QTaxon 216.pmd
The Quantile Framework® for Mathematics
WORKSHEET
QT-P-216: Create, compare, contrast, and evaluate different graphic representations of the same data.
Directions: For each item, choose the best answer. 1.
The line plot shows the heights of students in 2 classes.
50
55
60
65
Inches Which stem-and-leaf plot shows the same data?
A
4 8 8 5 0 2 4 4 5 6 8 6 0 0 1 2 3 5 6 7
B
4 8 8 5 0 2 4 4 4 5 6 8 6 0 0 0 1 2 2 5 6
C
4 8 8 5 0 2 4 4 4 5 6 8 8 6 0 0 0 1 2 2 5 6
D
4 8 8 5 0 2 4 4 4 5 6 8 8 6 0 0 0 1 2 5 5 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. © 2007 MetaMetrics, Inc. All rights reserved.
QT-P-216
Quantile Framework: WORKSHEET 2.
Which bar graph shows the same information in the pictograph? Calories Burned
Each symbol = 100 calories
A
Calories Burned
B
Calories Burned
400
4
300
3
200
2
100
1
0
0
Activity
C
Calories Burned
Activity
D
Calories Burned
4
400
3
300
2
200
1
100
0
0
Activity
Activity
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. © 2007 MetaMetrics, Inc. All rights reserved.
QT-P-216
Quantile Framework: WORKSHEET 3.
Mickey made a bar graph to show the results of a survey of favorite ice cream flavors.
200
Favorite Ice Cream Flavors
150 100 50 0
Which circle graph correctly shows the information? A
Favorite Ice Cream Flavors
B
Favorite Ice Cream Flavors
Cookies ’n Cream
Butter Pecan Strawberry
Chocolate
Cookies ’n Cream
Butter Pecan
Chocolate
Strawberry
Vanilla
Vanilla
C
Favorite Ice Cream Flavors
Chocolate
Butter Pecan
Vanilla
D
Favorite Ice Cream Flavors
Cookies ’n Cream
Cookies ’n Cream Chocolate
Vanilla
Strawberry Strawberry
Butter Pecan
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. © 2007 MetaMetrics, Inc. All rights reserved.
QT-P-216
Quantile Framework: WORKSHEET 4.
An online survey about favorite animal careers is summarized in the bar graph.
6,000
Favorite Career Involving Animals
5,000 4,000 3,000 2,000 1,000 0
Which pictograph shows these results? A
Favorite Career Involving Animals
B
Favorite Career Involving Animals
Circus-animal trainer
Circus-animal trainer
Rodeo star
Rodeo star
Pet store owner
Pet store owner
Zookeeper
Zookeeper
Veterinarian
Veterinarian = 1,000 people
C
Favorite Career Involving Animals
= 1,000 people
D
Favorite Career Involving Animals
Zookeeper
Zookeeper
Veterinarian
Veterinarian
Rodio star
Rodio star
Pet store owner
Pet store owner
Circus-animal trainer
Circus-animal trainer = 1,000 people
= 1,000 people
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. © 2007 MetaMetrics, Inc. All rights reserved.
QT-P-216
Quantile Framework: WORKSHEET 5.
Mrs. Carter made a stem-and-leaf plot of the scores on a math test.
Math Test Scores 9 8 7 6 5 4 3
0 1 0 3 2
0 1 2 5 9
2 1 5 5
3 7 8 8 3 3 4 6 6 7 6 9
Letter Grades for Test Scores A B C D F
= = = = =
90 80 70 60 50
-
100 89 79 69 69
Key: 7 2 represents 72 Which circle graph shows the same information?
A
Letter Grades of Math Test Scores D
B
Letter Grades of Math Test Scores
F F
C
B
D
A
C
A
B
C
Letter Grades of Math Test Scores
D
Letter Grades of Math Test Scores F
F D
A
D
A
C
C B
B
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. © 2007 MetaMetrics, Inc. All rights reserved.
QT-P-216
Quantile Framework: WORKSHEET
The bar graph shows the monthly totals of miles walked by the members of the walking club. Walking Club Totals Miled Walked
10 8 6
4 2
M
ay
ril Ap
Ja
nu ar y Fe br ua ry M ar ch
0
Month
Which line graph shows this information correctly? Walking Club Totals
B Miles Walked
9 8 4 2 1 0 Ja
Ja
nu
nu Fe ary br ua ry M ar ch Ap ril M ay
Miles Walked
10 8 6 4 2 0
Walking Club Totals
Fe ary br ua ry M ar ch Ap ril M ay
A
Month
Walking Club Totals
D
Walking Club Totals
10
Month
8 6 4 2 0 Fe ary br ua ry M ar ch Ap ril M ay
Ja
nu
Fe ary br ua ry M ar ch Ap ril M ay
8 6 4 2 0
nu
Miles Walked
10
Month
Ja
C Miles Walked
6.
Month
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. © 2007 MetaMetrics, Inc. All rights reserved.
QT-P-216
Quantile Framework: WORKSHEET Which is true concerning the two graphs below?
Price in Dollars
Price of CD 12 10 8 6 4 2 0
Store A Store B Store C
Store D
Price of CD Price in Dollars
7.
12 11 10 Store A Store B Store C Store D
A
same information, different scale on the vertical axis
B
same information, different scale on the horizontal axis
C
different information, prices are different
D
different information, stores are different
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. © 2007 MetaMetrics, Inc. All rights reserved.
Quantile Framework: WORKSHEET
QT-P-216
KEY 1. C 2. A 3. B 4. B 5. D 6. C 7. 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. © 2007 MetaMetrics, Inc. All rights reserved.
