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## KS.4.G.Geometry

Geometry
Draw and identify lines and angles, and classify shapes by properties of their lines and angles.
4.G.1. Draw points, lines, line segments, rays, angles (right, acute, obtuse, straight, reflex), and perpendicular and parallel lines. Identify these in two-dimensional figures.
Flip Charts Lines & Angles
Flip Charts Polygons
Flip Charts Polygons
Vocabulary Terms Angles
Vocabulary Terms Lines and Angles
Quiz, Flash Cards, Worksheet, Game & Study Guide Angles
Quiz, Flash Cards, Worksheet, Game & Study Guide Lines and Angles

4.G.2. Classify two-dimensional figures based on the presence or absence of parallel or perpendicular lines, or the presence or absence of angles (right, acute, obtuse, straight, reflex). Recognize and categorize triangles based on angles (acute, obtuse, equiang
Flip Charts Polygons
Flip Charts Polygons
Vocabulary Terms Polygon Characteristics
Quiz, Flash Cards, Worksheet, Game & Study Guide Polygon Characteristics

4.G.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.
Quiz, Flash Cards, Worksheet, Game & Study Guide Symmetry

## KS.4.MD.Measurement and Data

Measurement and Data
Solve problems involving measurement and conversion of measurements from a larger unit to a smaller unit.
4.MD.1. Know relative sizes of measurement units within one system of units including km, m, cm; kg, g; lb, oz; l, ml; hr, min, sec. Within a single system of measurement, express measurements in a larger unit in terms of a smaller unit. Record measurement equiva

4.MD.3. Apply the area and perimeter formulas for rectangles in real world and mathematical problems explaining and justifying the appropriate unit of measure. For example, find the width of a rectangular room given the area of the flooring and the length, by vie
Quiz, Flash Cards, Worksheet, Game & Study Guide Area
Quiz, Flash Cards, Worksheet, Game & Study Guide Area and Perimeter

## KS.4.NBT.Number and Operations in Base Ten

Number and Operations in Base Ten
Generalize place value understanding for multi-digit whole numbers. (Limited to whole numbers less than or equal to 1,000,000.)
4.NBT.1. Recognize that in a multi-digit whole number, a digit in one place represents ten times what it represents in the place to its right. For example, recognize that 70070=10 by applying concepts of place value and division.
Vocabulary Terms Compare and Order Numbers
Vocabulary Terms Compare and Order Numbers
Vocabulary Terms Estimation
Vocabulary Terms Expanding Numbers
Vocabulary Terms Greater Than/Less Than
Vocabulary Terms Place Value
Vocabulary Terms Place Value
Vocabulary Terms Place Value
Vocabulary Terms Rounding Numbers
Vocabulary Terms Whole Numbers to Millions
Quiz, Flash Cards, Worksheet, Game & Study Guide Add/Subtract/Multiply/Divide Decimals
Quiz, Flash Cards, Worksheet, Game & Study Guide Compare and Order Numbers
Quiz, Flash Cards, Worksheet, Game & Study Guide Compare and Order Numbers
Quiz, Flash Cards, Worksheet, Game & Study Guide Estimation
Quiz, Flash Cards, Worksheet, Game & Study Guide Expanding Numbers
Quiz, Flash Cards, Worksheet, Game & Study Guide Exponential & Scientific Notation
Quiz, Flash Cards, Worksheet, Game & Study Guide Greater Than/Less Than
Quiz, Flash Cards, Worksheet, Game & Study Guide Number Words and Place Value
Quiz, Flash Cards, Worksheet, Game & Study Guide Ordering and Comparing Numbers
Quiz, Flash Cards, Worksheet, Game & Study Guide Place Value
Quiz, Flash Cards, Worksheet, Game & Study Guide Place Value
Quiz, Flash Cards, Worksheet, Game & Study Guide Place Value
Quiz, Flash Cards, Worksheet, Game & Study Guide Rounding Numbers
Quiz, Flash Cards, Worksheet, Game & Study Guide Rounding to Nearest 10
Quiz, Flash Cards, Worksheet, Game & Study Guide Whole Numbers to Millions

