# Differentiated Problem Solving Recording Sheets - Editable, Digital & Printable

Subject
Resource Type
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Zip (10 MB|34 pages)
Standards
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### Description

These recording sheets are designed to be used with any word problem. All three formats foster detailed math modeling and descriptive answers. Each recording sheet includes space to record the question, create a model, and record the solution.

The in-depth responses your students can share on these recording sheets helps them exercise the standards for mathematical practice, and helps you collect detailed formative and summative assessment data for your math units.

Each format described below is offered as a ready-to-print PDF, an editable PowerPoint document (allows you to edit the text, not not the line width or images), and an uneditable Google slide (perfect for recording responses digitally).

Please open the preview to get a detailed look at each format.

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THREE FORMATS:Step By Step With Math Stick Kids & Step By Step With Bold Numbers
These two formats include detailed steps to guide students through the problem solving process. Both formats are perfect for students who need more scaffolding.

These steps can be edited within the PowerPoint document to fit your needs, but are uneditable on the digital Google slide version and the ready-to-print PDF.

Three steps for recording the question:
• Copy the problem carefully.
• Write a number next to each part of the problem.
• Highlight the question.

Three steps for creating a model:
• Solve each part of the problem using a model.
• Label your model with math vocabulary.
• Create another model showing the same solution in a different way.

Four steps for recording the solution:
• Answer each part of the problem accurately using complete sentences.
• Double check that each part of the problem is answered.
• Double check for capital letters and punctuation.

Structured Spaces
This format includes headings and open space for students to record the question, create a model, and record the solution. The steps for problem solving are not included on the page, making this format ideal for more advanced students who need less scaffolding as they problem solve.

A separate sheet with all 10 problem solving steps listed above is also included.

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Total Pages
34 pages
N/A
Teaching Duration
Lifelong tool
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### Standards

to see state-specific standards (only available in the US).
Look for and express regularity in repeated reasoning. Mathematically proficient students notice if calculations are repeated, and look both for general methods and for shortcuts. Upper elementary students might notice when dividing 25 by 11 that they are repeating the same calculations over and over again, and conclude they have a repeating decimal. By paying attention to the calculation of slope as they repeatedly check whether points are on the line through (1, 2) with slope 3, middle school students might abstract the equation (𝑦 – 2)/(𝑥 – 1) = 3. Noticing the regularity in the way terms cancel when expanding (𝑥 – 1)(𝑥 + 1), (𝑥 – 1)(𝑥² + 𝑥 + 1), and (𝑥 – 1)(𝑥³ + 𝑥² + 𝑥 + 1) might lead them to the general formula for the sum of a geometric series. As they work to solve a problem, mathematically proficient students maintain oversight of the process, while attending to the details. They continually evaluate the reasonableness of their intermediate results.
Look for and make use of structure. Mathematically proficient students look closely to discern a pattern or structure. Young students, for example, might notice that three and seven more is the same amount as seven and three more, or they may sort a collection of shapes according to how many sides the shapes have. Later, students will see 7 × 8 equals the well remembered 7 × 5 + 7 × 3, in preparation for learning about the distributive property. In the expression 𝑥² + 9𝑥 + 14, older students can see the 14 as 2 × 7 and the 9 as 2 + 7. They recognize the significance of an existing line in a geometric figure and can use the strategy of drawing an auxiliary line for solving problems. They also can step back for an overview and shift perspective. They can see complicated things, such as some algebraic expressions, as single objects or as being composed of several objects. For example, they can see 5 – 3(𝑥 – 𝑦)² as 5 minus a positive number times a square and use that to realize that its value cannot be more than 5 for any real numbers 𝑥 and 𝑦.
Attend to precision. Mathematically proficient students try to communicate precisely to others. They try to use clear definitions in discussion with others and in their own reasoning. They state the meaning of the symbols they choose, including using the equal sign consistently and appropriately. They are careful about specifying units of measure, and labeling axes to clarify the correspondence with quantities in a problem. They calculate accurately and efficiently, express numerical answers with a degree of precision appropriate for the problem context. In the elementary grades, students give carefully formulated explanations to each other. By the time they reach high school they have learned to examine claims and make explicit use of definitions.
Use appropriate tools strategically. Mathematically proficient students consider the available tools when solving a mathematical problem. These tools might include pencil and paper, concrete models, a ruler, a protractor, a calculator, a spreadsheet, a computer algebra system, a statistical package, or dynamic geometry software. Proficient students are sufficiently familiar with tools appropriate for their grade or course to make sound decisions about when each of these tools might be helpful, recognizing both the insight to be gained and their limitations. For example, mathematically proficient high school students analyze graphs of functions and solutions generated using a graphing calculator. They detect possible errors by strategically using estimation and other mathematical knowledge. When making mathematical models, they know that technology can enable them to visualize the results of varying assumptions, explore consequences, and compare predictions with data. Mathematically proficient students at various grade levels are able to identify relevant external mathematical resources, such as digital content located on a website, and use them to pose or solve problems. They are able to use technological tools to explore and deepen their understanding of concepts.
Model with mathematics. Mathematically proficient students can apply the mathematics they know to solve problems arising in everyday life, society, and the workplace. In early grades, this might be as simple as writing an addition equation to describe a situation. In middle grades, a student might apply proportional reasoning to plan a school event or analyze a problem in the community. By high school, a student might use geometry to solve a design problem or use a function to describe how one quantity of interest depends on another. Mathematically proficient students who can apply what they know are comfortable making assumptions and approximations to simplify a complicated situation, realizing that these may need revision later. They are able to identify important quantities in a practical situation and map their relationships using such tools as diagrams, two-way tables, graphs, flowcharts and formulas. They can analyze those relationships mathematically to draw conclusions. They routinely interpret their mathematical results in the context of the situation and reflect on whether the results make sense, possibly improving the model if it has not served its purpose.