Question

mrs. welch surveyed her students about how much they had grown over the past year. this is the data she gathered.
student growth over
the past year
(to the nearest $\frac{1}{2}$ inch)

$1\frac{1}{2}$	$1\frac{1}{2}$
$2\frac{1}{2}$	$2$
$\frac{1}{2}$	$1\frac{1}{2}$
$2\frac{1}{2}$	$\frac{1}{2}$
$1$	$2$
$1\frac{1}{2}$	$2$
$1\frac{1}{2}$	$\frac{1}{2}$
$3\frac{1}{2}$	$1\frac{1}{2}$
$1$	$1$
$1$	$2\frac{1}{2}$
$2$	$2$
$2\frac{1}{2}$	$1\frac{1}{2}$

① plot the data set on the line plot.
title
label

use the completed line plot to answer the questions.
② what is the greatest number of inches a student grew in a year?
about ____ inch(es) the least? about ____ inch(es)
③ what is the difference between the greatest and the least number of inches grown?
number model with unknown: __________ answer: ____ inch(es)

practice
circle the three equivalent fractions in each group.
④ $\frac{1}{4}, \frac{3}{6}, \frac{1}{8}, \frac{2}{8}, \frac{3}{12}$
⑤ $\frac{3}{4}, \frac{4}{8}, \frac{6}{8}, \frac{5}{6}, \frac{9}{12}$
⑥ $\frac{2}{3}, \frac{1}{5}, \frac{4}{6}, \frac{7}{12}, \frac{8}{12}$
⑦ $\frac{1}{2}, \frac{5}{10}, \frac{4}{8}, \frac{7}{12}$

Explanation:

Step1: Tally data values

First, count occurrences of each growth value:

• $\frac{1}{2}$: 3 times
• $1$: 3 times
• $1\frac{1}{2}$: 7 times
• $2$: 6 times
• $2\frac{1}{2}$: 5 times
• $3\frac{1}{2}$: 1 time

Step2: Answer question 2

Identify max and min values from data:
Greatest value = $3\frac{1}{2}$, Least value = $\frac{1}{2}$

Step3: Calculate difference (question3)

Subtract least from greatest:
$$3\frac{1}{2} - \frac{1}{2} = 3$$
Number model: $3\frac{1}{2} - \frac{1}{2} = x$

Step4: Find equivalent fractions (practice)

For group 4:

Simplify fractions:
$\frac{3}{6}=\frac{1}{2}$, $\frac{2}{8}=\frac{1}{4}$, $\frac{3}{12}=\frac{1}{4}$
Equivalent: $\frac{1}{4}, \frac{2}{8}, \frac{3}{12}$

For group 5:

Simplify fractions:
$\frac{4}{8}=\frac{1}{2}$, $\frac{6}{8}=\frac{3}{4}$, $\frac{9}{12}=\frac{3}{4}$
Equivalent: $\frac{3}{4}, \frac{6}{8}, \frac{9}{12}$

For group 6:

Simplify fractions:
$\frac{2}{3}=\frac{8}{12}$, $\frac{4}{6}=\frac{2}{3}$
Equivalent: $\frac{2}{3}, \frac{4}{6}, \frac{8}{12}$

For group 7:

Simplify fractions:
$\frac{5}{10}=\frac{1}{2}$, $\frac{4}{8}=\frac{1}{2}$
Equivalent: $\frac{1}{2}, \frac{5}{10}, \frac{4}{8}$

Answer:

1. (Line plot: Place 3 marks above $\frac{1}{2}$, 3 marks above $1$, 7 marks above $1\frac{1}{2}$, 6 marks above $2$, 5 marks above $2\frac{1}{2}$, 1 mark above $3\frac{1}{2}$)
2. Greatest: $3\frac{1}{2}$; Least: $\frac{1}{2}$
3. Number model: $3\frac{1}{2} - \frac{1}{2} = x$; Answer: $3$
4. Equivalent fractions: $\frac{1}{4}, \frac{2}{8}, \frac{3}{12}$
5. Equivalent fractions: $\frac{3}{4}, \frac{6}{8}, \frac{9}{12}$
6. Equivalent fractions: $\frac{2}{3}, \frac{4}{6}, \frac{8}{12}$
7. Equivalent fractions: $\frac{1}{2}, \frac{5}{10}, \frac{4}{8}$