Problem Solving - West Ada School District



Critical Content/Concept Web

Subject: __Mathematics__________________________________

Unit Topic:

Grade: 3rd

Possible Reporting Topics

RT 1 & 2: Number Systems, Relationships & Representations Students extend their understanding of the number system (whole numbers, decimals, and fractions) in various situations. They continue their work with place value models (e.g., base-10 blocks, grids, number line), and fractional models (number line, Cuisenaire rods, pictures) to deepen their knowledge of decimals and fractions. They understand that the size of a fractional part is relative to the size of the whole (unitizing) and use that understanding to make sense of addition and subtraction of fractions and decimals (e.g., ¼ of an hour is 15 minutes and/or ¼ of a dollar is $0.25). Students explore probability situations through various activities in real world situations and represent that information in fraction and decimal notation.

RT3: Addition and Subtraction Computation Students apply their understanding of fractions and fraction models to represent the addition and subtraction of fractions including unlike denominators. They understand that the size of a fractional part is relative to the size of the whole (unitizing) and use that understanding to make sense of addition and subtraction of fractions (e.g., ¼ of an hour is 15 minutes because ¼ + ¼ + ¼ + ¼ = 1 and 15 min. + 15 min. + 15 min. + 15 min = 1 hour). They apply their understandings of decimal models, place value, and properties to add and subtract decimals. They develop fluency with addition and subtraction of fractions and decimals, including problems involving measurement. They make reasonable estimates of fraction and decimal sums and differences.

RT 4: Multiplication and Division Computation Students apply their understanding of models for division and the relationship of division to multiplication as they develop efficient, accurate and generalizable procedures to find quotients involving multi-digit dividends. They analyze concepts of divisibility, such as factors, multiples, primes and composites as they relate to division and through analysis develop the "rules" for divisibility. Students select appropriate methods and apply them accurately to estimate quotients or calculate them mentally, depending on the context or numbers involved. They develop fluency with efficient procedures, including the standard algorithm, understand why the procedures work (place value) and use them to solve problems. They consider the context in which a problem is situated to select the most useful form of the quotient for the solution.

RT 5: Measurement Systems Students continue to develop their understanding of formal measurement systems, and performing unit conversions. Through hands-on activities, such as measuring the side lengths of rectangles in centimeters and then converting that measure to millimeters and meter equivalents, students develop a strong conceptual foundation for how units within a system compare to each other. Students measure the length, width and depth of three dimensional objects to calculate the volume as well as convert these measures into other units.

RT 6: Dimensional Measurement Relationships Students apply their previous understandings of perimeter and area of two-dimensional figures to develop an understanding of volume of three-dimensional figures. Through activities such as filling boxes with cubes, students gain a conceptual understanding of volume and apply this understanding to real-world problems. In addition, students understand and use the formula for volume.

RT 7: Algebraic Symbolism & Evaluation Students continue to develop an understanding of an unknown quantity by using a letter (variable) to represent the quantity. They solve for the unknown in computation situations, including the use of decimals and fractions in addition and subtraction contexts. They continue to develop an understanding of equality around the equal sign (=) and generate equivalent equations in computation situations involving decimals and fractions. Students continue to develop their understanding of patterns by analyzing growth situations that have a constant rate of change involving the addition and subtraction of fractions and decimals.

RT 8: Geometric Figures Students extend their understanding of two-dimensional shapes by using defining attributes in order to classify two-dimensional figures into categories. By analyzing the properties of two-dimensional shapes, students understand that attributes belonging to one category of figures (e.g., rectangles have 4 right angles) also apply to all subcategories of that category (e.g., squares are rectangles because they have 4 right angles). In addition, through activities such as building and drawing, students recognize volume as an attribute of three-dimensional space. Students relate their understanding of 2D shapes to 3D shapes. Students analyze the properties of 2D & 3D shapes, describing them by the number of edges, vertices or faces, as well as the shape(s) of faces. They develop an understanding of congruence and similarity as they explore shapes that look alike. Students come to understand congruent shapes as those that match exactly and similar shapes as those related by magnification and reduction. In addition, they extend their work with the first quadrant of the Cartesian coordinate system by plotting points.

|Grade: 3 |

|Subject: Math |

|Unit: Problem Solving Strategies |

|Enduring Understandings |Guiding Questions |

|EU 1: Mathematical reasoning and problem solving are part of all mathematics. |What strategy can be used to solve this problem? In what way can the mathematical reasoning be |

| |communicated mathematically? What product can be used to represent your solution? |

|EU 2: Measurement systems utilize standardized tools and units to measure attributes of objects. |What tools and units of measurement would I use to measure capacity, weight, temperature, and |

| |time? |

|EU 3: Measuring perimeter is an extension of measuring length. |What would be the appropriate units, strategies, and tools to use to solve problems related to |

| |perimeter? |

|EU 4: Describing, extending and generalizing rules help students develop their understanding of |How can I embed the analysis of patterns into the number line, ratio tables, and arrays? How can|

|patterns. |I generalize patterns by translating them using numbers and letters and representing the |

| |information in a table? |

|EU 5: Building, drawing, and analyzing two-dimensional shapes allow students to understand their|How can I describe, analyze, compare, and classify two-dimensional shapes by their sides and |

|attributes and properties. |angles? |

|EU 6: Using mental imagery of arrays and geometric shapes help develop spatial reasoning. |What are symmetry, vertex, angle, and side. How can 2D shapes be classified? What are lines of |

| |symmetry? |

|EU 7: Data can be gathered, organized, and displayed. |How can I share data using a chart? How can data help answer questions? |

