- The different tiers represent ways to differentiate instruction based on student experience and student achievement of lack there of.
Tier 1 task: for students who still need experience with having
question - How can 2 people share 3 brownies?
Tier 2 task: for students comfortable with halving and ready to try other strategies
question - How can 4 people share 3 brownies?
Tier 3 task: for students ready to solve tasks where students combine halving with new strategies.
question - How can 3 people share 5 brownies
Fractions Greater than 1
Something I already knew - The explanation that was given for 3 1/4. There are 4 4ths in one, 8 4ths in 2, 12 4ths in 3 and the last 4th gets us to 13.
AHA Moment - don't use the term "improper fractions" call them numbers greater than one. Improper doesn't mean the fraction is wrong. Improper fractions mean that you have something greater than one, and stress to students that an improper fraction and mixed numbers are equivalent ways to represent the same fraction.
Manipulatives that we can use to help with fractions
- Unifix cubes
- Linking cubes
- Egg cartons - example: use a string to have students find a half, and then students can divide that have by a third with another string.
- Paper folding, cutting or tearing
- Graphing paper
- Fraction strips
- Circular fractions (pie charts)
- 10 frames
- Geoboards and rubber bands or a print out of a geoboard that students can draw on
- Pattern blocks
- Beans and cups
- Hershey chocolate bars or other foods
Van de Wall pg 298
Figure 15.12 Examples of how to assess student fraction knowledge instead of testing the algorithm.
- the set model helps students recognize the whole
- The rods can be hard, but having students use the rods can help students visualize the fractional parts of the whole, can easily substitute linking cubes or paper.
- This figure tests ALL MODELS. Most teachers will just use the area model, which is a square or rectangle that you divide. It is a good idea to have students divide with all models.
- Teach all models separately
- The area model is by far the most difficult model for students to master, especially if they are given irregular figures.
- Students had to understand fractions greater than one, what a numerator is, what a denominator is, and recognize the whole in order to solve the problems in Figure 15.12.
Pluses about Mixed Numbers
- Separates whole fraction
- Quicker recognition
- Real world applications
Minuses about Mixed Numbers
- Can't do math
- Constantly have to change them to improper fractions or decimals when doing math operations
- Don't give you as much information in some cases (like algebra)
Pluses of Improper Fractions
- Easier to work with
- Preferred for algebra
Minuses of Improper Fractions
- Hard to visualize
- Real world applications, but are very technical and not applications we are going to give to our kids
The whole is always a separate piece of the fractions.
 |
| The wholes in this example are different, but the fractions are the same. The whole is always separate of the fraction. The part that you have and how many groups you have broken your whole into are the fraction. |
**Fundamental key to fractions is understanding to recognize the whole**
How to order fractions
- Benchmarks kids should be able to recognize to help them order fractons
- fractions should be close to zero,1/2 and 1
- When multiplying if the fraction is less than one the number will get smaller, if the fraction is larger than 1 it makes the number larger
- If you multiply by zero the number will get larger
- 1/2 helps break fraction into subgroups.
- Example 6/7 is close to 1, 1/10 is close to 0, 4/10 is close to 1/2, 5/7 goes between 1/2 and 1 (see example below - just comparing to 0, 1/2 and 1)
Homework
Van de Wall pgs 328 - 332
pgs 337 - 340
Problems from the Beckman hard back book - pgs 65 - 66 section 2.4 1, 5, 8
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