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# Florida Standards (NGSSS) Fourth Grade Mathematics resources

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Geometry

MACC.4.G.1. Draw and identify lines and angles, and classify shapes by properties of their lines and angles.

MACC.4.G.1.1. Draw points, lines, line segments, rays, angles (right, acute, obtuse), and perpendicular and parallel lines. Identify these in two-dimensional figures.

Flip Charts Lines & Angles

Flip Charts Lines, Angles & Circles

Flip Charts Lines, Angles & Circles

Flip Charts Math Grade 4

Flip Charts Math Grade 5

Flip Charts Polygons

Flip Charts Polygons

Quiz, Flash Cards, Worksheet, Game & Study Guide Angles

Quiz, Flash Cards, Worksheet, Game & Study Guide Lines and Angles

MACC.4.G.1.2. 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.

Flip Charts Math Grade 4

Flip Charts Polygons

Flip Charts Polygons

Quiz, Flash Cards, Worksheet, Game & Study Guide Polygon Characteristics

MACC.4.G.1.3. 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

Measurement and Data

MACC.4.MD.1. Solve problems involving measurement and conversion of measurements from a larger unit to a smaller unit.

MACC.4.MD.1.1. 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 equivalents in a two-column table. For example, know that 1 ft is 12 times as long as 1 in. Express the length of a 4 ft snake as 48 in. Generate a conversion table for feet and inches listing the number pairs (1, 12), (2, 24), (3, 36), ...

Flip Charts Customary & Metric Units of Measurement

Flip Charts Customary & Metric Units of Measurement

Flip Charts Math Grade 4

MACC.4.MD.1.3. Apply the area and perimeter formulas for rectangles in real world and mathematical problems. For example, find the width of a rectangular room given the area of the flooring and the length, by viewing the area formula as a multiplication equation with an unknown factor.

Quiz, Flash Cards, Worksheet, Game & Study Guide Area

Quiz, Flash Cards, Worksheet, Game & Study Guide Area and Perimeter

MACC.4.MD.3. Geometric measurement: understand concepts of angle and measure angles.

MACC.4.MD.3.5. Recognize angles as geometric shapes that are formed wherever two rays share a common endpoint, and understand concepts of angle measurement:

MACC.4.MD.3.5.a. ed with reference to a circle with its center at the common endpoint of the rays, by considering the fraction of the circular arc between the points where the two rays intersect the circle. An angle that turns through 1/360 of a circle is called a “one-degree angle,” and can be used to measure angles.

Flip Charts Lines & Angles

Flip Charts Lines, Angles & Circles

Flip Charts Lines, Angles & Circles

Flip Charts Math Grade 4

Flip Charts Math Grade 5

Quiz, Flash Cards, Worksheet, Game & Study Guide Angles

Quiz, Flash Cards, Worksheet, Game & Study Guide Lines and Angles

MACC.4.MD.3.5.b. An angle that turns through n one-degree angles is said to have an angle measure of n degrees.

Flip Charts Lines, Angles & Circles

Flip Charts Lines, Angles & Circles

Flip Charts Math Grade 5

Quiz, Flash Cards, Worksheet, Game & Study Guide Angles

Quiz, Flash Cards, Worksheet, Game & Study Guide Lines and Angles

MACC.4.MD.3.6. Measure angles in whole-number degrees using a protractor. Sketch angles of specified measure.

Flip Charts Lines, Angles & Circles

Flip Charts Lines, Angles & Circles

Flip Charts Math Grade 5

Quiz, Flash Cards, Worksheet, Game & Study Guide Angles

Quiz, Flash Cards, Worksheet, Game & Study Guide Lines and Angles

Number and Operations in Base Ten

MACC.4.NBT.1. Generalize place value understanding for multi-digit whole numbers.

MACC.4.NBT.1.1. 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 700 ÷ 70 = 10 by applying concepts of place value and division.

Flip Charts Adding & Subtracting Decimals

Flip Charts Adding & Subtracting Decimals

Flip Charts Adding & Subtracting Three-digit Numbers

Flip Charts Adding & Subtracting Three-digit Numbers

Flip Charts Box It Up

Flip Charts Math Grade 3

Flip Charts Math Grade 4

Flip Charts Place Value - Understanding Numbers

Flip Charts Place Value - Understanding Numbers

Flip Charts Star Mathematicians

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

MACC.4.NBT.1.2. Read and write multi-digit whole numbers using base-ten numerals, number names, and expanded form. Compare two multi-digit numbers based on meanings of the digits in each place, using >, =, and < symbols to record the results of comparisons.

