Add Tenths and Hundredths Together
10 min
Narrative
The purpose of this Warm-up is to elicit observations about fractions in tenths and in hundredths, and about equivalence, which will be useful when students find sums of tenths and hundredths later in the lesson. While students may notice and wonder many things about these diagrams, focus the discussion on the relationship between tenths and hundredths and how we might express equivalent amounts.
Launch
- Groups of 2
- Display the diagrams.
- “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
- Record responses.
Student Task
Each large square represents 1.
What do you notice? What do you wonder?
Sample Response
Students may notice:
- There are two square diagrams. One is partitioned into tenths. The other is partitioned into hundredths.
- The amount shaded on each diagram is the same.
- Each part in the first diagram is a long rectangle. The first rectangle is shaded, and half of the second rectangle is shaded.
- Each part in the second square is a small square. Fifteen squares are shaded.
- The shaded parts in the second diagram represents 10015.
Students may wonder:
- Why is the second rectangle in the first diagram shaded halfway?
- What fraction does the shaded parts in the first diagram represent?
Activity Synthesis (Teacher Notes)
- “What fraction does each part in the first diagram represent?” (One-tenth or 101) “What about in the second diagram?” (One-hundredth or 1001)
- “Can you see tenths in both diagrams? Where?” (Yes. Each rectangle in A is a tenth. Each group of small squares in B is a tenth.)
- “Can you see hundredths in both diagrams? Where?” (No, only in B. Each square is a hundredth.)
- “Do you think the shaded parts of the two diagrams represent the same fraction or different fractions? Which fraction(s)?” (The same fraction, 10015. Different fractions: The second square represents 10015, but I'm not sure about the first square.)
Standards
Addressing
- 4.NF.1·Explain why a fraction a/b is equivalent to a fraction (n × a)/(n × b) by using visual fraction models, with attention to how the number and size of the parts differ even though the two fractions themselves are the same size. Use this principle to recognize and generate equivalent fractions.
- 4.NF.A.1·Explain why a fraction <span class="math">\(a/b\)</span> is equivalent to a fraction <span class="math">\((n \times a)/(n \times b)\)</span> by using visual fraction models, with attention to how the number and size of the parts differ even though the two fractions themselves are the same size. Use this principle to recognize and generate equivalent fractions.
15 min
20 min
Knowledge Components
All skills for this lesson
No KCs tagged for this lesson
Add Tenths and Hundredths Together
10 min
Narrative
The purpose of this Warm-up is to elicit observations about fractions in tenths and in hundredths, and about equivalence, which will be useful when students find sums of tenths and hundredths later in the lesson. While students may notice and wonder many things about these diagrams, focus the discussion on the relationship between tenths and hundredths and how we might express equivalent amounts.
Launch
- Groups of 2
- Display the diagrams.
- “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
- Record responses.
Student Task
Each large square represents 1.
What do you notice? What do you wonder?
Sample Response
Students may notice:
- There are two square diagrams. One is partitioned into tenths. The other is partitioned into hundredths.
- The amount shaded on each diagram is the same.
- Each part in the first diagram is a long rectangle. The first rectangle is shaded, and half of the second rectangle is shaded.
- Each part in the second square is a small square. Fifteen squares are shaded.
- The shaded parts in the second diagram represents 10015.
Students may wonder:
- Why is the second rectangle in the first diagram shaded halfway?
- What fraction does the shaded parts in the first diagram represent?
Activity Synthesis (Teacher Notes)
- “What fraction does each part in the first diagram represent?” (One-tenth or 101) “What about in the second diagram?” (One-hundredth or 1001)
- “Can you see tenths in both diagrams? Where?” (Yes. Each rectangle in A is a tenth. Each group of small squares in B is a tenth.)
- “Can you see hundredths in both diagrams? Where?” (No, only in B. Each square is a hundredth.)
- “Do you think the shaded parts of the two diagrams represent the same fraction or different fractions? Which fraction(s)?” (The same fraction, 10015. Different fractions: The second square represents 10015, but I'm not sure about the first square.)
Standards
Addressing
- 4.NF.1·Explain why a fraction a/b is equivalent to a fraction (n × a)/(n × b) by using visual fraction models, with attention to how the number and size of the parts differ even though the two fractions themselves are the same size. Use this principle to recognize and generate equivalent fractions.
- 4.NF.A.1·Explain why a fraction <span class="math">\(a/b\)</span> is equivalent to a fraction <span class="math">\((n \times a)/(n \times b)\)</span> by using visual fraction models, with attention to how the number and size of the parts differ even though the two fractions themselves are the same size. Use this principle to recognize and generate equivalent fractions.