|Grade: 3 |

|Subject: Math |

|Unit: Problem Solving Strategies |

| AC = Assessment Code: P – Prompts R-Rubric V-Video |

|Critical Content and Skills O – Observation WS – Work Samples PO-Portfolio |

|PR-Products SA – Student Self-Assessment T – Tests |

|D- Dialogues |

|Students will Know That… |AC |Students will be able to… |AC |

|Results can be estimated and judged for reasonableness. |D, WS, T, P, SA |Estimate all computation to determine if it is reasonable. |D, WS, T, P, SA |

|There are a variety of strategies to find the same answer to problems. |D, WS, T, P, SA |Use rounding as a way of predicting. |D, WS, T, P, SA |

| Reasoning skills are used to recognize and express |D, WS, T, P, SA |Recognize if estimates are useful but different from an exact answer. |D, WS, T, P, SA |

|problems mathematically. | | | |

|Data can be collected and interpreted. |D, WS, T, P, SA |Use a variety of problem-solving strategies. |D, WS, T, P, SA |

|Measurement systems utilize standardized tools and units to measure attributes of |D, WS, T, P, SA |Use a variety of measurement tools. |D, WS, T, P, SA |

|objects. | | | |

|Graphs visually reflect data. |D, WS, T, P, SA | Collect and organize data for analysis |D, WS, T, P, SA |

|Data can be graphed in multiple forms. |D, WS, T, P, SA |Determine an appropriate method to display data collected |D, WS, T, P, SA |

|Shapes can be understood if you understand their attributes and properties. |D, WS, T, P, SA |Build, draw, and analyze two-dimensional shapes. |D, WS, T, P, SA |

Unit: Problem Solving Strategies Grade: 3

|Suggested Activities & Unit Resources: E.U. |Where is this |

| |unit located? |

|Dancing With Decimal by Rachel McAllen EU 1, 7 |Spalding |

|No Problem!, Vydra & McCall | |

|Favorite Problems by Dale Seymour EU 1, 4, 7 |EH |

|Math For Girls and Other Problem Solvers by Downie, Slesnick, Stenmark | |

|Continental Mathematics League: Best of CML Grades 2-6 (Multi-Step Problem Solving) EU 1, 4, 7 |EH |

|Logic books EU 1, 4, 7 |Frontier, EH |

|Resources that include mathematical patterns or unknowns in computation EU 1, 4 |Frontier |

|Checking Out Patterns (Dale Seymour Publications) | |

|Tangrams EU 1-7 |EH |

|Pentominoes EU 1-7 |Frontier, EH |

|Cuisenaire Rods (ETA Cuisenaire) EU1-4,6-7 |Frontier, EH |

|Tessellations (Lawrence Hall of Science) EU 1-7 |Frontier, EH |

|Mathematical Tool Box | |

|Pattern Blocks EU1,2, 5-7 |EH |

|Math By All Means: Probability (Marilyn Burns, Math Solutions Pub.) | |

|Checking Out Patterns by Dale Seymour | |

|Study of Cubes | |

| |

|It’s Alive and Kicking by Asa Kleiman (Prufrock Press) EU 1-7 5, 7 |EH |

|Primary Grade Challenge Math by Zaccro EU 1-7 |EH |

| | |

| | |

|Polydrons |EU 1-7 |EH |

|Zomes |EU 1-7 |EH |

|Graphing |EU 1, 2, 7 |Frontier |

|Probability | | |

|Critical Thinking Puzzles by Michael Pispenzio |EU 1,4,5,7 |EH |

|Critical Thinking Activities by Dale Seymour |EU 1,4,5,7 |Frontier |

| | | |

| | | |

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Unit Overview

Through a variety of hands-on activities, students will learn to choose appropriate problem solving techniques. They will explore problem solving, probability, data collection and analysis, graphing, and decimals.

Suggested Time Frame

6-8 weeks

Problem Solving Strategies

Unit Topic:

Problem Solving Strategies

Suggested Units: See “Suggested Activities and Unit Resources” at the end of this unit.

Support Materials: See “Suggested Activities & Unit Resources” at end of unit.

Possible Reporting Topics

RT 1: Number Systems

RT 2: Number Relationships and Representations

RT 3: Addition and Subtraction Computation

RT 4: Multiplication and Division Computation

RT 5: Measurement Systems

RT 6: Dimensional Measurement Relationships

RT 7: Algebraic Symbolism & Evaluation

RT 8: Geometric Figures

Critical Thinking

CR 1: Making Observations

CR 3: Asking & Answering Questions of Clarification

CR 4: Making & Judging Deductions

CR 5: Identifying Assumptions

CR 7: Deciding On an Action

CR 8: Defining Terms & Judging Definitions

CR 12: Focusing On a Question

CR 13: Making & Judging Inductions

Analytical Thinking

AN 1: Comparing & Contrasting

AN 2: Classifying

AN 4: Recognizing Attributes

AN 5: Pattern Finding & Completion

AN 6: Completing & Making Analogies

AN 7: Inferring

AN 9: Ranking, Prioritizing, Sequencing

AN 10: Analyzing

AN 11: Analyzing

AN 12: Evaluating

AN 13: Predicting

Creative Thinking

CV 2: Brainstorming

CV 3: Creative Thinking Processes (Flexibility)

Organizational Thinking

OR 1: Interpreting Data

OR 2: Mathematical Problem Solving

OR 3: Summarizing

OR 4: Memorization Techniques

OR 5: Decision Making Techniques

OR 6: Formulating Questions

OR 7: Goal Setting / Planning / Designing

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