today’s lesson, we will learn about unit fractions and how these unit fractions can used to model and create various fractions.

Using their fractions tiles, have students pull out the tile that represents the whole. They will use this to compare their models. Ask students to build 6 tenths. Ask them how we could draw a model to represent this. After students have modeled and drawn a representation, draw the model or have a student to draw the model on the board.

1/10	1/10	1/10	1/10	1/10	1/10

Ask students what all ten of the boxes represents (the whole) and why there are only 6 colored in. What do the unshaded boxes represent?

####### Explore: 2. Solving the Problem (10 – 15 minutes)

Display the Unit Fractions PowerPoint. Each slide contains one problem for students to solve. With partners, have students use their tiles to build different fractions and draw a model to represent it. They should use their colored pencils to color in the correct number of pieces out of the whole. Problems:

- • 3 eighths, build 7 eighths, build 10 eighths, build 1 and 5 eighths • 3 eighths, build 7 eighths, build 10 eighths, build 1 and 5 eighths
- • 2 eighths and 5 eighths, add 5 eighths and 5 eighths • 2 eighths and 5 eighths, add 5 eighths and 5 eighths
- • 3 eighths from 9 eighths • 3 eighths from 9 eighths
- • partners, one partner builds 7 eighths and one partner builds 12 eighths. What • partners, one partner builds 7 eighths and one partner builds 12 eighths. What do you notice? (If they aren’t sure, have them compare it to a whole.)
- • students build 6 eighths. How many different ways can 6/8 be decomposed or • students build 6 eighths. How many different ways can 6/8 be decomposed or broken apart (i.e. 2/8 + 4/8 or 3/8 + 3/8)?

As students are completing the task, monitor students to see how they are solving the problems. Select various students to share their solutions. You probably don’t need to go over every single one they built, but definitely take time to discuss the adding and subtracting questions. For the final question, start with the more complex equations and end with the ones that used only unit fractions to lead into the discussion of defining a unit fraction. (Recommendation would be to tell your students beforehand that they are going to share so that they are ready to share out about their model.)

####### Discuss: 3. Discussion of Solutions (15 – 25 minutes)

Start by asking 1-2 students to share their drawings of the first few fractions they built and labelled. As students share, highlight and add to an anchor chart the things you want students to do when drawing fraction models, such as having the whole divided evenly, correct labelling, shading, etc. Have selected students come up to demonstrate how they combined their tiles for the addition problems or how they decomposed to subtract. Finally, have students share all the ways they decomposed 6/8 finishing with 1/8 + 1/8 + 1/8 + 1/8 + 1/8 +1/8. Possible Questions:

- • did/didn’t your denominator change when adding/subtracting? • did/didn’t your denominator change when adding/subtracting?
- • does this unit fraction relate to the whole? • does this unit fraction relate to the whole?
- • fraction is two units less than what you have? Show me with your pieces. • fraction is two units less than what you have? Show me with your pieces.

NC DEPARTMENT OF PUBLIC INSTRUCTION FOURTH GRADE