Lesson Standard: Understand a fraction a/b with a >1 as a sum of fractions 1/b

b. Decompose a fraction into a sum of fractions with the same denominator in more than one way, recording each decomposition by an equation. Justify decompositions … using a visual fraction model.

Content Objective: Students will decompose a fraction into a sum of fractions with the same denominator in more than one way, recording each decomposition by an equation. Students will justify decompositions with a visual fraction model.

Mathematical practice(s): 1 Make sense of problems and persevere, 3 Construct Viable Arguments and Critique Reasoning, 4 Model with mathematics, 6 Attend to precision

Lesson Design / What will the teacher be doing? / What will the students be doing?
(Structured Student Interaction) / What will the teacher be listening for?
(what do we expect students to say?) / Probing Questions for Differentiation
Assessing Questions
(“stuck”) / Advancing Questions
(further learning)
Engage (Launch)
There were of pizza left over after dinner last night. Three people will pack some of the leftover pizza for lunch. There will be no pizza left after lunches are packed. What fraction of the pizza could each person pack? / Teacher will place problem on board.
Teacher will walk room looking for students that have solved the problem using different fractions.
Teacher will look for students to share their reasoning with the class. (3 students) / Students will answer the question on their whiteboard.
Students will work independently to solve the problem.
Students will show their boards to the teacher. / Numerator
Denominator
Parts
Using a fraction for the answer / Can both of these answers be right? / Can you solve it a different way?
Maybe I didn’t take of pizza. What is a possible answer now?
Activity or Task 1
The sum is . What could be my addition equation? Use a model to justify your equation. / Teacher will put problem on the board.
Teacher will ask students to discuss the problem with their partner (with pencils down) and work together to come up with the equation.
Teacher will direct partners to work on one piece of paper.
-Partner A will write the equation on the paper.
-Partner B will draw a model to justify the equation.
Teacher will walk room to monitor student work. / Pencils down – discuss what equation you would like to use to show the sum .
Students will show their work on one piece of paper.
Students will discuss the problem and work together to come up with the equation.
-Partner A will write the equation on the paper.
-Partner B will draw a model to justify the equation. / Write an equation
Draw a model
Unit fractions / Use a START
How would you use fraction pieces to help you with your model?
Does your model match your equation? / Can you model using a number line?
That wasn’t the equation I was thinking of … can you try to come up with my equation?
You have two addends. Can you write an addition equation with more than two addends?
Activity or Task 2
The sum is 1. What could be my addition equation? Use a model to justify your equation. / Teacher will put problem on the board.
Teacher will ask students to discuss the problem and work together to come up with the equation.
Teacher will direct partners to work on one piece of paper.
-Partner B will write the equation on the paper.
-Partner A will draw a model to justify the equation.
Teacher will look for a number line to use as a START. (Challenge students that work quickly to model on a number line)
Teacher will walk room to monitor student work. / Students will show their work on one piece of paper.
Students will discuss the problem and work together to come up with the equation.
-Partner B will write the equation on the paper.
-Partner A will draw a model to justify the equation. / Write an equation
Draw a model
Unit fractions
Number line / Use a START
How would you use fraction pieces to help you with your model?
Does your model match your equation? / Can you model using a number line?
That wasn’t the equation I was thinking of … can you try to come up with my equation?
You have two addends. Can you write an addition equation with more than two addends?
Activity or Task 3
The sum is 2. What could be my addition equation? Use a model to justify your equation. / Teacher will put the problem on the board. Teacher will hand out scratch paper for students to show their work.
Teacher will ask students to work independently to come up with the equation and the model.
Teacher will walk room to monitor student work. / Students will work independently to solve the problem. / Write an equation
Draw a model
Unit fractions / Thinking about how you solved the last two problems. How can you use that information to solve this problem?
How would you use fraction pieces to help you with your model?
Does your model match your equation? / Can you model using a number line?
That wasn’t the equation I was thinking of … can you try to come up with my equation?
You have two addends. Can you write an addition equation with more than two addends?
Can you use a different model to solve the problem?
Closure
The sum is 1. What could be my addition equation using only fractions? Use a model to justify your equation. / Students will work independently to solve the problem. / Thinking about how you solved the last few problems. How can you use that information to solve this problem?
How would you use fraction pieces to help you with your model?
Does your model match your equation?

There were of pizza left over after dinner last night. Three people will pack some of the leftover pizza for lunch. There will be no pizza left after lunches are packed. What fraction of the pizza could each person pack?

The sum is . What could be my addition equation? Use a model to justify your equation.

The sum is 1. What could be my addition equation? Use a model to justify your equation.

The sum is 2. What could be my addition equation? Use a model to justify your equation.

The sum is 1. What could be my addition equation using only fractions? Use a model to justify your equation.