3 5 Sample Math Task

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3–5 Sample

Math

Task

A Gift for Grandma

Anna wants to buy her grandmother a gift to thank her

grandmother for taking care of her after school. Anna

decides to buy a piece of jewelry. At the store she sees

that 1/2 of the jewelry is necklaces. 1/4 of the jewelry is

pins. The rest of the jewelry is 8 bracelets and 8 rings. How

many pieces of jewelry does the store have for Anna to

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A Gift for Grandma

Suggested Grade Span

Grades 3–5

Grade Level(s) in Which the Task Was Piloted

Grade 4

Task

Anna wants to buy her grandmother a gift to thank her grandmother for taking care of her after school. Anna decides to buy a piece of jewelry. At the store she sees that 1/2 of the jewelry is necklaces. 1/4 of the jewelry is pins. The rest of the jewelry is 8 bracelets and 8 rings. How many pieces of jewelry does the store have for Anna to decide what to buy for her grandmother?

Alternative Versions of the Task

More Accessible Version:

Anna wants to buy her grandmother a gift to thank her grand mother for taking care of her after school. Anna decides to buy a piece of jewelry. At the store she sees that 1/2 of the jewelry is necklaces. 1/4 of the jewelry is pins. The rest of the jewelry is 8 bracelets and 8 rings. How many pieces of jewelry does the store have for Anna to decide what to buy for her grandmother? Use the diagram to help organize your thinking.

More Challenging Version:

Anna wants to buy her grandmother a gift to thank her grandmother for taking care of her after school. Anna decides to buy a piece of jewelry. At the store she sees that 1/2 of the jewelry is necklaces. 1/4 of the jewelry is pins. The rest of the jewelry is a total of 16 bracelets and rings. There are 3 times as many bracelets as rings. How many of each piece of jewelry does the store have for Anna to decide what to buy for her grandmother? If necklaces

average $25, pins average $12, bracelets average $8 and rings average $30, about how much inventory is in this jewelry store?

Common Core Task Alignments Mathematical Practices: 1, 3, 4, 5, 6

Grade 3 Content Standards:

3.NBT.2, 3.NF.3a, 3.NF.3b, 3.NF.3d

4.NBT.4, 4.NF.1, 4.NF.2

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NCTM Content Standards and Evidence

Number and Operations Standard for Grades 3–5

Instructional programs from pre-kindergarten through grade 12 should enable students to:

•

Understand numbers, way of representing numbers, relationships between numbers, and number of systems.

• NCTM Evidence: Develop understanding of fractions as parts of unit wholes, as parts of a collection as locations on number lines, and as divisions of whole numbers.

• Exemplars Task-Specific Evidence: This task requires students to find the number in a collection by knowing a fraction of the collection.

Time/Context/Qualifiers/Tip(s) From Piloting Teacher

This is a short- to medium-length task.

Links

This task can link to a book by Richard Dennis, Fractions are Parts of Things.

Common Strategies Used to Solve This Task

Many students drew a representation to show all the jewelry and divided to show the half and fourth and noticed that the remaining fourth was worth 16 items.

Possible Solutions

Original Version:

If 16 items = 1/4 of the jewelry then 1/2 the items = 32 necklaces

1/4 the items = 16 pins

for a total of 64 pieces of jewelry

More Accessible Version:

Same as original task.

More Challenging Version:

32 necklaces, 16 pins, 12 bracelets, and 4 rings for a total of 64 pieces. (32 x $25) + (16 x $12) + (12 x $8) + (4 x $30) for a total of $1,208.

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Task-Specific Assessment Notes

General Notes: Be sure the representation is fairly accurate with equal parts.

Novice: The Novice will not be able to successfully engage in a strategy that will give a

correct total number of pieces of jewelry. There will be no mathematical language and if there is a drawing or representation, it will not represent the mathematics of the task. No attempt will be made to make a connection.

Apprentice: The Apprentice will have a strategy that could work but may make an error in computation. The pie graph or diagram may not be labeled or accurate and there will be one mathematical language term. An Apprentice may find a correct solution, but a connection will not be made.

Practitioner: The Practitioner will have the correct number of pieces of jewelry. All the supporting work needed to communicate his or her strategy and mathematical reasoning will be present. At least two mathematical terms will be used. A connection about the task or solution will be made. An accurate and appropriate mathematical representation will be constructed.

Expert: The Expert will achieve a correct solution. Evidence will be used to justify and support decisions made and conclusions reached, for example, by solving the task in more than one way to verify the solution. A sense of audience and purpose will be communicated by using precise mathematical language to consolidate mathematical thinking and to communicate ideas. Mathematical connections or observations are made and mathematical representations will be used to extend thinking and clarify or interpret the solution.

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Novice

There is no correct reasoning. The strategy would not lead to

a solution. The work does not demonstrate understanding of

fractional parts.

The student attempts to diagram the types of jewelry but does not label work. S/he uses no mathematical language or

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Apprentice

The student does not show understanding of equal parts. The

work is partially correct for 1/2 representing necklaces and eight braclets and eight pins. The answer

is incorrect.

The student attempts to represent ideas but does not show quarter or

eighth correctly on the circle graph.

Some correct reasoning is used and there is partial understanding of fractions. The student is able to

communicate some mathematical ideas and

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Practitioner

There is adequate basis of reasoning. The student uses a systematic approach. The circle graph is accurate

and appropriate. The strategy would work.

The student is able to communicate mathematical

ideas and uses the terms, circle graph, 1/2, 1/4, 1/8,

2/8 and total amount. The student makes the

connection that if a necklace is bought, 31 pieces will be left.

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Expert

The student uses a circle graph to interpret fractional choices and uses the information to use

LCD to verify the solution.

The student makes connections of what jewelry

will be left with different selections.

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Expert (cont.)

The student uses an alternative strategy of LCD to justify and support her/his

first answer.

The student is able to communicate mathematical ideas. The student uses the terms, pie graph, key and LCD,

as well as whole and correct fractions.