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

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

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.

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.

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.

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

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.

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

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.

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

Number & Operations in Base Ten: students learn to work with the base-ten system and build place value understanding.
problem_activity: Task
Materials
ruler, meter sticks, yard sticks, measuring tape
paper
crayons
Actions
Part 1
Explain that students will be working in pairs to determine the length of each partner’s foot. Ask what tools would be appropriate for determining length.  Chart student thinking about appropriate tools, and today’s goal of  using standard measurement tools such as rulers, yard sticks, meter sticks, or measuring tape.
Ask student pairs to consider the unit(s) that would give the most precise measure of the length of a student’s foot.  If students struggle with this idea, the teacher might model using his/her foot as an example considering yards, meters, feet, inches and centimeters.
Ask student pairs to identify the unit they will work with and predict the length of each partner’s foot and record their estimations.  Estimates should be recorded in units.
Part 2
Have one student from each pair stand on a blank sheet of paper and have his/her partner make a mark at the student’s heel and another at the toe.
Then, together, have the pair measure the distance between the two marks to determine the length of the first student’s foot and record the length.  Students may have to find the closest unit.
Have students then find the difference between the estimation and actual length.
Repeat with the second student, using a different color to make the marks.  The second student should stand at the same endpoint as the first student so that students can visually compare the two representations and compare the number of the distance in units in part three.
Part 3
Working in pairs, have students compare the distances between the lengths of each student’s foot.
Class Discussion
Engaging in a class discussion will support students in thinking about the mathematical ideas embedded within the task.
What tool did you use and why?
How was that tool helpful?
If you were going to measure _____ (a desk, a whiteboard, an eraser), would you use the same tool? Why?
How long was your foot? What was your estimate? What was the difference?
What unit did you use to measure? How did you decide to use ______? Why is the unit important?
How long was your partner’s foot? What was his/her estimate? What was the difference?
What was the difference between the length of your foot and the length of your partner’s foot? How did you find the difference?
What did you notice about finding the difference? Is there more than one way to find the difference? (This might be an opportunity to discuss finding the difference by measuring how much longer one length is than the other or by using an operation such as addition to add up from the smallest length to the larger length or by subtracting the smaller length from the larger length.)


correct_option_index: 2