Flip Charts Box It Up

Flip Charts Math Grade 4

Flip Charts Place Value - Understanding Numbers

Flip Charts Place Value - Understanding Numbers

Flip Charts Star Mathematicians

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

MACC.4.NBT.1.3. Use place value understanding to round multi-digit whole numbers to any place.

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

MACC.4.NBT.2. Use place value understanding and properties of operations to perform multi-digit arithmetic.

MACC.4.NBT.2.4. Fluently add and subtract multi-digit whole numbers using the standard algorithm.

Flip Charts Adding & Subtracting Three-digit Numbers

Flip Charts Adding & Subtracting Three-digit Numbers

Flip Charts Columns Across

Flip Charts Function Machine

Flip Charts Magic Squares

Flip Charts Math Grade 3

Flip Charts Step It Up

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

MACC.4.NBT.2.5. 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 arrays, and/or area models.

Flip Charts Columns Across

Flip Charts Dividing Two-digit Numbers

Flip Charts Dividing Two-digit Numbers

Flip Charts Division Concepts & Strategies

Flip Charts Division Concepts & Strategies

Flip Charts Function Machine

Flip Charts Magic Squares

Flip Charts Math Grade 3

Flip Charts Math Grade 4

Flip Charts Math Grade 5

Flip Charts Multiplication Concepts & Strategies

Flip Charts Multiplication Concepts & Strategies

Flip Charts Multiplication Table

Flip Charts Multiplication Table

Flip Charts Multiplying & Dividing Decimals

Flip Charts Multiplying & Dividing Decimals

Flip Charts Multiplying Two-digit Numbers

Flip Charts Multiplying Two-digit Numbers

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 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 Division/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

MACC.4.NBT.2.6. 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 calculation by using equations, rectangular arrays, and/or area models.

Flip Charts Columns Across

Flip Charts Dividing Two-digit Numbers

Flip Charts Dividing Two-digit Numbers

Flip Charts Function Machine

Flip Charts Magic Squares

Flip Charts Math Grade 4

Flip Charts Math Grade 5

Flip Charts Multiplying & Dividing Decimals

Flip Charts Multiplying & Dividing Decimals

Flip Charts Multiplying Two-digit Numbers

Flip Charts Multiplying Two-digit Numbers

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

Number and Operations - Fractions

MACC.4.NF.1. Extend understanding of fraction equivalence and ordering.

MACC.4.NF.1.1. 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 generate equivalent fractions.

Flip Charts Adding & Subtracting Fractions

Flip Charts Adding & Subtracting Fractions

Flip Charts All About Fractions

Flip Charts All About Fractions

Flip Charts Box It Up

Flip Charts Fraction Concepts

Flip Charts Fraction Concepts

Flip Charts Math Grade 3

Flip Charts Math Grade 4

Flip Charts Math Grade 5

Flip Charts Ratio, Proportion & Percent

Flip Charts Triangle Tricks

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

MACC.4.NF.1.2. Compare two fractions with different numerators and different denominators, e.g., by creating common denominators or numerators, or by comparing to a benchmark fraction such as 1/2. Recognize that comparisons are valid only when the two fractions refer to the same whole. Record the results of comparisons with symbols >, =, or <, and justify the conclusions, e.g., by using a visual fraction model.

Flip Charts All About Fractions

Flip Charts All About Fractions

Flip Charts Box It Up

Flip Charts Math Grade 3

Flip Charts Triangle Tricks

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

MACC.4.NF.2. Build fractions from unit fractions by applying and extending previous understandings of operations on whole numbers.

MACC.4.NF.2.3. Understand a fraction a/b with a > 1 as a sum of fractions 1/b.

MACC.4.NF.2.3.a. Understand addition and subtraction of fractions as joining and separating parts referring to the same whole.

Flip Charts Adding & Subtracting Fractions

Flip Charts Adding & Subtracting Fractions

Flip Charts Math Grade 4

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

MACC.4.NF.2.3.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 decompositions, e.g., by using a visual fraction model. Examples: 3/8 = 1/8 + 1/8 + 1/8 ; 3/8 = 1/8 + 2/8 ; 2 1/8 = 1 + 1 + 1/8 = 8/8 + 8/8 + 1/8.

