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Chapter 8 Performance Assessment 15

Name

Tammy is planning her training for a 15-mile race. She wants to run in the nearby park, on the trails shown in the map.

1. For the first few days of her training, Tammy wants to runabout �

14� of the length of the race. Explain how to estimate

how far she should run.

2. Describe a path in the park that is close to �14� of 15. Explain

how to estimate the length of this path.

3. Find �14� of 15 miles and the exact length of the path you

chose in Exercise 2. With the path you chose, will Tammyrun more or less than �

14� of 15? How much more or less?

4. Tammy wants to increase her distance every few days to�13�, �

12�, �

34� of 15 miles, and then the whole 15 miles. Repeat the

process above and complete the table. To describe eachpath, use L for the lodge and M for a marker. For example,a path from the lodge to marker 1 to marker 2 and backwould be L to M1 to M2 and back.

2 mi18

2 mi38

1 mi141 mi

18

mi34

Marker1

Marker2

Marker5

Marker4

Marker3

Lodge

1 mi18

1 mi121 mi

14

1 mi78

Chapter 8 Performance Assessment

1413

Goal Path DifferenceLength of PathFraction of 15 MilesEstimate Exact Estimate Exact

1234

© P

ears

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Ed

ucat

ion,

Inc

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16 Chapter 8 Performance Assessment

Chapter 8 Performance Assessment

Teacher Notes Scoring RubricConcepts and Skills This activity requires students to:• estimate sums and products of mixed

numbers.• multiply fractions, whole numbers, and

mixed numbers.• add and subtract fractions and mixed

numbers.

Guiding the Activity• Encourage students to look for compatible

numbers like 1�78� and 1�

18� when they are

adding more than two mixed numbers.

Answers1. To estimate �

14� � 15, change 15 to 16, which

is a multiple of the denominator 4. A goodestimate is �

14� of 16 or 4. Tammy should run

about 4 miles.2. Sample answer: The lodge to marker 1 to

marker 3 and back is close to 4 miles; �34� � 1�

18� is about 1 � 1 � 2 and 2 � 2 � 4.

3. 3�34� mi; Sample answers based on the path

described in Exercise 2: 3�34� mi; the path is

the same as �14� of 15.

4. Sample answers are shown.

3 mi34 3 mi

34

4 mi14 mi

34

mi18

mi14

14

13

Goal Path DifferenceLength of PathFraction of 15 Miles

Estimate Exact Estimate Exact

4 mi

5 mi

4 mi 0

over 4 mi

L to M1to M3

and back

L to M5and back5 mi

7 mi12 7 mi

58

12

8 mi 7 miL to M1to M3to M4to M5to L

11 mi14 11 mi

34

14

12 mi 12 miL to M1to M2to M5to L

twice

Level Standard to be achieved for performance at specified level

4 Full Achievement The studentadded, subtracted, and multipliedfractions, whole numbers, and mixednumbers without error. The studentshowed a thorough understanding of estimating sums and products ofmixed numbers. Explanations werewell written.

3 Substantial Achievement The student added, subtracted, and multiplied fractions, whole numbers,and mixed numbers with only minorerrors. The student showedconsiderable understanding ofestimating sums and products ofmixed numbers. Explanations werebasically well written.

2 Partial Achievement The studentmade considerable errors adding,subtracting, and multiplying fractions,whole numbers, and mixed numbers.The student showed littleunderstanding of estimating sumsand products of mixed numbers.Explanations were fairly complete,but not well written.

1 Little Achievement The studentmade numerous errors adding,subtracting, and multiplying fractions,whole numbers, and mixed numbers.The student showed little or nounderstanding of estimating sumsand products of mixed numbers.Explanations were missing or unclear.

0 No Achievement The studentprovided a completely incorrectresponse, one that was notinterpretable, or no response at all.