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WhiteSpace.gif (818 bytes) How old?                                                                Algebra, Level 2

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There is a family with four children. Between each child there is an age difference of 2 years. The oldest child, Maryanne is less than 11 years old. The youngest child, Tom, is older than 5. In between Maryanne and Tom are the twins – Claudia and Cassie. What is the age of each child in this family?

What is the problem about?
This problem involves age relationships as number sentences, where students can use mathematical symbols: =, <, > for the relationships "is equal to", "is less than" and "is greater than" respectively.
The problem also involves concepts of measurement like "older" and "younger".
The problem requires students to use common sense and logic to realise that twins will be of the same age and the age range is from 6 to 10.

Achievement Objectives
Algebra, level 2
- use the mathematical symbols =,<,> for the relationships "is equal to", "is less than" and "is greater than".
Mathematical Processes
– devise and use problem solving strategies.

Resources
- Cards with the symbols =, >, <
- Copymaster of the problem (English)
- Pictures of 4 children

Specific learning outcomes
Children will be able to:
- write and talk about number sentences using =, <, >.
- make simple deductions

Teaching Sequence

  1. Display the 4 pictures – ask the children to make statements that could be true using the pictures.
  2. Ask the children to make statements about the pictures using the >, < symbols.
  3. Read the problem to the class.
  4. Discuss the words older, younger and twins.
  5. Brainstorm for ways to solve the problem.
  6. As the students work on the problem, ask them to explain their thinking using the <, > symbols. (unless you sepcfically ask the children to use the symbols we believe its liley that they won't use them in the solution). Ask them to explain how they know which symbol to use.
  7. Encourage the children to use the symbols in their record of the solution.
  8. Share the solutions.

Solution
If the oldest child is less than 11 and the youngest child is more than 5, the ages of the children will be between 5 and 11. So write all the numbers between 5 and 11, that is 6, 7, 8, 9, 10.
As there is a difference of 2 years between each year of birth, the ages must be 6, 8 and 10.
So Maryanne’s age = 10 (check 10 < 11); and Tom’s age = 6 (check 6 > 5); and Claudia’s age = 8 (check 10 – 2 = 8 and/or 6 + 2 = 8); and Cassie’s age = 8 (check 8 = 8). 
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