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Bean brains

This is a level 4 number activity from the Figure It Out series. It is focused on finding equivalent proportions. A PDF of the student activity is included.

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Tags

  • AudienceKaiako
  • Learning AreaMathematics and Statistics
  • Resource LanguageEnglish
  • Resource typeActivity
  • SeriesFigure It Out

About this resource

Figure It Out is a series of 80 books published between 1999 and 2009 to support teaching and learning in New Zealand classrooms.

This resource provides the teachers’ notes and answers for one activity from the Figure It Out series. A printable PDF of the student activity can be downloaded from the materials that come with this resource.

Specific learning outcomes:

  • Find equivalent proportions.
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Bean brains

Achievement objectives

NA4-4: Apply simple linear proportions, including ordering fractions.

Required materials

  • Figure It Out, Level 3–4, Number, Book 1, "Bean brains", page 9
  • coloured beans or multilink cubes
  • a classmate

See Materials that come with this resource to download:

  • Bean brains activity (.pdf)

Activity

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Students can solve these problems by writing fractions. For example, in question 1, half of the beans are red (1/2 of 10 = 5), and in question 2, three-quarters of the beans are red (3/4 of 100 = 75).

In question 5, the students need to recognise that 3 will not divide evenly into 10, 100, or 1 000, and so there cannot be exactly one blue bean and two orange beans out of every three beans.

This concept is important when students come to write fractions as decimals because it helps to explain why 1/3 is expressed as a recurring decimal (1/3 = 0.3).

Setting the information out in tables can help solve these problems.

For example, for question 3:

Table displaying 'Beans in sample and beans in jar. There are 2 blue beans, 3 green beans making 5 total. There are 100 times more beans in the jar than in the same.

Find the number that 5 is multiplied by to get 100 (20).

Now complete the table by multiplying the other numbers in the table by the same number:

Table displaying 'Beans in sample and beans in jar. There are 2 blue beans, 3 green beans.There are 40 blue beans and 60 green beans in the jar.

An easy way to solve this problem is to use double number lines.

4 number lines totally the ratio of beans in the sample to the ones in the jar.

1.

5

2.

75 red, 25 yellow

3.

40 blue, 60 green

4.

375 blue, 625 yellow

5.

a. He is wrong because none of the jars’ contents can be divided equally into groups of 3.

b. Multiples of 3. The closest to the numbers already in the jar would be 9 beans, 99 beans, and 999 beans.

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