4.OA: Operations and Algebraic Thinking

4.OA.A: Use the four operations with whole numbers to solve problems.

4.OA.A.1: Interpret a multiplication equation as a comparison, e.g., 35 = 5 × 7, as 35 is 5 times as many as 7. Represent verbal multiplicative comparisons as equations.

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

4.OA.A.2: Multiply or divide to solve word problems involving multiplicative comparison.

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

4.OA.B: Gain familiarity with factors and multiples.

4.OA.B.4: Find all factor pairs for a whole number in the range 1–100.

4.OA.B.4.a: Recognize that a whole number is a multiple of each of its factors.

Factor Trees (Factoring Numbers)
Pattern Flip (Patterns)

4.OA.B.4.b: Determine whether a given whole number in the range 1–100 is a multiple of a given one-digit number.

Factor Trees (Factoring Numbers)
Pattern Flip (Patterns)

4.OA.B.4.c: Determine whether a given whole number in the range 1–100 is prime or composite.

Factor Trees (Factoring Numbers)
Finding Factors with Area Models

4.OA.C: Generate and analyze patterns.

4.OA.C.5: Generate a number or shape pattern that follows a given rule. Identify and explain features of the pattern that were not explicit in the rule itself.

Finding Patterns
Function Machines 1 (Functions and Tables)
Pattern Flip (Patterns)

4.NBT: Number and Operations in Base Ten

4.NBT.A: Generalize place value understanding for multi-digit whole numbers, less than or equal to 1,000,000.

4.NBT.A.1: Recognize that in a multi-digit whole number, a digit in any place represents ten times as much as it represents in the place to its right.

Cannonball Clowns (Number Line Estimation)
Cargo Captain (Multi-digit Subtraction)
Modeling Whole Numbers and Decimals (Base-10 Blocks)
Whole Numbers with Base-10 Blocks

4.NBT.A.2: Read and write multi-digit whole numbers using standard form, expanded form, and word form. Compare two multi-digit numbers based on meanings of the digits and each place, recording the results of comparisons with the symbols >, =, and <.

Cannonball Clowns (Number Line Estimation)
Modeling Whole Numbers and Decimals (Base-10 Blocks)
Whole Numbers with Base-10 Blocks

4.NBT.A.3: Use place value understanding or visual representation to round multi-digit whole numbers to any place.

Rounding Whole Numbers (Number Line)

4.NBT.B: Use place value understanding and properties of operations to perform multidigit arithmetic on whole numbers less than or equal to 1,000,000.

4.NBT.B.4: Fluently use the standard algorithm for multi-digit whole-number addition and subtraction.

Adding Whole Numbers and Decimals (Base-10 Blocks)
Cargo Captain (Multi-digit Subtraction)
Subtracting Whole Numbers and Decimals (Base-10 Blocks)
Whole Numbers with Base-10 Blocks

4.NBT.B.5: Multiply a whole number of up to four digits by a one-digit whole number, and multiply two two-digit numbers.

4.NBT.B.5.a: Use strategies based on place value and the properties of operations.

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

4.NBT.B.5.b: Illustrate and explain the calculation by using equations, rectangular arrays, and/or area models.

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

4.NBT.B.6: Find whole-number quotients and remainders with up to four-digit dividends and one-digit divisors.

4.NBT.B.6.a: Use strategies based on place value, the properties of operations, and/or the relationship between multiplication and division.

Factor Trees (Factoring Numbers)

4.NBT.B.6.b: Illustrate and explain the calculation by using rectangular arrays, area models, and/or equations.

No Alien Left Behind (Division with Remainders)

4.NF: Number and Operations - Fractions

4.NF.A: Extend understanding of fraction equivalence and ordering.

4.NF.A.1: Explain why a fraction a/b is equivalent to a fraction (n x a)/(n x b) by using visual fraction models, with attention to how the numbers and sizes of the parts differ even though the two fractions themselves are the same size. Use this principle to recognize and generate equivalent fractions, including fractions greater than 1.

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)

4.NF.A.2: Compare two fractions with different numerators and different denominators, by creating common denominators or numerators, or by comparing to a benchmark fraction such as 1/2.

4.NF.A.2.b: Record the results of comparisons with symbols >, =, or <, and justify the conclusions, by using a visual fraction model and/or verbal reasoning.

Equivalent Fractions (Fraction Tiles)
Fraction Artist 1 (Area Models of Fractions)
Fraction Artist 2 (Area Models of Fractions)
Fraction Garden (Comparing Fractions)
Modeling Fractions (Area Models)

4.NF.B: Build fractions from unit fractions by applying and extending previous understandings of operations on whole numbers.

4.NF.B.3: Understand a fraction a/b with a > 1 as a sum of fractions 1/b.

4.NF.B.3.a: Understand addition and subtraction of fractions as joining and separating parts referring to the same whole.