4.NBT.2. Read and write multi-digit whole numbers using base-ten numerals, number names, expanded form, and unit form. Compare two multi-digit numbers based on meanings of the digits in each place, using >, <, =, and ≠ symbols to record the results of comparisons.
Vocabulary Terms Compare and Order Numbers
Vocabulary Terms Compare and Order Numbers
Vocabulary Terms Expanding Numbers
Vocabulary Terms Greater Than/Less Than
Vocabulary Terms Place Value
Vocabulary Terms Whole Numbers to Millions
Quiz, Flash Cards, Worksheet, Game & Study Guide Algebra
Quiz, Flash Cards, Worksheet, Game & Study Guide Compare and Order Numbers
Quiz, Flash Cards, Worksheet, Game & Study Guide Compare and Order Numbers
Quiz, Flash Cards, Worksheet, Game & Study Guide Expanding Numbers
Quiz, Flash Cards, Worksheet, Game & Study Guide Exponential & Scientific Notation
Quiz, Flash Cards, Worksheet, Game & Study Guide Greater Than/Less Than
Quiz, Flash Cards, Worksheet, Game & Study Guide Greater Than/Less Than
Quiz, Flash Cards, Worksheet, Game & Study Guide Number Words and Place Value
Quiz, Flash Cards, Worksheet, Game & Study Guide Number Words to 1,000
Quiz, Flash Cards, Worksheet, Game & Study Guide Ordering and Comparing Numbers
Quiz, Flash Cards, Worksheet, Game & Study Guide Place Value
Quiz, Flash Cards, Worksheet, Game & Study Guide Whole Numbers to Millions

4.NBT.3. Use place value understanding to round multi-digit whole numbers to any place.
Vocabulary Terms Estimation
Vocabulary Terms Rounding Numbers
Quiz, Flash Cards, Worksheet, Game & Study Guide Estimation
Quiz, Flash Cards, Worksheet, Game & Study Guide Estimation
Quiz, Flash Cards, Worksheet, Game & Study Guide Estimation
Quiz, Flash Cards, Worksheet, Game & Study Guide Rounding
Quiz, Flash Cards, Worksheet, Game & Study Guide Rounding Numbers
Quiz, Flash Cards, Worksheet, Game & Study Guide Rounding to Nearest 10

Use place value understanding and properties of operations to perform multi-digit arithmetic.
4.NBT.4. Fluently (efficiently, accurately, and flexibly) add and subtract multi-digit whole numbers using an efficient algorithm (including, but not limited to: traditional, partial-sums, etc.), based on place value understanding and the properties of operations.
Vocabulary Terms Double Digit Subtraction
Vocabulary Terms Regrouping
Vocabulary Terms Word Problems
Quiz, Flash Cards, Worksheet, Game & Study Guide 3 Digit Addition
Quiz, Flash Cards, Worksheet, Game & Study Guide 3 Digit Subtraction
Quiz, Flash Cards, Worksheet, Game & Study Guide 4 Digit Addition
Quiz, Flash Cards, Worksheet, Game & Study Guide Addition/Subtraction
Quiz, Flash Cards, Worksheet, Game & Study Guide Associative Property
Quiz, Flash Cards, Worksheet, Game & Study Guide Commutative Property
Quiz, Flash Cards, Worksheet, Game & Study Guide Commutative/Associative Properties
Quiz, Flash Cards, Worksheet, Game & Study Guide Double Digit Addition
Quiz, Flash Cards, Worksheet, Game & Study Guide Double Digit Subtraction
Quiz, Flash Cards, Worksheet, Game & Study Guide Multi-step Word Problems
Quiz, Flash Cards, Worksheet, Game & Study Guide Regrouping
Quiz, Flash Cards, Worksheet, Game & Study Guide Word Problems

