# Instructional Task: Grade 5

## For the Birds

### Task

Mr. and Mrs. Ray notice that the cardinals at the bird feeder in their yard eat about one-fourth inch of birdseed two times every day. The bird feeder is shaped like a cylinder and is fifteen inches in height. The bird feeder holds ten pounds of birdseed when completely full. Mr. and Mrs. Ray are going on vacation for four weeks. Mr. Ray is worried that the cardinals will not have enough birdseed in the bird feeder to eat for four weeks. Mrs. Ray says if the bird feeder is completely full of birdseed there will be enough birdseed to last four weeks. Is Mrs. Ray correct? Show all your mathematical thinking.

### Alternative Versions of Task

#### More Accessible Version

Mr. and Mrs. Ray notices that the cardinals in his yard eat ½ inch of birdseed every day. The feeder is shaped like a cylinder. The cylinder is ten inches in height. Mr. and Mrs. Ray are going on vacation for two weeks. Mr. Ray is worried that his cardinals will not have enough birdseed in the bird feeder to eat for two weeks. Mrs. Ray says if the bird feeder is completely full of birdseed there will be enough birdseed to last two weeks. Is Mrs. Ray correct? Show all your mathematical thinking.

#### More Challenging Version

Mr. and Mrs. Ray notice that the cardinals at the bird feeder in their yard eat about one-fourth inch of birdseed two times every day. The bird feeder is shaped like a cylinder and is fifteen inches in height. The bird feeder holds ten pounds of birdseed when completely full. Mr. and Mrs. Ray are going on vacation for four weeks. Mr. Ray is worried that the cardinals will not have enough birdseed in the bird feeder to eat for four weeks. Mrs. Ray says if the bird feeder is completely full of birdseed, there will be enough birdseed to last four weeks. Is Mrs. Ray correct? Mr. Ray buys birdseed for three dollars seventy-seven cents per pound. How much does it cost Mr. Ray to fill his feeder to the top? Show all your mathematical thinking.

### Dividing With Fractions Unit

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 whole number by a unit fraction. Students will also compare the quotient to a given amount.

### Underlying Mathematical Concepts

- Fractional part of a whole
- Meaning of division
- Fraction notation
- Unit fractions
- Division of a whole number by a unit fraction

### Possible Problem-Solving Strategies

- Model (manipulatives)
- Diagram/Key
- Table
- Number line

### Formal Mathematical Language and Symbolic Notation

- Model
- Diagram/Key
- Table
- Number line
- Inch (", in.), foot (', ft.)
- Pound (lb, lbs)
- Week, day
- Fractions (1/4, 2/4, 1/2 ...)
- Cylinder
- Height
- Total/Sum
- Multiples
- Equation
- Area model
- Greater than (>)/Less than (<)
- Unit
- Numerator/Denominator
- Rule (1/2 • d = i)
- Variables
- Pattern

### Possible Solutions

Mrs. Ray is correct.

#### More Accessible Version Solution

Mrs. Ray is correct.

#### More Challenging Version Solution

Mrs. Ray is correct. It will cost Mr. Ray $37.70 to fill his bird feeder to the top.

### Possible Connections

Below are some examples of mathematical connections. Your students may discover some that are not on this list.

- There is enough birdseed for two more days.
- The birdseed is multiples of 1/2.
- 10 lbs of birdseed equals 160 ounces.
- 1/2 in. is 0.5 of an inch.
- 2/4 is equivalent to 1/2.
- Relate to a similar task and state a math link.
- Solve more than one way to verify the answer.
- Patterns: Day +1, Birdseed +1/2".
- Rules: 1/2 · d = i (d is day and i is inches).