same amount how much did each person eat? What fraction of the three cakes did each person eat?

Mrs Martian had just baked 6 chocolate cakes and suddenly she heard a knock on the door. Guess what? 4 friends had come to visit in their flash car! They were really hungry so she cut up the cakes and they shared them between them. She didn’t eat any because she had already had lunch. If they each ate the same amount how much did each person eat? What fraction of the 4 cakes did each person eat?

Mrs Martian had just baked 6 small chocolate cakes and suddenly she heard a knock on the door. Guess what? 5 friends had come to visit in their flash car! They were really hungry so she cut up the cakes and they shared them between them. She didn’t eat any because she had already had lunch. If they each ate the same amount how much did each person eat? What fraction of the six cakes did each person eat?

Mrs Martian had just baked 8 small chocolate cakes and suddenly she heard a knock on the door. Guess what? 5 friends had come to visit in their flash car! They were really hungry so she cut up the cakes and they shared them between them. She didn’t eat any because she had already had lunch. If they each ate the same amount how much did each person eat? What fraction of the six cakes did each person eat?

Mrs Martian had just baked 11 chocolate cakes and suddenly she heard a knock on the door. Guess what? 5 friends had come to visit in their flash car! They were really hungry so she cut up the cakes and they shared them between them. She didn’t eat any because she had already had lunch. If they each ate the same amount how much did each person eat? What fraction of the six cakes did each person eat?

8 Mrs Martian had just baked 1 chocolate cake and suddenly she heard a knock on the door. Guess what? 2 friends had come to visit in their flash car! They were really hungry so she cut up the cake and they shared the bits between the three of them. She ate one quarter of the cake, her friend Ruby ate another quarter but Wade had just had an ice cream so he only ate one eighth. Mrs Martian put the rest in the refrigerator for her children. How much did she put away?

Mrs Martian had just baked 1 chocolate cake and suddenly she heard a knock on the door. Guess what? 2 friends had come to visit in their flash car! They were really hungry so she cut up the cake and the three shared the bits between them. She ate one half of the cake, her friend Ruby ate one quarter but Wade had just had an ice cream so he ate one eighth. Mrs Martian put the rest in the refrigerator for her children. How much did she put away?

Mrs Martian had just baked 1 chocolate cake and suddenly she heard a knock on the door. Guess what? 2 friends had come to visit in their flash car! They were really hungry so she cut up the cake and the three shared the bits between them. She ate one third of the cake, her friend Ruby ate one quarter but Wade had just had an ice cream so he ate one twelfth. Mrs Martian put the rest in the refrigerator for her children. How much did she put away?

9 Mrs Martian loves to bake.

She has made some small cakes for her three children. They are all really hungry so they cut the cakes up and share them between the three of them. How much does each child get?

Mrs Martian loves to bake.

10 She has made some small cakes for her three children. They are all really hungry so they cut the cakes up and share them between the three of them. How much does each child get? Mrs Martian loves to bake.

She has made four small cakes for her three children. Maureen comes home from school first and she eats half a cake, then Mere comes home and she eats two quarters of a cake. Finally Greedy Martian comes home and eats one whole cake and three quarters of another cake. Mrs Martian looks at what is left and tells the children they are not allowed to eat any more because their father wants some cake too. How much is left for him? OR Mrs Martian loves to bake.

She has made six small cakes for her three children. Maureen comes home from school first and she eats a two cakes and a third of another cake, then Mere comes home and she eats one cake and two quarters of another cake. Finally Greedy Martian comes home and eats two whole cakes and three quarters of another cake. Mrs Martian looks at what is

11 left and tells the children they are not allowed to eat any more because their father wants some cake too. How much is left for him?