Proper Fractions-Assessment Task - LearnAlberta.ca · • name and record fractions for the parts of a whole or a set ... Math Live – Proper Fractions: Assessment Task . The government

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Math Live – Proper Fractions: Assessment Task

Grade: 4 Strand: Number Outcome: 8 SPECIFIC LEARNER OUTCOME – Number

N8 Demonstrate an understanding of fractions less than or equal to one by using concrete, pictorial and symbolic representations to: • name and record fractions for the parts of a whole or a set • compare and order fractions • model and explain that for different wholes, two identical fractions may not represent the same quantity • provide examples of where fractions are used.

PROCESSES Communication (C), Connections (CN), Mental Mathematics and Estimation (ME), Problem Solving (PS), Reasoning (R), Technology (T), Visualization (V)

C, CN, PS, R, V EVIDENCE the student has achieved the outcomes

Each student will: • Analyze different pictorial representations of fractions. • Build models of fractions using manipulatives. • Draw and compare representations of proper fractions. • Describe proper fractions by relating the symbolic representation of a fraction to its

pictorial representation. TEACHER NOTES • In the assessment task, students will be asked to demonstrate their understanding of

fractions as parts of a whole and as parts of a set. They will first identify models that represent the fraction of all Aboriginal Canadians under the age of 15 (2/6). Students then describe how they decided which models represent this fraction. Next, students will build two models of another fraction and draw a representation of their model, explaining the similarities and differences between the models. Finally, students explain the role of equal parts, numerators, and denominators in proper fractions.

• Students should have access to a variety of manipulatives to represent fractions including tiles, paper for fraction strips, and counters such as chips and grid paper.

• Students should understand that proper fractions can represent parts of a whole or parts of a set. They should also be able to explain the importance of “equal-sized” parts in creating fractions as well as the role of the numerator and denominator. Some representations students may draw for fractions are:

Some misconceptions to watch for are:

a) identifying parts as the denominator. “2/6” rather than 2/8

b) confusing the numerator and denominator. “shaded portion represents 2/6”

c) thinking all fractions are symmetrical “does not represent 2/6”

• Fractions as parts of sets do not need to be like objects in shape or size!

Circles represent 2/4 of this set

• Early finishers can make fraction strips to find out which represents a larger fraction:

1/5 (all Canadians younger than 15), or 2/6 (all Aboriginal Canadians younger than 15).



Math Live – Proper Fractions: Assessment Task The government estimates that about 1/5 of all Canadians are 14 years old or younger. About 2/6 of the total Aboriginal population are 14 years old or younger.

Population by Age

0-14 years old

15-34 years old

35 years and older

All Canadians 1/5 3/10 1/2

All Aboriginal Canadians 2/6 5/12 1/4

1. Circle the models below that represent the fraction 2/6.

2. Choose another fraction from the chart above. Use manipulatives to build two different types of models of this fraction. Draw a picture of your models below. Explain how your two models are alike and how they are different.


3. Choose two of the models you circled in Question 1 and explain how you decided they represented 2/6. Choose one model that you did not circle and tell why it doesn’t represent 2/6. Use words and pictures to show your reasoning.


Math Live – Proper Fractions: Scoring Guide Level

Criteria Wow!

Analyzes different pictorial

representations of proper fractions

Question #1

Correctly identifies the

six models that

Draws and compares pictorial representations of proper fractions

Question #2

Draws uniquely different models of the

same fraction and compares them in clear mathematical

terms

Describes proper fractions

Question #3 Describes models

using precise mathematical criteria and clearly explains the misconception contained in the counter-example

Yes

represent 2/6 Draws different models of the same

fraction and compares them using some

mathematical language

Describes the models using some

mathematical terms and describes the

fraction represented by the counter-

example

Yes, but…

Identifies the six models that represent

2/6 as well as one other which does not

represent 2/6

Draws similar models of the same fraction

and/or compares them in only general

terms

Describes the models in general terms

and/or simply names the fraction

represented by the counter-example

No, but…

Fails to identify the six fractions that represent 2/6

Draws models of two different fractions and/or compares

them with little or no evidence of

understanding of fractions

Describes the models in vague or incorrect terms and/or fails to

describe the counter- example in a

mathematical way

Insufficient / Blank

No score awarded due to insufficient

evidence of student learning based on the requirements of the

assessment task



assessment task



assessment task



Wow!

The government estimates that about 1/5 of all Canadians are 14 years old or younger. About 2/6 of the total Aboriginal population are 14 years old or younger.

Population by Age

0-14 years old

15-34 years old

35 years and older






Wow!

3. Choose two of the models you circled in Question 1 and explain how you

decided they represented 2/6. Choose one model that you did not circle and tell why it doesn’t represent 2/6. Use words and pictures to show your reasoning.


Yes



Population by Age

0-14 years old

15-34 years old

35 years and older






Yes 3. Choose two of the models you circled in Question 1 and explain how you



Yes, but



Population by Age

0-14 years old

15-34 years old

35 years and older






Yes, but 3. Choose two of the models you circled in Question 1 and explain how you



No, but



Population by Age

0-14 years old

15-34 years old

35 years and older






No, but 3. Choose two of the models you circled in Question 1 and explain how you


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Proper Fractions-Assessment Task - LearnAlberta.ca · • name and record fractions for the parts of a whole or a set ... Math Live – Proper Fractions: Assessment Task . The government