# Instructional Task: Grade 5

## Collecting Basketball Cards

### Task

Kent and Allie collect basketball cards. Kent has twenty cards and Allie has thirty cards. Kent’s mom says that if Kent helps take care of his little brother while she prepares dinner, she will give Kent five cards every Monday. Allie’s mom says that if Allie helps fold the laundry, she will give Allie four cards every Monday. Allie tells Kent that she will always have more cards, but Kent isn’t sure about that. Will Allie always have more basketball cards than Kent? Show all of your mathematical thinking.

### Alternative Versions of Task

#### More Accessible Version

Kent and Allie collect basketball cards. Kent has ten cards and Allie has fifteen cards. Kent’s mom says that if Kent helps take care of his little brother while she prepares dinner, she will give Kent five cards every Monday. Allie’s mom says that if Allie helps fold the laundry, she will give Allie four cards every Monday. Allie tells Kent that she will always have more cards, but Kent isn’t sure about that. Will Allie always have more basketball cards than Kent? Show all of your mathematical thinking.

#### More Challenging Version

Kent and Allie collect basketball cards. Kent has twelve cards and Allie has thirty cards. Kent’s mom says that if Kent helps take care of his little brother while she prepares dinner, she will give Kent twelve cards every Monday. Allie’s mom says that if Allie helps fold the laundry, she will give Allie ten cards every Monday. Allie tells Kent that she will always have more cards, but Kent isn’t sure about that. Will Allie always have more basketball cards than Kent? Show all of your mathematical thinking.

### Common Core Content Standards and Evidence

**
5.OA Operations and Algebraic Thinking**

*Analyze patterns and relationships.*

3. Generate two numerical patterns using two given rules. Identify apparent
relationships between corresponding terms. Form ordered pairs
consisting of corresponding terms from the two patterns, and graph the
ordered pairs on a coordinate plane. *For example, given the rule "Add
3" and the starting number 0, and given the rule "Add 6" and the
starting number 0, generate terms in the resulting sequences, and
observe that the terms in one sequence are twice the corresponding terms
in the other sequence. Explain informally why this is so.*

### Exemplars Task-Specific Evidence

This task requires students to use two rules to generate two different numerical sequences. Students also need to extend the numerical sequences, and determine and compare the totals.

### Common Core Standards of Mathematical Practice

**MP.1** Make sense of problems and persevere in solving them.**MP.3** Construct viable arguments and critique the reasoning of others.**MP.4** Model with mathematics.** ****MP.5** Use appropriate tools strategically.**MP.6** Attend to precision.**MP.7** Look for and make use of structure.

### Underlying Mathematical Concepts

- Generate two numerical patterns using two given rules
- Comparison
- Number sense to 75

### Possible Problem-Solving Strategies

- Model (manipulatives)
- Diagram/Key
- Table
- Number line
- Graph (Students may independently select graph paper.)

### Possible Mathematical Vocabulary/Symbolic Representation

- Model
- Diagram/Key
- Table
- Graph
- Number line
- Pattern
- Total/Sum
- Day, week, month
- Ordinal numbers: 1st, 2nd, 3rd ...
- Greater than (>)/Less than (<)
- Multiples
- Variable
- Rules: (5 • d) + 20 = K, (4 • d) + 30 = A
- Per
- Axis
- Input/Output

### Possible Solutions

No, Allie is not correct.

#### More Accessible Version Solution

No, Allie is not correct.

#### More Challenging Version Solution

No, Allie is not correct.

### Possible Connections

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

- The patterns are Kent's cards +5 (multiples of 5), Allie's cards +4 (multiples of 4), Mondays +1.
- It will take 11 weeks for Kent to have more cards than Allie.
- At the 11th Monday Kent has a total of 75 cards.
- At the 11th Monday Allie has a total of 74 cards.
- Kent has 1 more card than Allie by the 11th Monday.
- Generalize and apply rules for any number of Mondays.
- Graph each person's cards to compare.
- Relate to a similar task and state a math link.
- Solve more than one way to verify the answer.