# Problem of the Week Problem A and Solution Measure Me

## Problem

Arezoo, Femke, Jackson, Nya, and Elisabeth made a table that recorded their heights at different stages of their lives.

Name Height at Birth Height at Age 6 Adult Height
Arezoo $$44$$ cm $$106$$ cm $$1.51$$ m
Femke $$47$$ cm $$104$$ cm $$153$$ cm
Jackson $$49$$ cm $$108$$ cm $$2$$ m
Nya $$48$$ cm $$1.11$$ m $$189$$ cm
Elisabeth $$52$$ cm $$1$$ m and $$19$$ cm $$1.84$$ m
1. Who grew the most between birth and age $$6$$? Who grew the least between birth and age $$6$$? Justify your answers.

2. Using estimation, arrange the list of friends from least growth to most growth from age $$6$$ to adulthood.

## Solution

1. One way to solve this is to convert all of the measurements into centimetres and then find the difference between each person’s height at age 6 and at birth.

Name Height at Birth Height at Age 6 Height Difference
Arezoo $$44$$ cm $$106$$ cm $$106 - 44 = 62$$ cm
Femke $$47$$ cm $$104$$ cm $$104 - 47 = 57$$ cm
Jackson $$49$$ cm $$108$$ cm $$108 - 49 = 59$$ cm
Nya $$48$$ cm $$111$$ cm $$111 - 48 = 63$$ cm
Elisabeth $$52$$ cm $$119$$ cm $$119 - 52 = 67$$ cm

Elisabeth grew the most between birth and age $$6$$.
Femke grew the least between birth and age $$6$$.

2. We will estimate the growth of each person by rounding numbers to the nearest $$10$$ cm.

Name Approximate Height at Age 6 Approximate Adult Height Approximate Difference
Arezoo $$110$$ cm $$150$$ cm $$150 - 110 = 40$$ cm
Femke $$100$$ cm $$150$$ cm $$150 - 100 = 50$$ cm
Jackson $$110$$ cm $$200$$ cm $$200 - 110 = 90$$ cm
Nya $$110$$ cm $$190$$ cm $$190 - 110 = 80$$ cm
Elisabeth $$120$$ cm $$180$$ cm $$180 - 120 = 60$$ cm

When we list the friends in order by approximate growth between age $$6$$ and adulthood, from least growth to most growth, we get:

Arezoo, Femke, Elisabeth, Nya, and Jackson

It turns out that if we determine the actual difference between each person’s adult height and height at age $$6$$, and then list the friends in order from least growth to most growth, we would get the same ordering. However, this will not always be the case. For example, if Arezoo’s adult height had been $$1.54$$ m and Femke’s adult height had been $$151$$ cm, then the order when approximating would have been the same as above, but the actual order would have been Femke, Arezoo, Elisabeth, Nya, Jackson.