Non-unit Fractions
10 min
Narrative
The purpose of this Warm-up is to elicit the idea that we can think about multiple equal parts in a diagram and use fractions to refer to them, which will be useful when students identify fractions in diagrams and shade diagrams to show a specific fraction in a later activity. While students may notice and wonder many things about these images, the fact that more than one of the equal parts of the square is shaded, the fraction underneath the third diagram, and how the shaded parts could be described are the important discussion points.
When students articulate what they notice and wonder, they have an opportunity to attend to precision in the language they use to describe what they see (MP6). They might first propose less formal or imprecise language, and then restate their observation with more precise language in order to communicate more clearly.
Launch
- Groups of 2
- Display the image.
- “What do you notice? What do you wonder?”
- 1 minute: quiet think time
Teacher Instructions
- “Discuss your thinking with your partner.”
- 1 minute: partner discussion
- Share and record responses.
Student Task
What do you notice? What do you wonder?
Solution Steps (5)
- 1Observe squares partitioned into fourths→Each square has 4 equal parts
- 2Count shaded parts in each square→1st: 1 part, 2nd: 2 parts, 3rd: 3 parts, 4th: 4 parts
- 3Connect numerator to shaded parts→3 in 3/4 means 3 parts are shaded
- 4Connect denominator to total parts→4 in 3/4 means 4 equal parts total
- 5Name fractions for multiple parts→1 fourth, 2 fourths, 3 fourths, 4 fourths
Sample Response
- Each square shows one more part shaded compared to the square to its left.
- Some of the squares have more than 41 shaded.
- The first square shows 41.
- The second square shows 21.
- There’s a fraction below the third square.
- The top part of the fraction has a 3.
- Why is more than one piece shaded sometimes?
- Why are we shading one more piece each time?
- Could each of the big squares be showing a different fraction?
- Does the 3 stand for the 3 shaded parts?
Activity Synthesis (Teacher Notes)
- “What do you think the 3 and the 4 stand for in the number below the third square?” (The 4 stands for the 4 equal parts in the square. The 3 stands for the number of parts that are shaded.)
- “Sometimes we may want to talk about more than one part and we can describe those parts with a number.”
- “What do we call the parts in each square?” (Fourths)
- “How many fourths are shaded in the first square?” (1)
- “How many fourths are shaded in the second square? Third square?” (2, and 3)
- “How many fourths are shaded in the last image?” (4)
- “We can refer to the shaded parts in each image by describing the number of fourths: 1 fourth, 2 fourths, 3 fourths, and 4 fourths.”
- “We’ll look at how to write these amounts in the next activity.”
Standards
- 3.NF.1·Understand a fraction 1/b as the quantity formed by 1 part when a whole is partitioned into b equal parts; understand a fraction a/b as the quantity formed by a parts of size 1/b.
- 3.NF.A.1·Understand a fraction <span class="math">\(1/b\)</span> as the quantity formed by 1 part when a whole is partitioned into <span class="math">\(b\)</span> equal parts; understand a fraction <span class="math">\(a/b\)</span> as the quantity formed by <span class="math">\(a\)</span> parts of size <span class="math">\(1/b\)</span>.
15 min
20 min
Knowledge Components
All skills for this lesson
Non-unit Fractions
10 min
Narrative
The purpose of this Warm-up is to elicit the idea that we can think about multiple equal parts in a diagram and use fractions to refer to them, which will be useful when students identify fractions in diagrams and shade diagrams to show a specific fraction in a later activity. While students may notice and wonder many things about these images, the fact that more than one of the equal parts of the square is shaded, the fraction underneath the third diagram, and how the shaded parts could be described are the important discussion points.
When students articulate what they notice and wonder, they have an opportunity to attend to precision in the language they use to describe what they see (MP6). They might first propose less formal or imprecise language, and then restate their observation with more precise language in order to communicate more clearly.
Launch
- Groups of 2
- Display the image.
- “What do you notice? What do you wonder?”
- 1 minute: quiet think time
Teacher Instructions
- “Discuss your thinking with your partner.”
- 1 minute: partner discussion
- Share and record responses.
Student Task
What do you notice? What do you wonder?
Solution Steps (5)
- 1Observe squares partitioned into fourths→Each square has 4 equal parts
- 2Count shaded parts in each square→1st: 1 part, 2nd: 2 parts, 3rd: 3 parts, 4th: 4 parts
- 3Connect numerator to shaded parts→3 in 3/4 means 3 parts are shaded
- 4Connect denominator to total parts→4 in 3/4 means 4 equal parts total
- 5Name fractions for multiple parts→1 fourth, 2 fourths, 3 fourths, 4 fourths
Sample Response
- Each square shows one more part shaded compared to the square to its left.
- Some of the squares have more than 41 shaded.
- The first square shows 41.
- The second square shows 21.
- There’s a fraction below the third square.
- The top part of the fraction has a 3.
- Why is more than one piece shaded sometimes?
- Why are we shading one more piece each time?
- Could each of the big squares be showing a different fraction?
- Does the 3 stand for the 3 shaded parts?
Activity Synthesis (Teacher Notes)
- “What do you think the 3 and the 4 stand for in the number below the third square?” (The 4 stands for the 4 equal parts in the square. The 3 stands for the number of parts that are shaded.)
- “Sometimes we may want to talk about more than one part and we can describe those parts with a number.”
- “What do we call the parts in each square?” (Fourths)
- “How many fourths are shaded in the first square?” (1)
- “How many fourths are shaded in the second square? Third square?” (2, and 3)
- “How many fourths are shaded in the last image?” (4)
- “We can refer to the shaded parts in each image by describing the number of fourths: 1 fourth, 2 fourths, 3 fourths, and 4 fourths.”
- “We’ll look at how to write these amounts in the next activity.”
Standards
- 3.NF.1·Understand a fraction 1/b as the quantity formed by 1 part when a whole is partitioned into b equal parts; understand a fraction a/b as the quantity formed by a parts of size 1/b.
- 3.NF.A.1·Understand a fraction <span class="math">\(1/b\)</span> as the quantity formed by 1 part when a whole is partitioned into <span class="math">\(b\)</span> equal parts; understand a fraction <span class="math">\(a/b\)</span> as the quantity formed by <span class="math">\(a\)</span> parts of size <span class="math">\(1/b\)</span>.