Summative Assessment Task: Grade 4
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.
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.
Exemplars Task-Specific Evidence
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)
- Area models
- Number line
Formal Mathematical Language and Symbolic Notation
- Area model
- Number line
- Mixed number
- Equivalent/Equal to
- Per1 1/3, 4/3 ...
- Greater than (>)/Less than (<)
The nine friends shared 12 muffins equally.
Scoring Rationales and Corresponding Anchor Papers
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.
- Relate to a similar task and state a math link.