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Q-A: Reason quantitatively and use units to solve problems

**Standards**:

- Q-A.1. Use units as a way to understand problems and to guide the solution of multi-step problems; choose and interpret units consistently in formulas; choose and interpret the scale and the origin in graphs and data display.
- Q-A.2. Define appropriate quantities for the purpose of descriptive modeling.
- Q-A.3. Choose a level of accuracy appropriate to limitations on measurement when reporting quantities.

**Technology-enhanced investigations:**

LearnZillion:

- Lesson set: Use units as a way to understand and solve problems: Five video lessons: Write the meaning of expressions in practical terms, convert units by using dimensional analysis, determine the correct unit for an answer, understand line graphs by interpreting their scales, use units to determine the appropriateness of an answer. Aligns with Q-A.1.
- Lesson set: Define appropriate quantities for the purpose of descriptive modeling: Four video lessons: Use units to guide the solution to a problem, determine reasonableness of an answer using estimation, choose appropriate units, choose appropriate scales for graphs. Aligns with Q-A.2.
- Lesson set: Choose a level of accuracy appropriate to limitations on measurement: Four video lessons: Determine appropriate level of accuracy, find the quantity that most limits the answer, consider limitations of measuring tools, estimate values on a graph. Aligns with Q-A.3.

NCTM Illuminations: Flowing Through Mathematics: Simulate water flowing from a tube through a hole in the bottom. The diameter of the hole can be adjusted and data can be gathered for the height or volume of water in the tube at any time.

Shodor Interactivate: Triangle Explorer: Learners study the nature of triangles and their area, and can investigate problem solving strategies.

Wolfram Demonstrations Project: Download the free Wolfram CDF player to interact with the following manipulative. There is 1 manipulative addressing Q-A.2:

- Optimal Queue of Cars: Aligns with Q-A.2, Algebra standards CED-A.2, CED-A.3, and Function standard BF-A.1

**Multiple Choice:**

Khan Academy: Practice questions with videos.

- Units of Measurement in Modeling: Aligns with Q-A.3.

OpenEd:

- Units: 4 questions combine multiple choice and free response. Includes related review resources. Aligns with Q-A.1.
- Appropriate quantities for modeling: 5 questions combine multiple choice and free response. Includes related review resources. Aligns with Q-A.2 and mathematical practice standard MP4--model with mathematics.
- Accuracy: 5 questions combine multiple choice and free response. Includes related review resources. Aligns with Q-A.3.

**Constructed-response:**

Consortium for Mathematics and Its Applications (COMAP): Mathematical Modeling Handbook (Sample). This sample mathematical modeling module aligns to Common Core Standards. It contains teacher guidance for implementation and student questions to complete during their investigation:

- The module
*For the Birds*aligns to number and quantity standards Q-A.1 and Q-A.2, and algebra standard CED-A.4.

Khan Academy: Practice questions with videos.

- Units: Aligns with Q-A.1.
- Working with units algebraically: Aligns with Q-A.1.

MathBitsNotebook: Algebra 1: Working with Units includes lessons on significant figures and accuracy and error in measurement, then practice problems on working with units and error in measurement. Use with Q-A.1, Q-A.2, and Q-A.3.

**Performance tasks:**

Illustrative Mathematics:

- Traffic Jam: This task aligns with Q-A, all three standards in the cluster.
- Felicia’s Drive: Aligns with Q-A.1 and Q-A.3.
- Accuracy of Carbon 14 dating II: Aligns with Q-A.3 and function standard LE-A.4.

Inside Mathematics: MARS Task: Swimming Pool: This task aligns with standards Q-A.1, Q-A.2, and Q-A.3. Students work with trapezoids, rates and time graphs in a real context.

Mathematics Assessment Project: Standards: High School: Number and Quantity: Quantities: http://map.mathshell.org/stds.php?standardid=1300

- Task 407: Modeling Population Growth: Having Kittens
- Apprentice Task: Leaky Faucet
- Apprentice Task: Yogurt

Mathematics Vision Project, Secondary 1 Student Edition: Getting Ready Module: This module contains 10 classroom tasks. Task 3: Serving Up Symbols; and Task 4: Examining Units align with Q-A.1. Task 1: Checkerboard Borders; and Task 2: Building More Checkerboard Borders align with Q-A.2. Tasks 1-3 also include algebra standard SSE-A.1. The remaining six tasks addressed in this module include algebra standards REI-A.1, REI-B.3, and CED-A.4.

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