Adding Fractions (Fraction Tiles)
Fraction Artist 2 (Area Models of Fractions)
Fractions Greater than One (Fraction Tiles)
Modeling Fractions (Area Models)

4.NF.B.3.b: Decompose a fraction into a sum of fractions with the same denominator in more than one way, recording each decomposition by an equation. Justify the conclusions by using a visual fraction model and/or verbal reasoning.

Adding Fractions (Fraction Tiles)
Equivalent Fractions (Fraction Tiles)
Fraction Artist 1 (Area Models of Fractions)
Fraction Artist 2 (Area Models of Fractions)

4.NF.B.3.c: Add and subtract mixed numbers with like denominators by replacing the mixed number with an equivalent fraction and/or by using properties of operations and the relationship between addition and subtraction.

Fractions Greater than One (Fraction Tiles)
Improper Fractions and Mixed Numbers

4.NF.B.3.d: Solve word problems involving addition and subtraction of fractions, including mixed numbers, with the same denominator. Justify the conclusions using a visual fraction model and/or verbal reasoning.

Adding Fractions (Fraction Tiles)
Fractions Greater than One (Fraction Tiles)
Improper Fractions and Mixed Numbers

4.NF.B.4: Apply and extend previous understandings of multiplication to multiply a fraction by a whole number.

4.NF.B.4.a: Understand a fraction a/b as a multiple of 1/b.

Fraction Artist 1 (Area Models of Fractions)
Fraction Artist 2 (Area Models of Fractions)
Modeling Fractions (Area Models)

4.NF.B.4.b: Understand a multiple of a/b as a multiple of 1/b, and use this understanding to multiply a fraction by a whole number.

Fraction Artist 1 (Area Models of Fractions)
Fraction Artist 2 (Area Models of Fractions)
Modeling Fractions (Area Models)

4.NF.C: Understand decimal notation for fractions, and compare decimal fractions.

4.NF.C.5: Express a fraction with denominator 10 as an equivalent fraction with denominator 100, and use this technique to add two fractions with respective denominators 10 and 100.

Fraction, Decimal, Percent (Area and Grid Models)

4.NF.C.6: Use decimal notation to represent fractions with denominators 10 or 100.

Fraction, Decimal, Percent (Area and Grid Models)

4.NF.C.7: Compare two decimals to hundredths by reasoning about their size.

4.NF.C.7.b: Record the results of the comparisons with the symbols >, =, and <, and justify the conclusions using visual representations and/or verbal reasoning.

Fraction, Decimal, Percent (Area and Grid Models)
Modeling Decimals (Area and Grid Models)
Treasure Hunter (Decimals on the Number Line)

4.MD: Measurement and Data

4.MD.A: Solve problems involving measurement and conversion of measurements from a larger unit to a smaller unit.

4.MD.A.1: Know relative sizes of measurement units within any one system of units.

4.MD.A.1.a: Within a single system of measurement, express measurements in a larger unit in terms of a smaller unit.

Cannonball Clowns (Number Line Estimation)

4.MD.A.2: Use the four operations to solve word problems involving measurements.

4.MD.A.2.a: Include problems involving simple fractions or decimals.

Road Trip (Problem Solving)
Weight and Mass

4.MD.A.2.c: Represent measurement quantities using diagrams such as number line diagrams that feature a measurement scale.

Cannonball Clowns (Number Line Estimation)
Treasure Hunter (Decimals on the Number Line)

4.MD.A.3: Apply the area and perimeter formulas for rectangles in real-world and mathematical problems.

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

4.MD.C: Geometric measurement: Understand concepts of angle and measure angles.

4.MD.C.7: Solve addition and subtraction problems to find unknown angles on a diagram in real-world and mathematical problems.

4.MD.C.7.b: Recognize angle measure as additive. When an angle is decomposed into non-overlapping parts, the angle measure of the whole is the sum of the angle measures of the parts.

Investigating Angle Theorems

4.G: Geometry

4.G.A: Draw and identify lines and angles, and classify shapes by properties of their lines and angles

4.G.A.1: Draw points, lines, line segments, rays, angles (right, acute, obtuse), and perpendicular and parallel lines. Identify these in two-dimensional figures.

Classifying Quadrilaterals
Classifying Triangles

4.G.A.2: Classify two-dimensional figures based on the presence or absence of parallel or perpendicular lines, or the presence or absence of angles of a specified size. Recognize right triangles as a category, and identify right triangles.

Classifying Quadrilaterals
Classifying Triangles

4.G.A.3: Recognize a line of symmetry for a two-dimensional figure as a line across the figure such that the figure can be folded along the line into matching parts. Identify line-symmetric figures and draw lines of symmetry.

Quilting Bee (Symmetry)
Rock Art (Transformations)