3.MP: Mathematical Practices

(Framing Text): Students become mathematically proficient in engaging with mathematical content and concepts as they learn, experience, and apply these skills and attitudes

3.MP.1: Make sense of problems and persevere in solving them.

Biconditional Statements
Conditional Statements
Estimating Population Size
Pattern Flip (Patterns)

3.MP.1.a: Explain the meaning of a problem, look for entry points to begin work on the problem, and plan and choose a solution pathway. When a solution pathway does not make sense, look for another pathway that does. Explain connections between various solution strategies and representations. Upon finding a solution, look back at the problem to determine whether the solution is reasonable and accurate, often checking answers to problems using a different method or approach.

Biconditional Statements
Fraction, Decimal, Percent (Area and Grid Models)
Improper Fractions and Mixed Numbers
Linear Inequalities in Two Variables
Modeling One-Step Equations
Multiplying with Decimals
Pattern Flip (Patterns)
Polling: City
Solving Equations on the Number Line
Using Algebraic Expressions

3.MP.2: Reason abstractly and quantitatively.

Conditional Statements
Estimating Population Size

3.MP.3: Construct viable arguments and critique the reasoning of others.

Biconditional Statements

3.MP.3.a: Use stated assumptions, definitions, and previously established results to construct arguments. Explain and justify the mathematical reasoning underlying a strategy, solution, or conjecture by using concrete referents such as objects, drawings, diagrams, and actions. Listen to or read the arguments of others, decide whether they make sense, ask useful questions to clarify or improve the arguments, and build on those arguments.

Biconditional Statements
Conditional Statements

3.MP.4: Model with mathematics.

Estimating Sums and Differences

3.MP.5: Use appropriate tools strategically.

Elapsed Time

3.MP.5.a: Consider the tools that are available when solving a mathematical problem, whether in a real-world or mathematical context. Choose tools that are relevant and useful to the problem at hand, such as drawings, diagrams, technologies, and physical objects and tools, as well as mathematical tools such as estimation or a particular strategy or algorithm.

Segment and Angle Bisectors

3.MP.6: Attend to precision.

Biconditional Statements
Fraction, Decimal, Percent (Area and Grid Models)
Using Algebraic Expressions

3.MP.6.a: Communicate precisely to others by crafting careful explanations that communicate mathematical reasoning by referring specifically to each important mathematical element, describing the relationships among them, and connecting their words clearly to representations. Calculate accurately and efficiently, and use clear and concise notation to record work.

Arithmetic Sequences
Finding Patterns
Fraction, Decimal, Percent (Area and Grid Models)
Function Machines 2 (Functions, Tables, and Graphs)
Geometric Sequences
Pattern Flip (Patterns)

3.MP.7: Look for and make use of structure.

Pattern Flip (Patterns)

3.MP.7.a: Recognize and apply the structures of mathematics such as patterns, place value, the properties of operations, or the flexibility of numbers. See complicated things as single objects or as being composed of several objects.

Arithmetic Sequences
Finding Patterns
Function Machines 2 (Functions, Tables, and Graphs)
Geometric Sequences
Pattern Flip (Patterns)

3.MP.8: Look for and express regularity in repeated reasoning.

Arithmetic Sequences
Arithmetic and Geometric Sequences
Finding Patterns
Geometric Sequences
Pattern Finder
Pattern Flip (Patterns)

3.MP.8.a: Notice repetitions in mathematics when solving multiple related problems. Use observations and reasoning to find shortcuts or generalizations. Evaluate the reasonableness of intermediate results.

Arithmetic Sequences
Arithmetic and Geometric Sequences
Geometric Sequences

3.OA: Operations and Algebraic Thinking

(Framing Text): Represent and solve problems involving multiplication and division within 100.

3.OA.1: Interpret products of whole numbers, such as interpret 5 × 7 as the total number of objects in 5 groups of 7 objects each.

Chocomatic (Multiplication, Arrays, and Area)
Critter Count (Modeling Multiplication)

3.OA.2: Interpret whole-number quotients of whole numbers.

No Alien Left Behind (Division with Remainders)

3.OA.3: Use multiplication and division within 100 to solve word problems in situations involving equal groups, arrays, and measurement quantities.

