Fraction Models

Grade 3, Unit 4, Module 3, Session 2 The teacher uses prepared unit fraction “cookie pieces” adhered to the white board for students to move them around in order to arrange them from least to greatest. On another day, students create their own set of unit fraction “cookies” and make observations about them. Eventually, they work with cut red paper strips to fold, cut and label unit fraction licorice whips.

Fractions on a Ruler: Licorice

Ask participants to find these sheets and crayons on their tables and to work with tablemates to fill in the clocks and write their observations, e.g.,1 = 60 minutes or twelve 5 minute segment; ½ = 30 minutes or 30/60 or 3 sets of ten minutes, etc. Grade 5, U2M1S3, SB 34

Work through this page of the problem string together Work through this page of the problem string together. Grade 5 U2M1S4 T5 & 6

Grade 5, Unit 2, Module 1, Session 4 Ask participants to locate the Clock Fractions Problem String pages on their table and to work with their tablemates to complete this problem string with your guidance.

Ask participants to locate the money pieces on their table Ask participants to locate the money pieces on their table. What do they notice? What relationships do they see? (Money Pieces in Instructor Tub and include my own pieces to have enough.) Have them to use the pieces to model the solutions to the problems presented in this problem string.

Ask people to share their own ideas about relating fraction work to money models.

Money & Clock Fractions: Student Posters

Clocks or Money?

Ask participants to use the tiles included in the MLC instructor tubs (and on their tables) to build a 4 x 6 array of tile and then work through the problems pictured below together.

Ask participants to locate the Egg Carton Fraction pages pictured below and work together to complete each problem. Show large black line of egg carton and explain how I might conduct the beginning of this as a whole group lesson.

Egg Carton Fractions Ask tablemates to use crayons and pencils or pens to complete this page. Tell them that their eggs need to be adjacent (top/bottom, side by side) with no gaps in between. Grade 4, U3M1S5 SB89

At the end of this presentation, there will be a Work Place with the fraction kits for them to use. Students would have made their own but I have provided 8 sets for this activity.

Explain that another Work Place after this presentation will involve geoboard fractions and relationships. There will also be an independent practice page of Fractions and Mixed Numbers on a Number Line. This could also be an example of working with the teacher while Work Places are in progress.

Explain that they’ll be using the pieces later in the workshop for computation.

From Grade 3, Unit 4, Module 3, Session 3, HC 75 & 76 Ask participants to work together at their tables to complete the two Fractions, Fractions, Fractions pages.

Providing a couple of rulers at each table could be helpful for folks to determine fractional segments but approximations would be fine too.

Preparing the River Trail These are photographs of students working on the fifth grade Bridges River Trail posters in Canby, OR.

Determining the Fractional Parts

Finished Trail

Finished Trail

Finished Trail

Warmup: Mental Math 1/2 of 44 1/4 of 44 1/8 of 44 Grade 5, Unit 2, Module 2, Session 3 Double Number Lines Fractions as Operators Warmup: Mental Math 1/2 of 44 1/4 of 44 1/8 of 44 1/4 of 16 2/4 of 16 3/4 of 16 1/5 of 25 2/5 of 25 4/5 of 25 One of the purposes of the above problems, is to get students thinking of fractions as operators.

The Double Number Line Model The double number line model is helpful because it begs for action. Once you put the total length on the end, you start by finding a unit fraction of that length. The double number line is a handy tool to solve problems with a variety of denominators, unlike the previous problems in the unit where the denominators were limited to factors of 100 (money) or 60 (clock). Now students can create a line of any length that works with the denominators at hand.

Mr. Miles is a teacher who is training on a nearby hiking trail to run a race. In his training he walks to warm up and then he jogs or runs. One day, he walked 1/10 of the trail and then he ran 1/4 of the trail. How much of the trail did he cover that day? What might be a trail length that will work well to find 1/10 and 1/4 of the length? What fraction of the trail has he covered?

What is a shorter trail length you could use? 0 km ____ km •On another day, Mr. Miles walked 1/7 of the trail and ran 3/5 of it. 0 km ____ km

On another day, Mr. Miles walked and ran 7/8 of the trail, and then he walked back 1/3 of the trail. How far from the beginning of the course is he now? What fractional amount of the course is that? 0 km 24 km

Some Fraction Work Places Grade 3

Model this Work Place before sending folks out to choose a place to start their work.

After quickly showing the materials available to their use during the next 20 minutes or so, stress the opportunity to choose where to work and with whom they’ll work. Explain that they’ll be expected to be “at work” during the entire time.

Personal Practice Using fraction kits to solve problems: