Week 2: Ways to Add and Subtract Fractions

On Tuesday this week we discussed the different ways you can represent fractions as well as adding and subtracting fractions. 

These were the topics discussed.

Spatial Relationships are having a picture of a number including where it lies on a number line.

One/Two More/Less: If you have 5/4, what is 1/4 more/less? What is 2/4 more/less?

ex: 5/4 + 1/4 = 6/4, 5/4 - 1/4 = 4/4 = 1, 5/4 + 2/4 = 7/4, 5/4 - 2/4 = 3/4

Benchmarks of 0, 1/2, and 1... is it about or below 1/2? How far away is it from 1?

Part-Part-Whole: Knowing 3/4 can be (1/2+1/4) or (1/4+1/4+1/4)

ex: 7/5

Spatial Relationship: 

One/Two More/Less: 

7/5 + 1/5 = 8/5, 7/5 - 1/5 = 6/5, 7/5 + 2/5 = 9/5, 7/5 - 2/5 = 5/5 = 1

Benchmarks: More than 1, 1 + 2/5 = 7/5

Part-Part-Whole:

(1/5+1/5+1/5+1/5+1/5+1/5+1/5), (1+2/5), (2-3/5)

One Thursday we went over showing how to represent fractions in diagrams

Running Task: If I ran 1/3 of an hour and then walked for 1/4 of an hour, how much time would that be? What fraction of an hour is that?

They ran for 20 minutes + 15 minutes, thats 35 minutes total or 35/60 minutes.

The Clock Model

Traditional Method of Adding and Subtracting Fractions:

ex: 15 3/8 + 11 7/16

  15 3/8                 15 6/16

+ 11 7/16  ----> + 11 7/16 ----> 26 13/16

  15 3/8                15 6/16

- 11 7/16 ---->  -  11 7/16 ----> 3 15/16

Week 1 of Blog: The Role of Unit

During the activity for this week, it had to do with using manipulatives to show fractions. The manipulatives used were hexagons. Each hexagon is part of a whole unit. If there is 2 hexagons, then one of those hexagons represents 1/2 or one half of the whole unit.

The single yellow hexagon represents 1/2 and the two hexagons stacked represents the whole unit below.

After that, we used smaller manipulatives like green triangles, blue rhombi and red trapezoids to show the fractions than can be made with the different shapes inside 

Six green triangles can fit in the single yellow hexagon. Therefore, you can cut a hexagon in 6 different ways.

Three blue rhombi can fit in the single yellow hexagon. One rhombus makes 1/3 of the hexagon.

Two trapezoids make up the single yellow hexagon. One trapezoid makes 1/2 of the hexagon.