Chocomatic (Multiplication, Arrays, and Area)
Critter Count (Modeling Multiplication)
No Alien Left Behind (Division with Remainders)

3.OA.4: Determine the unknown whole number in a multiplication or division equation relating three whole numbers.

Factor Trees (Factoring Numbers)

(Framing Text): They demonstrate understanding of the properties of multiplication and the relationship between multiplication and division.

3.OA.6: Understand division as an unknown-factor problem. Understand the relationship between multiplication and division (multiplication and division are inverse operations).

Factor Trees (Factoring Numbers)

(Framing Text): Represent and solve problems involving multiplication and division within 100.

3.OA.7: Fluently multiply and divide.

3.OA.7.a: Fluently multiply and divide within 100, using strategies such as the relationship between multiplication and division or properties of operations. (For example, knowing that 8 x 5 = 40, one knows 40 ÷ 5 = 8).

Critter Count (Modeling Multiplication)
Factor Trees (Factoring Numbers)
Multiplying Decimals (Area Model)
No Alien Left Behind (Division with Remainders)
Pattern Flip (Patterns)

3.OA.7.b: By the end of Grade 3, know from memory all products of two one-digit numbers.

Critter Count (Modeling Multiplication)
Factor Trees (Factoring Numbers)
Multiplying Decimals (Area Model)
Pattern Flip (Patterns)

(Framing Text): Students use the four operations to identify and explain patterns in arithmetic.

3.OA.8: Solve two-step word problems.

3.OA.8.a: Solve two-step word problems using the four operations. Know how to perform operations in the conventional order when there are no parentheses to specify a particular order (Order of Operations). (Limit to problems posed with whole numbers and having whole number answers.)

Cargo Captain (Multi-digit Subtraction)
Critter Count (Modeling Multiplication)
No Alien Left Behind (Division with Remainders)
Number Line Frog Hop (Addition and Subtraction)
Using Algebraic Equations
Using Algebraic Expressions

3.OA.8.b: Represent two-step problems using equations with a letter standing for the unknown quantity. Create accurate equations to match word problems.

Cargo Captain (Multi-digit Subtraction)
Critter Count (Modeling Multiplication)
No Alien Left Behind (Division with Remainders)
Number Line Frog Hop (Addition and Subtraction)
Using Algebraic Equations
Using Algebraic Expressions

3.OA.8.c: Assess the reasonableness of answers using mental computation and estimation strategies, including rounding.

Cargo Captain (Multi-digit Subtraction)
Critter Count (Modeling Multiplication)
No Alien Left Behind (Division with Remainders)
Number Line Frog Hop (Addition and Subtraction)
Using Algebraic Equations
Using Algebraic Expressions

3.OA.9: Identify arithmetic patterns (including patterns in the addition table or multiplication table), and explain them using properties of operations.

Pattern Flip (Patterns)

3.NBT: Number and Operations in Base Ten

(Framing Text): Use place value understanding and properties of operations to perform multi-digit arithmetic. A range of algorithms may be used.

3.NBT.1: Use place value understanding to round whole numbers to the nearest 10 or 100.

Rounding Whole Numbers (Number Line)

3.NBT.2: Fluently add and subtract within 1,000 using strategies and algorithms based on place value, properties of operations, and/or the relationship between addition and subtraction.

Adding Fractions (Fraction Tiles)
Adding Whole Numbers and Decimals (Base-10 Blocks)
Cargo Captain (Multi-digit Subtraction)
Fractions Greater than One (Fraction Tiles)
Number Line Frog Hop (Addition and Subtraction)
Rounding Whole Numbers (Number Line)
Subtracting Whole Numbers and Decimals (Base-10 Blocks)
Target Sum Card Game (Multi-digit Addition)
Whole Numbers with Base-10 Blocks

3.NF: Number and Operations—Fractions

(Framing Text): Develop understanding of fractions as numbers.

3.NF.1: Understand that a unit fraction has a numerator of one and a non-zero denominator.

3.NF.1.a: Understand a fraction 1/b as the quantity formed by one part when a whole is partitioned into b equal parts.

