B2.2 Understand and recall commonly used percents, fractions, and decimal equivalents.
Activity 1: The cube (Using Commonly Used Percents, Fractions and Decimal Numbers)
Materials
- Transparent cubes with hundreds scale to place base ten material
- 9 hundreds flats
- 9 tens rods
- 10 unit cubes
Represent a quantity in the cube using the flats, rods and unit cubes. The student must represent this quantity using percents, fractions and decimal numbers.
Suggestions
- Begin the activity by placing the 9 flats, the 9 rods and the 10 unit cubes.
- Place 5 flats in the cube.
What quantity is represented in the cube?
Represent as a percent, fraction and decimal number.
- Place only the 10 unit cubes.
What quantity is represented in the cube?
Represent as a percent, fraction and decimal number.
- Place 20 unit cubes in the cube.
What quantity is represented in the cube?
Represent as a percent, fraction and decimal number.
Answer
the full cube = 100%, fraction 1, decimal=1.0
* The full cube represents the whole.
It is important to place quantities in the cube that represent commonly used percentages/fractions/decimal numbers to help the student develop a mental representation of their values
Examples
1 %, 5 %, 10 %, 12,5 %, 25 %, 50 %, 75 %, 100 %
With these benchmarks, question students so that they can make connections to deduce the new quantity in the cube.
What quantity is represented in the cube?
Represent as a percent, fraction and decimal number.
* The student can do the work over time, but if they know that 10 squares are equal to 1%… if they double the number of unit cubes then 20 unit cubes should be 2% of the total amount. This type of exercise helps with understanding the concept.
Variation
If a lot of base ten material is available, place a cube with a different quantity at each table, divide the students into teams of 3, and make different work stations.
Activity 2: Face-To-Face (Mental Math and Percents, Decimal Numbers and Fractions Equivalents)
Materials
- cards with statements
Two students sit face to face. One of the students has a series of cards and turns them over one at a time to the other student, who must answer as many problems correctly as possible within one minute. They record the score. Afterwards, they switch roles.
Examples of problems on the cards
- Card 1 : 50% is equivalent to ?
- Card 2 : If \(\frac{1}{5}\) = 20 % then \(\frac{3}{5}\) is = ?
- Card 3: What percent is \(\frac{2}{8}\) equal to?
- Card 4 : \(\frac{1}{{100}}\) is equivalent to?
- Card 5: There are 100 blocks on the table, the student takes \(\frac{3}{4}\). How many blocks are there?
- Card 6: 0.05 of $1 000 = ?
- Card 7 : If 1% = 0.01 then 5% = ?
- Card 8: What percent does half of \(\frac{1}{4}\) represent?