options: Operations & Algebra: students learn to solve problems using algebraic thinking and operations such as addition, subtraction, multiplication, and division. They may learn to identify and explain arithmetic patterns, evaluate or manipulate numerical expressions, and reason with equations and inequalities.

Measurement & Data: students learn to work with data and measure attributes such as time, money, length, area, and volume. They may learn to compare measurements to operations and convert between different units of measure.

Ratios & Proportional Relationships: students learn to recognize, describe, represent, and reason with ratios, rates, proportional relationships, and percent.

Counting & Cardinality: students learn to know number names and the count sequence, count to tell the number of objects, and compare numbers.

Number & Operations in Base Ten: students learn to work with the base-ten system and build place value understanding.

Geometry: students learn to classify geometric figures by their properties, and understand and compare the relationships between them. Students develop and use formulas to compute lengths, areas, and volumes, and they use transformations to generate new shapes and compare existing ones. Geometry can be studied with and without coordinates.

Number & Operations - Fractions: students learn to understand fractions as numbers and may work with them using addition, subtraction, multiplication, and division.

Functions: students learn to define, use, and evaluate functions to model relationships between quantities.

Modeling: students learn to choose and use appropriate mathematics and statistics to analyze real-world empirical situations, improve decisions, and report on their conclusions and the reasoning behind them.

Number Systems and Quantity: students learn to understand the complex number system and reason quantitatively.

Statistics & Probability: students learn to analyze and produce data distributions, and build understanding of univariate and bivariate data. They learn to interpret data, make statistical inferences, justify conclusions, understand rules of probability, and use probability to make decisions.
problem_activity: Narrative
The purpose of this activity is for students to solve problems about dividing a whole number by a unit fraction in a way that makes sense to them. The context of quilt making is used so students can visualize a strip of paper that is a whole number length being cut into fractional sized pieces. As students describe how the problems are similar and different, listen for the authentic language they use to describe division. The paper strip, or tape, is a helpful diagram to use when dividing a whole number by a unit fraction because students recognize important relationships between the divisor, dividend, and quotient (MP7). For example, if the length of the strip stays the same, but the size of the piece gets smaller, then the number of pieces will get bigger.
This activity uses
MLR2 Collect and Display.
Advances: Conversing, Reading, Writing.
Launch
Groups of 2
Refer to the picture from the warm up.
“If the blue strip of fabric under the woman’s chin is 1 meter long, about how long is the short gray strip next to it?” (
\(\frac{1}{6}\)
meter)
Activity
1–2 minutes: independent think time
8–10 minutes: partner work time
MLR2 Collect and Display
Circulate, listen for, and collect the language students use to describe what was the same and different about the strategies they used to determine the number of pieces of paper for each color. Listen for:
The size of the piece changed.
The pieces were shorter.
There were more pieces.
I made more cuts.
Record students’ words and phrases on a visual display and update it throughout the lesson.
Student Facing
Below are diagrams that show strips of different colored paper. Each strip is 2 feet long. The paper strips will be cut into different sized pieces.
The red strip will be cut into pieces that are
\(\frac{1}{2}\)
foot long. How many pieces will there be?
[IMG]
The green strip will be cut into pieces that are
\(\frac{1}{3}\)
foot long. How many pieces will there be?
[IMG]
The yellow strip will be cut into pieces that are
\(\frac{1}{4}\)
foot long. How many pieces will there be?
[IMG]
Describe what was the same about the problems you solved. Describe what was different.
Student Response
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Advancing Student Thinking
Students may not immediately make a connection with the situation and division, since the number of pieces that results (the quotient) is greater than the number of feet being divided (the dividend). Consider asking, “How does this situation represent division?” Allow students to recognize that the cuts are similar to partitions in a diagram, or sharing. They may also recognize that the quotient represents the number of groups, while the fraction being divided is the size of each group. Have them write a division equation for each situation, if it helps. They will write division equations in the next activity.
Activity Synthesis
“Are there any other words or phrases that are important to include on our display?”
As students share responses, update the display by adding (or replacing) language, diagrams, or annotations.
Remind students to borrow language from the display as needed.
Display:
\(2 \div \frac {1}{2} = 4\)
\(2 \div \frac {1}{3} = 6\)
\(2 \div \frac {1}{4} = 8\)
“How do these equations represent the problems about the paper strips?” (The 2 is for 2 feet of paper, and the fractions show the size of the pieces that the paper is being cut into. The 4, 6, and 8 are the number of pieces of each color of paper.)


correct_option_index: 6