4.NBT.5. Multiply a whole number of up to four digits by a one-digit whole number, and multiply two two-digit numbers, using strategies based on place value and the properties of operations. Illustrate and explain the calculation by using equations, rectangular ar
Vocabulary Terms Division
Vocabulary Terms Division/Multiplication
Vocabulary Terms More Multiplication
Vocabulary Terms Multiplication
Vocabulary Terms Multiplication
Vocabulary Terms Multiplication
Quiz, Flash Cards, Worksheet, Game & Study Guide Commutative/Associative Properties
Quiz, Flash Cards, Worksheet, Game & Study Guide Division
Quiz, Flash Cards, Worksheet, Game & Study Guide Division/Multiplication
Quiz, Flash Cards, Worksheet, Game & Study Guide More Multiplication
Quiz, Flash Cards, Worksheet, Game & Study Guide Multi-step Word Problems
Quiz, Flash Cards, Worksheet, Game & Study Guide Multiplication
Quiz, Flash Cards, Worksheet, Game & Study Guide Multiplication
Quiz, Flash Cards, Worksheet, Game & Study Guide Multiplication
Quiz, Flash Cards, Worksheet, Game & Study Guide Odd/Even
Quiz, Flash Cards, Worksheet, Game & Study Guide Word Problems

4.NBT.6. Find whole-number quotients and remainders with up to four-digit dividends and one-digit divisors, using strategies based on place value, the properties of operations, and/or the relationship between multiplication and division. Illustrate and explain the
Vocabulary Terms Division
Vocabulary Terms Division
Vocabulary Terms Division/Multiplication
Quiz, Flash Cards, Worksheet, Game & Study Guide Division
Quiz, Flash Cards, Worksheet, Game & Study Guide Division
Quiz, Flash Cards, Worksheet, Game & Study Guide Division
Quiz, Flash Cards, Worksheet, Game & Study Guide Division/Multiplication

## KS.4.NF.Number and Operations – Fractions

Number and Operations – Fractions
Extend understanding of fraction equivalence and ordering. (Limited to fractions with denominators 2, 3, 4, 5, 6, 8, 10, 12, 100)
4.NF.1. Explain why a fraction a/b is equivalent to a fraction n⋅a/n⋅b by using visual fraction models, with attention to how the number and size of the parts differ even though the two fractions themselves are the same size. Use this principle to recognize and g
Flip Charts Fraction Concepts
Flip Charts Fraction Concepts
Vocabulary Terms Equivalent Fractions
Quiz, Flash Cards, Worksheet, Game & Study Guide Equivalent Fractions
Quiz, Flash Cards, Worksheet, Game & Study Guide Fractions
Quiz, Flash Cards, Worksheet, Game & Study Guide Fractions/Decimals

4.NF.2. Compare two fractions with different numerators and different denominators, (e.g. by creating common numerators or denominators, or by comparing to a benchmark fraction such as 1/2.) Recognize that comparisons are valid only when the two fractions refer t
Vocabulary Terms Comparing Fractions
Vocabulary Terms Less Than, Greater Than
Quiz, Flash Cards, Worksheet, Game & Study Guide Compare and Order Fractions
Quiz, Flash Cards, Worksheet, Game & Study Guide Comparing Fractions
Quiz, Flash Cards, Worksheet, Game & Study Guide Equivalent Fractions to 1/2
Quiz, Flash Cards, Worksheet, Game & Study Guide Fractions
Quiz, Flash Cards, Worksheet, Game & Study Guide Fractions/Decimals
Quiz, Flash Cards, Worksheet, Game & Study Guide Less Than, Greater Than
Quiz, Flash Cards, Worksheet, Game & Study Guide Ordering Fractions

