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Standards-based assessment and Instruction

# Math 3-5

## 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 decide what to buy for her grandmother?

Grades 3-5

Grade 4

### Alternative Versions of 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?

### 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.

### Task Specific Assessment Notes

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

Task Specific Rubric/Benchmark Descriptors
Click on a level for student example.
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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