WORKSHEET
QT-P-216: Create, compare, contrast, and evaluate different graphic representations of the same data.
Directions: For each item, choose the best answer. 1.
The line plot shows the heights of students in 2 classes.
50
55
60
65
Inches Which stem-and-leaf plot shows the same data?
A
4 8 8 5 0 2 4 4 5 6 8 6 0 0 1 2 3 5 6 7
B
4 8 8 5 0 2 4 4 4 5 6 8 6 0 0 0 1 2 2 5 6
C
4 8 8 5 0 2 4 4 4 5 6 8 8 6 0 0 0 1 2 2 5 6
D
4 8 8 5 0 2 4 4 4 5 6 8 8 6 0 0 0 1 2 5 5 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. © 2007 MetaMetrics, Inc. All rights reserved.
QT-P-216
Quantile Framework: WORKSHEET 2.
Which bar graph shows the same information in the pictograph? Calories Burned
Each symbol = 100 calories
A
Calories Burned
B
Calories Burned
400
4
300
3
200
2
100
1
0
0
Activity
C
Calories Burned
Activity
D
Calories Burned
4
400
3
300
2
200
1
100
0
0
Activity
Activity
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. © 2007 MetaMetrics, Inc. All rights reserved.
QT-P-216
Quantile Framework: WORKSHEET 3.
Mickey made a bar graph to show the results of a survey of favorite ice cream flavors.
200
Favorite Ice Cream Flavors
150 100 50 0
Which circle graph correctly shows the information? A
Favorite Ice Cream Flavors
B
Favorite Ice Cream Flavors
Cookies ’n Cream
Butter Pecan Strawberry
Chocolate
Cookies ’n Cream
Butter Pecan
Chocolate
Strawberry
Vanilla
Vanilla
C
Favorite Ice Cream Flavors
Chocolate
Butter Pecan
Vanilla
D
Favorite Ice Cream Flavors
Cookies ’n Cream
Cookies ’n Cream Chocolate
Vanilla
Strawberry Strawberry
Butter Pecan
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. © 2007 MetaMetrics, Inc. All rights reserved.
QT-P-216
Quantile Framework: WORKSHEET 4.
An online survey about favorite animal careers is summarized in the bar graph.
6,000
Favorite Career Involving Animals
5,000 4,000 3,000 2,000 1,000 0
Which pictograph shows these results? A
Favorite Career Involving Animals
B
Favorite Career Involving Animals
Circus-animal trainer
Circus-animal trainer
Rodeo star
Rodeo star
Pet store owner
Pet store owner
Zookeeper
Zookeeper
Veterinarian
Veterinarian = 1,000 people
C
Favorite Career Involving Animals
= 1,000 people
D
Favorite Career Involving Animals
Zookeeper
Zookeeper
Veterinarian
Veterinarian
Rodio star
Rodio star
Pet store owner
Pet store owner
Circus-animal trainer
Circus-animal trainer = 1,000 people
= 1,000 people
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. © 2007 MetaMetrics, Inc. All rights reserved.
QT-P-216
Quantile Framework: WORKSHEET 5.
Mrs. Carter made a stem-and-leaf plot of the scores on a math test.
Math Test Scores 9 8 7 6 5 4 3
0 1 0 3 2
0 1 2 5 9
2 1 5 5
3 7 8 8 3 3 4 6 6 7 6 9
Letter Grades for Test Scores A B C D F
= = = = =
90 80 70 60 50
-
100 89 79 69 69
Key: 7 2 represents 72 Which circle graph shows the same information?
A
Letter Grades of Math Test Scores D
B
Letter Grades of Math Test Scores
F F
C
B
D
A
C
A
B
C
Letter Grades of Math Test Scores
D
Letter Grades of Math Test Scores F
F D
A
D
A
C
C B
B
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. © 2007 MetaMetrics, Inc. All rights reserved.
QT-P-216
Quantile Framework: WORKSHEET
The bar graph shows the monthly totals of miles walked by the members of the walking club. Walking Club Totals Miled Walked
10 8 6
4 2
M
ay
ril Ap
Ja
nu ar y Fe br ua ry M ar ch
0
Month
Which line graph shows this information correctly? Walking Club Totals
B Miles Walked
9 8 4 2 1 0 Ja
Ja
nu
nu Fe ary br ua ry M ar ch Ap ril M ay
Miles Walked
10 8 6 4 2 0
Walking Club Totals
Fe ary br ua ry M ar ch Ap ril M ay
A
Month
Walking Club Totals
D
Walking Club Totals
10
Month
8 6 4 2 0 Fe ary br ua ry M ar ch Ap ril M ay
Ja
nu
Fe ary br ua ry M ar ch Ap ril M ay
8 6 4 2 0
nu
Miles Walked
10
Month
Ja
C Miles Walked
6.
Month
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. © 2007 MetaMetrics, Inc. All rights reserved.
QT-P-216
Quantile Framework: WORKSHEET Which is true concerning the two graphs below?
Price in Dollars
Price of CD 12 10 8 6 4 2 0
Store A Store B Store C
Store D
Price of CD Price in Dollars
7.
12 11 10 Store A Store B Store C Store D
A
same information, different scale on the vertical axis
B
same information, different scale on the horizontal axis
C
different information, prices are different
D
different information, stores are different
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. © 2007 MetaMetrics, Inc. All rights reserved.
Quantile Framework: WORKSHEET
QT-P-216
KEY 1. C 2. A 3. B 4. B 5. D 6. C 7. 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. © 2007 MetaMetrics, Inc. All rights reserved.
