B1.6 Count to 10 by halves, thirds, fourths, fifths, sixths, eighths, and tenths, with and without the use of tools.
Activity 1: Counting Tenths
Materials
- interlocking cubes
- ten frames
Provide students with 2 or 3 ten frames and interlocking cubes (or tokens). Tell students that for this activity, the ten frame represents a whole. If the frame is a whole, ask the students what each of its squares represents (a tenth: \(\frac{1}{{10}}\)).
Tell students that since they have been in school, they have been counting by 1, 2, 5, 10, and so on. Now, students will count by one tenth. For every one tenth counted, they will place a cube or token on their ten frame.
Out loud and in choir, count by one tenth with students and observe them placing a cube/token on each square in their frame.
Pause and ask students what they notice (10 one tenths make a whole). It is important to do this so that the students realize that each one tenth has a role to play.
Continue to count by one tenth as you continue to fill in the second ten frame.
Out loud and in choir, count with students, saying 11 one tenths, 12 one tenths, 13 one tenths, 14 one tenths, 15 one tenths, 16 one tenths, 17 one tenths, 18 one tenths, 19 one tenths, 20 one tenths.
Pause again and ask students what they notice (20 one tenths make two wholes).
Students must realize that they can continue to count even if a whole is reached. Also, only the numerator changes while the denominator remains the same.
We can also make the connection that once we exceed a whole, we get improper fractions or mixed numbers: for example, 12 one tenth is written : \(\frac{{12}}{{10}}\) or \(1\frac{2}{{10}}\).
Activity 2: Counting Game
Description
Using unit fractions (for example, one one-seventh, two one-sevenths, ...) when counting fractions, such as parts of the area of a rectangle, rather than using whole numbers to count them (for example, 1, 2, 3…) contribute to the development of fraction sense.
Materials
Optional: number lines and/or manipulatives such as Cuisenaire rods or five or ten frames
Where Is the Math?
Understanding the unit fraction is essential to developing fraction sense. When students count fourths, they say: 1 one fourth, 2 one fourths, 3 one fourths, 4 one fourths , and so on. This type of activity allows students to understand that they are counting fourths and allows them to count beyond the whole.
Learning Goals
The purpose of this learning situation is to get the student to:
- learn to count fractions in a variety of ways to develop the concept of magnitude;
- count unit fractions to count beyond the whole (for example, 15 one fourths);
- develop mental computation strategies.
Directions
Students stand in a circle. One student chooses a unit fraction, say one fifth.
The first student says "1 one fifth," the second student says "2 one fifths," the third student says "3 one fifths," and so on.
When a student arrives at a whole number (for example, "5 one fifths"), that person claps his or her hands and then says the equivalent whole number (in this case, 1).
This activity continues so that it counts well beyond 1.
Once all students have had a chance to name and count in unit fractions, ask questions that are designed to develop their fraction sense.
Game Variations
Use manipulatives or models to count unit fractions. (for example, five or ten frames, fractional strips of paper, show jumps on a number line, and so on)
One student chooses a unit fraction (for example, one sixth). After that, students must move around and group together to be able to represent 1, 2, or 3 wholes (for example, to create 2 wholes by counting one sixths, groups of 12 students would need to be formed).
Make a sound or gesture when you get to each whole.
Ask students to represent the fraction they are at when a sound or gesture is made.
Possible Observations
Students could:
- make connections between counting unit fractions and counting other types of units, such as units of measure;
- create many variations of the game.
Note: The testing of this activity found that counting unit fractions leads students to understand the relationship between improper fractions and mixed numbers. In addition, it contributes greatly to understanding the whole, especially when talking about set and area models.
Questions to Ask
- If all the students in the class are counting in fourths, how many "one fourths" will we have counted in total (for example, if there are 27 students, we will have counted 27 one fourths or 6 and three one fourths).
- How many "whole" numbers did we count? Did we end our activity with a whole number? Why or why not?
- How many "fourths" will we need to create the whole? How do you know?
Source: free translation Fraction Pathways.