Standards-based assessment and Instruction

## Sharing Muffins

Nine friends are going to equally share some muffins. Each muffin is the same size. Each friend gets one and one-third muffins. How many muffins did the nine friends equally share? Show all your mathematical thinking.

### Adding and Subtracting Fractions Unit

The Adding and Subtracting Fractions Unit involves using a variety of methods to join or separate fractional parts referring to the same whole. Methods may include replacing mixed numbers with equivalent fractions; using properties of operations and the relationship between addition and subtraction; and using visual models of fractions. Questions to answer may include:

• Why must we use the same whole when adding or subtracting fractional parts?
• How can a number line be used to represent adding or subtracting fractions
• How can benchmark fractions help to determine whether a sum or difference makes sense?

### Math Concepts and Skills Covered

The student solves problems by developing and using strategies for addition and subtraction. The student:

• Finds the sum of a multiple of 10 and a one-digit number (up to 99) in problem situations.
• Develops, applies and explains strategies used to add and subtract within 20, such as making 10 and decomposing a number leading to a 10.
• Creates problem situations when given a number sentence involving addition or subtraction of numbers within 20; solves the problems created.
• Represents word problems involving addition and subtraction of numbers up to 20.
• Applies properties of operations to add and subtract two or three numbers– if 4 + 3 = 7 is known, then 3 + 4 = 7 is also known.

This task requires students to solve addition and subtraction problems with mixed numbers involving like denominators.

### Underlying Mathematical Concepts

• Fraction notation
• Equivalent fractions
• Addition/Subtraction of mixed numbers with like denominators

### Possible Problem-Solving Strategies

• Model (manipulatives)
• Diagram/Key
• Area models
• Table
• Number line

### Formal Mathematical Language and Symbolic Notation

• Model
• Diagram/Key
• Table
• Area model
• Number line
• Mixed number
• Numerator/Denominator
• Whole
• Equivalent/Equal to
• Sum/Total
• Pattern
• Dozen
• Per1 1/3, 4/3 ...
• Greater than (>)/Less than (<)

### Possible Solutions

The nine friends shared 12 muffins equally.

### Possible Connections

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

• 12 muffins is a dozen.
• Half a muffin would be a bigger portion than 1/3, but you would need to buy more muffins to share.
• The patterns are friend +1, muffins +1 1/3.
• Show all the improper fractions.
• Solve more than one way to verify the answer.
• Continue the pattern for more friends.

Our teacher-friendly tasks are designed to support both the Common Core and Citywide instructional expectations. GO Math! alignments are also available.
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## Here's What People Are Saying

One additional benefit of using the modeling format has been that teachers not only saw an Exemplars mathematics lesson modeled as intended, but they have also had the opportunity to see numerous quality strategies for communicating with students. They have seen students enticed to communicate their thoughts to peers as well as communicating their explanations on paper. Teachers have seen best practices for establishing a working community in the classroom...

Shirley McKee

Elementary Consultant

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