The Quantile Framework® for Mathematics
WORKSHEET
QT-G-302: Use the Pythagorean Theorem and its converse
to solve problems.
Directions: For each item, choose the best answer.
1.
The local playground would like to
build a 13-foot slide. The slide is
5 feet above the ground.
2.
Joe’s bike ramp begins 7 feet above
the ground. The ramp itself will fit in a
space that is exactly 20 feet in length.
13 feet
5 feet
x
7 feet
20 feet
Ground Space
How much ground space will be needed
for this slide?
To the nearest foot, how long is the
path, x, up the ramp?
A
4 feet
A
20 feet
B
5 feet
B
21 feet
C
7 feet
C
22 feet
D
12 feet
D
23 feet
THIS WORKSHEET IS THE PROPERTY OF METAMETRICS, INC. AND IS INTENDED FOR INSTRUCTIONAL USE ONLY.
No portion of this worksheet may be reproduced in any form for commercial use or resale. MetaMetrics, Quantile,
Quantile Framework and the Quantile symbol are trademarks or U.S. registered trademarks of MetaMetrics, Inc.
© 2008 MetaMetrics, Inc. All rights reserved.
QT-G-302
Quantile Framework: WORKSHEET
3.
What is the length of side a in the
right triangle shown below?
(Round answer to the nearest tenth.)
5.
16
a
4.
23
A
7.0 units
B
16.5 units
C
22.3 units
D
28.0 units
A rectangle measures 6 centimeters
by 4 centimeters. What is the best
estimate for the measure of a diagonal
in this rectangle?
A
3 centimeters
B
5 centimeters
C
7 centimeters
6.
What is the length of a leg of a right
triangle when its hypotenuse measures
11.2 cm and its other leg measures
4.5 cm? (Round answer to the nearest
hundredth.)
A
6.70 cm
B
10.26 cm
C
12.02 cm
D
105.19 cm
Which of these measures could not
be the lengths of the sides of a
right triangle?
A
4, 10, 16
B
5, 12, 13
C
7, 24, 25
D
8, 15, 17
D 12 centimeters
THIS WORKSHEET IS THE PROPERTY OF METAMETRICS, INC. AND IS INTENDED FOR INSTRUCTIONAL USE ONLY.
No portion of this worksheet may be reproduced in any form for commercial use or resale. MetaMetrics, Quantile,
Quantile Framework and the Quantile symbol are trademarks or U.S. registered trademarks of MetaMetrics, Inc.
© 2008 MetaMetrics, Inc. All rights reserved.
QT-G-302
Quantile Framework: WORKSHEET
7.
Which triangle will have an
irrational number for the length
of its hypotenuse?
8.
Which triangle must be a right
triangle?
A
A
2
6
3
2 3
4
B
B
14
9
2
12
3
C
C
6
5
4
3
D
3
10
D
10
11
8
6
THIS WORKSHEET IS THE PROPERTY OF METAMETRICS, INC. AND IS INTENDED FOR INSTRUCTIONAL USE ONLY.
No portion of this worksheet may be reproduced in any form for commercial use or resale. MetaMetrics, Quantile,
Quantile Framework and the Quantile symbol are trademarks or U.S. registered trademarks of MetaMetrics, Inc.
© 2008 MetaMetrics, Inc. All rights reserved.
Quantile Framework: WORKSHEET
9.
How long are the legs of the right
triangle? (Round answer to the
nearest centimeter.)
24 cm
x cm
x cm
A
17 cm
B
15 cm
C
14 cm
D
12 cm
THIS WORKSHEET IS THE PROPERTY OF METAMETRICS, INC. AND IS INTENDED FOR INSTRUCTIONAL USE ONLY.
No portion of this worksheet may be reproduced in any form for commercial use or resale. MetaMetrics, Quantile,
Quantile Framework and the Quantile symbol are trademarks or U.S. registered trademarks of MetaMetrics, Inc.
© 2008 MetaMetrics, Inc. All rights reserved.
QT-G-302
Quantile Framework: WORKSHEET
QT-G-302
KEY
1. D
2. B
3. B
4. C
5. B
6. A
7. B
8. A
9. A
The Quantile Framework for Mathematics™ uses a common, developmental scale to measure both the student’s
mathematical achievement and the difficulty of mathematical tasks for a student. The Quantile Framework uses a
Quantile measure to describe (1) a student’s mathematical achievement and (2) the difficulty of specific mathematical
skills and concepts. The Quantile Framework empowers teachers to target instruction, forecast student understanding
and improve mathematics instruction and achievement. The mathematics curriculum, the materials to teach
mathematics and the students themselves are all described with the same metric.
The Quantile Framework takes the guesswork out of mathematics instruction. With a student’s Quantile measure, a
teacher can match students to resources, like this worksheet, in order to help a student with practicing a mathematics
concept they have just learned or those in which the student requires more instruction.
This Quantile Framework worksheet can be used in the following ways:
1.
2.
3.
4.
5.
6.
7.
As a whole-class practice activity on this skill/concept
As individualized practice for a specific student or group of students
As an informal diagnostic tool to assess prior knowledge of this skill/concept
As an informal whole class or individualized assessment
As part of a center, laminated, for a group of students or for individual practice
As homework for the whole-class or an individual student
As a parent resource to indicate the type of questions this skill or concept covers
THIS WORKSHEET IS THE PROPERTY OF METAMETRICS, INC. AND IS INTENDED FOR INSTRUCTIONAL USE ONLY.
No portion of this worksheet may be reproduced in any form for commercial use or resale. MetaMetrics, Quantile,
Quantile Framework and the Quantile symbol are trademarks or U.S. registered trademarks of MetaMetrics, Inc.
© 2008 MetaMetrics, Inc. All rights reserved.