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Standards-based assessment and Instruction

Instructional Task: Grade 4

 

 

 

A Raspberry Pie

Task

Tony makes a raspberry pie to share with two of his friends. Tony cuts the pie into eight equal pieces. Tony eats two pieces. Lisa eats one piece. Jill eats one piece. Tony says there is one-half of the pie left. Lisa says there is three-fourths of the pie left. Who is correct? Show all your mathematical thinking.

Alternative Versions of Task

More Accessible Version

Tony makes a raspberry pie to share with his friend, Lisa. Tony cuts the pie into four equal pieces. Tony eats one piece. Lisa decides not to eat any pie. Tony says there is one-half of the pie left. Lisa says there is three-fourths of the pie left. Who is correct? Show all your mathematical thinking.

More Challenging Version

Tony makes a raspberry pie to share with two of his friends. Tony cuts the pie into twelve equal pieces. Tony eats two pieces. Lisa eats one piece. Jill eats one piece. Tony says there is one-half of the pie left. Lisa says there is three-fourths of the pie left. Who is correct? 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.

Exemplars Task-Specific Evidence

This task requires students to solve addition and subtraction problems with fractions involving like denominators referring to the same whole. Students also have to find equivalent fractions and make comparisons.

Underlying Mathematical Concepts

  • Addition and subtraction of fractions 
  • Joining and separating parts referring to the same whole
  • Equivalent fractions
  • Comparison of fractions

Possible Problem-Solving Strategies

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

Possible Mathematical Vocabulary/Symbolic Representation

  • Model
  • Diagram/Key
  • Table
  • Area Model
  • Number line
  • Fraction
  • 1/8, 2/8, 1/4 ...
  • Whole
  • Per
  • Numerator/Denominator
  • Greater than (>)/Less than (<)
  • Equivalent/Equal to (=)
  • Total

Possible Solutions

Tony is correct.

 

 

 

 

 

 

 

More Accessible Version Solution

Lisa is correct.

More Challenging Version Solution

Neither Tony or Lisa is correct. There is 1/3 of the pie left.

Possible Connections

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

  • Tony ate the most pie.
  • Lisa and Jill ate an equal amount of pie.
  • Lisa and Jill ate a total of 2/8 or 1/4 pie.
  • If one whole piece is left for 3 friends to share, they would have to section the piece into thirds.
  • Solve more than one way to verify the answer.
  • Relate to a similar task and state a math link.
  • The amount of pie eaten equals the amount of pie left to eat.
  • An equal share is 1/3 piece of pie each.

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Here's What People Are Saying

'We need to start,' said my students last week. They told me to hurry up, read the problem and pass out the paper. This is a noticeable change in student attitudes toward problem solving. They are no longer meek, frightened, inhibited problem solvers.

Karen McKee's first grade classroom Easthampton, NY

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