Flip Charts All About Fractions

Flip Charts All About Fractions

Flip Charts Math Grade 3

MACC.4.NF.2.3.c. Add and subtract mixed numbers with like denominators, e.g., by replacing each mixed number with an equivalent fraction, and/or by using properties of operations and the relationship between addition and subtraction.

Flip Charts Math Grade 5

Flip Charts Operations with Mixed Numbers

Flip Charts Operations with Mixed Numbers

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

MACC.4.NF.2.3.d. 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

MACC.4.NF.2.4. Apply and extend previous understandings of multiplication to multiply a fraction by a whole number.

MACC.4.NF.2.4.a. Understand a fraction a/b as a multiple of 1/b. For example, use a visual fraction model to represent 5/4 as the product 5 × (1/4), recording the conclusion by the equation 5/4 = 5 × (1/4).

Flip Charts Adding & Subtracting Fractions

Flip Charts Adding & Subtracting Fractions

Flip Charts All About Fractions

Flip Charts All About Fractions

Flip Charts Box It Up

Flip Charts Fraction Concepts

Flip Charts Fraction Concepts

Flip Charts Math Grade 3

Flip Charts Math Grade 4

Flip Charts Math Grade 5

Flip Charts Multiplying & Dividing Fractions

Flip Charts Multiplying & Dividing Fractions

Flip Charts Operations with Mixed Numbers

Flip Charts Operations with Mixed Numbers

Flip Charts Our Atmosphere

Flip Charts Triangle Tricks

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

MACC.4.NF.2.4.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. 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.)

Flip Charts Math Grade 5

Flip Charts Multiplying & Dividing Fractions

Flip Charts Multiplying & Dividing Fractions

MACC.4.NF.2.4.c. 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 people at the party, how many pounds of roast beef will be needed? Between what two whole numbers does your answer lie?

Flip Charts Math Grade 5

Flip Charts Multiplying & Dividing Fractions

Flip Charts Multiplying & Dividing Fractions

MACC.4.NF.3. Understand decimal notation for fractions, and compare decimal fractions.

MACC.4.NF.3.5. 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.

Flip Charts Box It Up

Quiz, Flash Cards, Worksheet, Game & Study Guide Decimals/Fractions

MACC.4.NF.3.6. 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.

Flip Charts Box It Up

Quiz, Flash Cards, Worksheet, Game & Study Guide Decimals/Fractions

MACC.4.NF.3.7. 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 symbols >, =, or <, and justify the conclusions, e.g., by using a visual model.

Flip Charts All About Decimals

Flip Charts All About Decimals

Flip Charts Math Grade 3

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

Operations and Algebraic Thinking

MACC.4.OA.1. Use the four operations with whole numbers to solve problems.

MACC.4.OA.1.1. 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.

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

MACC.4.OA.1.2. 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.

Quiz, Flash Cards, Worksheet, Game & Study Guide Problem Solving

Quiz, Flash Cards, Worksheet, Game & Study Guide Word Problems

MACC.4.OA.1.3. Solve multistep word problems 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 equations with a letter standing for the unknown quantity. Assess the reasonableness of answers using mental computation and estimation strategies including rounding.

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

MACC.4.OA.2. Gain familiarity with factors and multiples.

MACC.4.OA.2.4. Find all factor pairs for a whole number in the range 1–100. Recognize that a whole number is a multiple of each of its factors. Determine whether a given whole number in the range 1–100 is a multiple of a given one-digit number. Determine whether a given whole number in the range 1–100 is prime or composite.

Flip Charts Math Grade 5

Flip Charts Multiplying & Dividing Fractions

Flip Charts Multiplying & Dividing Fractions

Flip Charts Operations with Mixed Numbers

Flip Charts Operations with Mixed Numbers

Quiz, Flash Cards, Worksheet, Game & Study Guide Common Factors

MACC.4.OA.3. Generate and analyze patterns.

MACC.4.OA.3.5. Generate a number or shape pattern that follows a given rule. Identify apparent features of the pattern that were not explicit in the rule itself. For example, given the rule “Add 3” and the starting number 1, generate terms in the resulting sequence and observe that the terms appear to alternate between odd and even numbers. Explain informally why the numbers will continue to alternate in this way.

Quiz, Flash Cards, Worksheet, Game & Study Guide Patterns

Quiz, