Summative Assessment Task: Grade 5
Mrs. Mason volunteers to make one prize ribbon for each of the forty-seven students who will attend math camp. Mrs. Mason will decorate each prize ribbon with sequins. Mrs. Mason buys packages of sequins. Each package holds one-fourth of a pound of sequins. Each package has enough sequins to decorate six prize ribbons. How many packages of sequins does Mrs. Mason need to buy to make the prize ribbons? How many pounds of sequins does Mrs. Mason have to buy to make the prize ribbons? What part of a pound of sequins will be used to make each prize ribbon? Show all your mathematical thinking.
The Dividing with Fractions Unit develops meaning for situations involving dividing a whole number by a unit fraction and dividing a unit fraction by a whole number. Questions asked when dividing whole numbers provide meaning for situations involving division with fractions:
- When a quantity is shared equally, what is the size of each share? When 1/4 is shared equally among 5, what is the size of each share: 1/4 ÷ 5 = ▢ ?
- How many groups of a given size are in this whole number? How many 1/4s are in 5: 5 ÷ 1/4 = ▢ ?
Math Concepts and Skills Covered
The student develops and uses strategies for positive rational number computation in order to solve problems. The student is expected to:
- Describe situations in which a unit fraction is divided by a whole number and a whole number is divided by a unit fraction.
- Represent the division of a unit fraction by a whole number and the division of a whole number by a unit fraction such as 1/4 ÷ 5 and 5 ÷ 1/4 using objects and pictorial models such as area models.
Exemplars Task-Specific Evidence
This task requires students to divide a unit fraction by a whole number. Students also need to find the sum of like fractions.
Underlying Mathematical Concepts
- Fractional part of a whole
- Multiples of a whole
- The meaning of division
- Division of a unit fraction by a whole number
- Addition of like fractions
Possible Problem-Solving Strategies
- Model (manipulatives)
- Number line
Possible Mathematical Vocabulary/Symbolic Representation
- Number line
- Pound (lb)
- Ounce (oz)
- Equivalent/Equal to
- 1/4, 1/24 ...
- 0.25 ...
- Rules: 6 • p = r, 1/4 • p = t
Mrs. Mason needs to buy 8 packages of sequins, which is 2 pounds of sequins. 1/24 of a pound of sequins will make one prize ribbon.
Scoring Rationales and Corresponding Anchor Papers
Below are some examples of mathematical connections. Your students may discover some that are not on this list.
- Mrs. Mason has 1/24 lb of sequins left to make 1 more prize ribbon.
- Patterns: Packages +1, Total ribbons +6, Total pounds per package +1/4
- Rules: 6 · p = r, 1/4 · p = t (p is package, t is total pounds, r is ribbons).
- Generalize and apply the rules, and graph functions.
- 2 pounds of sequins is 32 ounces.
- Relate to a similar task and state a math link.
- Solve more than one way to verify the answer is correct.