Build fractions from unit fractions by applying and extending previous understandings of operations on whole numbers. (Limited to fractions with denominators 2, 3, 4, 5, 6, 8, 10, 12, 100)
4.NF.3. Understand a fraction a/b with a > 1 as a sum of fractions 1/b.
4.NF.3a. Understand addition and subtraction of fractions as joining and separating parts referring to the same whole.
Quiz, Flash Cards, Worksheet, Game & Study Guide Add/Subtract Fractions
Quiz, Flash Cards, Worksheet, Game & Study Guide Add/Subtract Fractions
Quiz, Flash Cards, Worksheet, Game & Study Guide Adding Fractions
Quiz, Flash Cards, Worksheet, Game & Study Guide Number Line
Quiz, Flash Cards, Worksheet, Game & Study Guide Subtracting Fractions

4.NF.3b. Decompose a fraction into a sum of fractions with the same denominator in more than one way, recording each decomposition by an equation. Justify decompositions, e.g. by using a visual fraction model.

4.NF.3c. Add and subtract mixed numbers with like denominators, e.g. by replacing each mixed number with an equivalent fraction (simplest form is not an expectation), and/or by using properties of operations and the relationship between addition and subtraction.
Quiz, Flash Cards, Worksheet, Game & Study Guide Add/Subtract Fractions
Quiz, Flash Cards, Worksheet, Game & Study Guide Adding Fractions
Quiz, Flash Cards, Worksheet, Game & Study Guide Subtracting Fractions

4.NF.3d. Solve word problems involving addition and subtraction of fractions referring to the same whole and having like denominators, e.g. by using visual fraction models and equations to represent the problem.
Quiz, Flash Cards, Worksheet, Game & Study Guide Add/Subtract Fractions

4.NF.4. Apply and extend previous understandings of multiplication (refer to 2.OA.3, 2.OA.4, 3.OA.1, 3.NF.1, 3.NF.2) to multiply a fraction by a whole number.
4.NF.4a. Understand a fraction a/b as a multiple of 1/b. For example, use a visual fraction model to represent 5/4 as 5 copies of 1/4, recording the conclusion by the equation 5/4 = 5 ⋅ 1/4.
Flip Charts Fraction Concepts
Flip Charts Fraction Concepts
Vocabulary Terms Comparing Fractions
Vocabulary Terms Decimals/Fractions
Vocabulary Terms Equivalent Fractions
Vocabulary Terms Simplify Fractions
Quiz, Flash Cards, Worksheet, Game & Study Guide Add/Subtract Decimals
Quiz, Flash Cards, Worksheet, Game & Study Guide Add/Subtract Fractions
Quiz, Flash Cards, Worksheet, Game & Study Guide Add/Subtract Fractions
Quiz, Flash Cards, Worksheet, Game & Study Guide Adding Fractions
Quiz, Flash Cards, Worksheet, Game & Study Guide Compare and Order Fractions
Quiz, Flash Cards, Worksheet, Game & Study Guide Comparing Fractions
Quiz, Flash Cards, Worksheet, Game & Study Guide Decimals/Fractions
Quiz, Flash Cards, Worksheet, Game & Study Guide Equivalent Fractions
Quiz, Flash Cards, Worksheet, Game & Study Guide Equivalent Fractions to 1/2
Quiz, Flash Cards, Worksheet, Game & Study Guide Fractions
Quiz, Flash Cards, Worksheet, Game & Study Guide Fractions
Quiz, Flash Cards, Worksheet, Game & Study Guide Number Line
Quiz, Flash Cards, Worksheet, Game & Study Guide Ordering Fractions
Quiz, Flash Cards, Worksheet, Game & Study Guide Pattern Blocks
Quiz, Flash Cards, Worksheet, Game & Study Guide Probability
Quiz, Flash Cards, Worksheet, Game & Study Guide Probability
Quiz, Flash Cards, Worksheet, Game & Study Guide Simplify Fractions
Quiz, Flash Cards, Worksheet, Game & Study Guide Subtracting Fractions

4.NF.4b. Understand a multiple of a/b as a multiple of 1/b, and use this understanding to multiply a fraction by a whole number. For example, use a visual fraction model to express 3 ⋅ 2/5 as 6 ⋅ 1/5, recognizing this product as 6/5. (In general, n ⋅ a/b = n⋅a/b.)

