Lesson 1

Counting by Unit Fractions

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Content

B 1.6

Key Concepts

Using unit fractions (e.g., one one-seventh, two one-sevenths, etc.) when counting fractional amounts, such as regions in a rectangle, rather than using a whole number count (e.g., 1, 2 ,3 ...), reinforces the meaning of the fraction.

Learning Goal

We want students to understand...

learn how to count fractions in various ways, developing a sense of magnitude;
count using unit fractions to go beyond one whole (e.g., 15 one-fourths);
develop the ability to calculate halves and wholes mentally based on unit fractions counting.

Success Critera

I can count by unit fractions up to 10

Social Emotional Learning Focus #4: Build Relationships and Communicate Effectively, as students apply the mathematical process of communicating: express and understand mathematical thinking and use appropriate math terminology in a variety of representations so students can work collaboratively on math problems- expressing their thinking, listening to the thinking of others.

This is the link to the Social Emotional Learning Skills in Mathematics and the Mathematical Processes

https://www.dcp.edu.gov.on.ca/en/curriculum/elementary-mathematics/grades/g4-math/strands#strand-a

Minds On

Fractions Pathways Lesson

Students “count up” using unit fractions (¼, ⅓, ⅕ etc.) The students or teacher can choose any unit fractions, and the teacher or students can set game rules such as: "When you get to one whole, stand up and state the quantity as both a fraction and as a whole".

Note: this game is similar to a well-known number game called BUZZ.

Choose one to start off with that the students have a basic understanding of, such as halves.

Instructional sequence

Start in a circle(if distance teaching, choose a small group of students, post the list in the chat), and have students count the unit fraction of your (or a student’s choice). If the fraction selected is 1/4 for example, the first person in the circle would say “1 one-fourth”; the second person would say “2 one-fourths”; the third person would say “3 one-fourths”, and so on. When a student arrives at a whole number (such as 4 one-fourths), they need to stand up and say the whole number equivalent.(This continues for each whole number, for example, the student that gets 8 one-fourths needs to say “two”.)

Count up to 10. Be sure students count

Teacher Background: A unit fraction is the base unit of any fraction and always has a numerator of 1. For example one-fourth is 1 one-fourth of the fourths. 2 one-fourths are 2 one-fourth units. When we count these fourths, we use the language "1 one-fourth", "2 one-fourths", "3 one-fourths", "4 one-fourths", "5 one-fourths" and so on. This helps students understand that we are counting units that are fourths and this allows us to count beyond one whole, such as 5 one-fourths.

Action!

Continue the Minds On game with different unit fractions.

N.B. You may want to continue this counting game daily as an opening activity while working in this unit.

Teacher Background: A unit fraction is the base unit of any fraction and always has a numerator of 1. For example one-fourth is 1 one-fourth of the fourths. 2 one-fourths are 2 one-fourth units. When we count these fourths, we use the language "1 one-fourth", "2 one-fourths", "3 one-fourths", "4 one-fourths", "5 one-fourths" and so on. This helps students understand that we are counting units that are fourths and this allows us to count beyond one whole, such as 5 one-fourths.

consolidation Questions

When finished counting by one unit fraction to 10, ask these questions:

If each person counted (insert unit fraction ie. ¼) in our count, how many one-fourths would we have counted in total to get to 10?
How many wholes did we count? Did we end on a whole?
How many (insert unit fraction) units did it take to make one? How do you know?

Independent Task/Assessment Opportunities

Have them record on Explain Everything, counting by various unit fractions to 10. Or do one on one interviews.

Technology/manipulatives

virtual manipulative

Fraction Strips (by Mathies)

in DSB1 App Catalogue