In solving this problem students use the equality and inequality symbols : =, <, > to express family age relationships. As they do so, they become increasingly familiar with the meaning of each symbol: "is equal to", "is less than" and "is greater than" respectively. Students also use the comparative language of "older" and "younger".
There are four children in Marie's family. She is less than 11 years old and is the oldest. There's a two year age difference to twins, Grace and Lily, who come next. Tom, who is older than 5 is two years younger than the twins. How old are each of the children?
- Have students talk with each other about the ages of their brothers and sisters, using words older, younger.
- Using the >, < symbols record some comparative age statements for the siblings of one student.
- Ask what symbol would be used to show the age of twins (=), and why this is so.
- Read the problem to the class, emphasising that students should be able to show their solution.
- As the students work on the problem, ask them to explain their thinking using the <, > symbols.
- Share the solutions.
Write a problem using <, > or = age clues for the people in your family. Ask a classmate to see if they can solve your problem.
Marie is less than 11 and Tom is more than 5. The ages of the children are therefore 6, 7, 8, 9 or 10. The problem requires students to use common sense and logic to recognise that twins are the same age and the age range is from 6 to 10.
As there is a difference of 2 years between each year of birth, the ages must be 6, 8 and 10.
Marie’s age = 10 (check 10 < 11); and Tom’s age = 6 (check 6 > 4); and Grace’s age = 8 (check 10 – 2 = 8 and/or 6 + 2 = 8); and Lily's age = 8 (check 8 = 8).