4.NF.4c. Solve word problems involving multiplication of a fraction by a whole number (e.g. by using visual fraction models and equations to represent the problem.) For example, if each person at a party will eat 3/8 of a pound of roast beef, and there will be 5 p

Understand decimal notation for fractions, and compare decimal fractions. (Students are expected to learn to add decimals by converting them to fractions with the same denominator, in preparation for general fraction addition in grade 5.)
4.NF.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. For example, express 3/10 as 30/100, and add 3/10 + 4/100 = 34/100.
Vocabulary Terms Decimals/Fractions
Quiz, Flash Cards, Worksheet, Game & Study Guide Decimals/Fractions

4.NF.6. Use decimal notation for fractions with denominators 10 or 100. For example, rewrite 0.62 as 62/100; describe a length as 0.62 meters; locate 0.62 on a number line diagram.
Vocabulary Terms Decimals/Fractions
Quiz, Flash Cards, Worksheet, Game & Study Guide Decimals/Fractions

4.NF.7. Compare two decimals to hundredths by reasoning about their size. Recognize that comparisons are valid only when the two decimals refer to the same whole. Record the results of comparisons with the relational symbols >, < =, or ≠, and justify the conclusi
Vocabulary Terms Less Than, Greater Than
Vocabulary Terms Ordering Decimals
Quiz, Flash Cards, Worksheet, Game & Study Guide Fractions/Decimals
Quiz, Flash Cards, Worksheet, Game & Study Guide Less Than, Greater Than
Quiz, Flash Cards, Worksheet, Game & Study Guide Ordering Decimals

## KS.4.OA.Operations and Algebraic Thinking

Operations and Algebraic Thinking
Use the four operations with whole numbers to solve problems.
4.OA.1. Interpret a multiplication equation as a comparison, (e.g. interpret 35 = 5⋅7 as a statement that 35 is 5 times as many as 7 and 7 times as many as 5.) Represent verbal statements of multiplicative comparisons as multiplication equations.
Vocabulary Terms Evaluate Open Sentences
Quiz, Flash Cards, Worksheet, Game & Study Guide Determine the One Operation Function
Quiz, Flash Cards, Worksheet, Game & Study Guide Evaluate Open Sentences
Quiz, Flash Cards, Worksheet, Game & Study Guide Open Number Sentences
Quiz, Flash Cards, Worksheet, Game & Study Guide Word Problems

4.OA.2. Multiply or divide to solve word problems involving multiplicative comparison, (e.g. by using drawings and equations with a symbol for the unknown number to represent the problem, distinguishing multiplicative comparison from additive comparison.)
Vocabulary Terms Problem Solving
Quiz, Flash Cards, Worksheet, Game & Study Guide Problem Solving
Quiz, Flash Cards, Worksheet, Game & Study Guide Word Problems

4.OA.3. Solve multi-step word problem posed with whole numbers and having whole number answers using the four operations, including problems in which remainders must be interpreted. Represent these problems using situation equations and/or solution equations with
Vocabulary Terms Problem Solving
Vocabulary Terms Word Problems
Quiz, Flash Cards, Worksheet, Game & Study Guide Multi-step Word Problems
Quiz, Flash Cards, Worksheet, Game & Study Guide Problem Solving
Quiz, Flash Cards, Worksheet, Game & Study Guide Word Problems
Quiz, Flash Cards, Worksheet, Game & Study Guide Word Problems

Gain familiarity with factors and multiples.
4.OA.4. Find all factor pairs for a whole number in the range 1 to 100. Recognize that a whole number is a multiple of each of its factors. Determine whether a given whole number in the range 1 to 100 is a multiple of a given one-digit number. Determine whether a