Equivalent Fractions (Fraction Tiles)
Fraction Artist 1 (Area Models of Fractions)
Fraction Artist 2 (Area Models of Fractions)
Fraction Garden (Comparing Fractions)
Fraction, Decimal, Percent (Area and Grid Models)
Modeling Fractions (Area Models)
Toy Factory (Set Models of Fractions)

3.NF.1.b: Understand a fraction a/b as the quantity formed by a parts of size 1/b. For example: 1/4 + 1/4 + 1/4 = 3/4.

Equivalent Fractions (Fraction Tiles)
Fraction Artist 1 (Area Models of Fractions)
Fraction Artist 2 (Area Models of Fractions)
Fraction Garden (Comparing Fractions)
Fraction, Decimal, Percent (Area and Grid Models)
Modeling Fractions (Area Models)
Toy Factory (Set Models of Fractions)

3.NF.2: Understand a fraction as a number on the number line; represent fractions on a number line diagram.

3.NF.2.a: Represent a fraction 1/b on a number line diagram by defining the interval from 0 to 1 as the whole and partitioning it into b equal parts. Recognize that each part has size 1/b and that the endpoint of the part based at 0 locates the number 1/b on the number line.

Fraction Garden (Comparing Fractions)
Fractions Greater than One (Fraction Tiles)
Modeling Fractions (Area Models)

3.NF.2.b: Represent a fraction a/b on a number line diagram by marking off a lengths 1/b from 0. Recognize that the resulting interval has size a/b and that its endpoint locates the number a/b on the number line.

Fraction Garden (Comparing Fractions)
Fractions Greater than One (Fraction Tiles)
Modeling Fractions (Area Models)

3.NF.3: Explain equivalence of fractions in special cases, and compare fractions by reasoning about their size.

3.NF.3.a: Understand two fractions as equivalent if they are the same size, or the same point on a number line.

Adding Fractions (Fraction Tiles)
Equivalent Fractions (Fraction Tiles)
Factor Trees (Factoring Numbers)
Fraction Artist 1 (Area Models of Fractions)
Fraction Artist 2 (Area Models of Fractions)
Fraction Garden (Comparing Fractions)
Fractions Greater than One (Fraction Tiles)
Modeling Fractions (Area Models)
Toy Factory (Set Models of Fractions)

3.NF.3.b: Recognize and generate simple equivalent fractions, such as 1/2 = 2/4, 4/6 = 2/3. Explain why the fractions are equivalent by using a visual fraction model, for example.

Adding Fractions (Fraction Tiles)
Equivalent Fractions (Fraction Tiles)
Factor Trees (Factoring Numbers)
Fraction Artist 1 (Area Models of Fractions)
Fraction Artist 2 (Area Models of Fractions)
Fraction Garden (Comparing Fractions)
Fractions Greater than One (Fraction Tiles)
Modeling Fractions (Area Models)
Toy Factory (Set Models of Fractions)

3.NF.3.c: Express whole numbers as fractions, and recognize fractions that are equivalent to whole numbers.

Equivalent Fractions (Fraction Tiles)

3.NF.3.d: Compare two fractions with the same numerator or the same denominator by reasoning about their size. Recognize that comparisons are valid only when the two fractions refer to the same whole. Record the results of comparisons with the symbols >, =, or <, and justify the conclusions, for example, by using a visual fraction model.

Adding Fractions (Fraction Tiles)
Equivalent Fractions (Fraction Tiles)
Fraction Artist 1 (Area Models of Fractions)
Fraction Artist 2 (Area Models of Fractions)
Fraction Garden (Comparing Fractions)
Fractions Greater than One (Fraction Tiles)
Modeling Fractions (Area Models)
Toy Factory (Set Models of Fractions)

3.MD: Measurement and Data

(Framing Text): Solve problems involving measurement and estimation of intervals of time, liquid volumes, and masses of objects.

3.MD.1: Tell and write time to the nearest minute and measure time intervals in minutes. Solve word problems involving addition and subtraction of time intervals in minutes, for example, by representing the problem on a number line diagram.

Elapsed Time

3.MD.2: Measure and estimate liquid volumes and masses of objects using standard units of grams (g), kilograms (kg), milliliters (ml), and liters (l). (Excludes compound units such as cubic centimeters [cc or cm3] and finding the geometric volume of a container.) Add, subtract, multiply, or divide to solve one-step word problems involving masses of objects or volumes of liquids that are given in the same units, for example, by using drawings (such as a beaker with a measurement scale) to represent the problem. (Excludes multiplicative comparison problems.)

Balancing Blocks (Volume)
Cannonball Clowns (Number Line Estimation)

(Framing Text): Represent and interpret data.

3.MD.3: Draw a scaled picture graph and a scaled bar graph to represent a data set with several categories. Solve one- and two-step “how many more” and “how many less” problems using information presented in scaled bar graphs.

Forest Ecosystem
Graphing Skills
Mascot Election (Pictographs and Bar Graphs)
Reaction Time 1 (Graphs and Statistics)

3.MD.4: Generate measurement data by measuring lengths using rulers marked with halves and fourths of an inch. Show the data by making a line plot where the horizontal scale is marked off in appropriate units-whole numbers, halves, or quarters.

Reaction Time 2 (Graphs and Statistics)

(Framing Text): Understand concepts of area and relate area to multiplication and addition.

3.MD.5: Recognize area as an attribute of plane figures and understand concepts of area measurement.

3.MD.5.a: A square with side length one unit, called “a unit square,” is said to have “one square unit” of area, and can be used to measure area.

Balancing Blocks (Volume)
Chocomatic (Multiplication, Arrays, and Area)
Fido's Flower Bed (Perimeter and Area)

3.MD.5.b: A plane figure which can be covered without gaps or overlaps by n unit squares is said to have an area of n square units.

Balancing Blocks (Volume)
Chocomatic (Multiplication, Arrays, and Area)
Fido's Flower Bed (Perimeter and Area)

3.MD.6: Measure area by counting unit squares (square centimeters, square meters, square inches, square feet, and improvised units).

Balancing Blocks (Volume)
Chocomatic (Multiplication, Arrays, and Area)
Fido's Flower Bed (Perimeter and Area)

3.MD.7: Relate area to the operations of multiplication and addition (refer to 3.OA.5).

3.MD.7.a: Find the area of a rectangle with whole-number side lengths by tiling it, and show that the area is the same as would be found by multiplying the side lengths.

Chocomatic (Multiplication, Arrays, and Area)
Fido's Flower Bed (Perimeter and Area)

3.MD.7.b: Multiply side lengths to find areas of rectangles with whole-number side lengths in the context of solving real-world and mathematical problems, and represent whole-number products as rectangular areas in mathematical reasoning.

Chocomatic (Multiplication, Arrays, and Area)
Fido's Flower Bed (Perimeter and Area)

3.MD.7.c: Use tiling to show in a concrete case that the area of a rectangle with whole-number side lengths a and b + c is the sum of a x b and a x c. Use area models to represent the distributive property in mathematical reasoning.

Balancing Blocks (Volume)
Chocomatic (Multiplication, Arrays, and Area)
Fido's Flower Bed (Perimeter and Area)

3.MD.7.d: Recognize area as additive. Find areas of rectilinear figures by decomposing them into non- overlapping rectangles and adding the areas of the non-overlapping parts, applying this technique to solve real-world problems.

Chocomatic (Multiplication, Arrays, and Area)

(Framing Text): Recognize perimeter as an attribute of plane figures and distinguish between linear and area measures.

3.MD.8: Solve real-world and mathematical problems involving perimeters of polygons, including finding the perimeter given the side lengths, finding an unknown side length, and exhibiting rectangles with the same perimeter and different areas or with the same area and different perimeters.

Fido's Flower Bed (Perimeter and Area)

3.G: Geometry

(Framing Text): Reason with shapes and their attributes.

3.G.1: Understand that shapes in different categories (for example, rhombuses, rectangles, and others) may share attributes (for example, having four sides), and that the shared attributes can define a larger category (for example, quadrilaterals). Recognize rhombuses, rectangles, and squares as examples of quadrilaterals, and draw examples of quadrilaterals that do not belong to any of these subcategories.

Classifying Quadrilaterals

3.G.2: Partition shapes into parts with equal areas. Express the area of each part as a unit fraction of the whole.

Fraction Artist 1 (Area Models of Fractions)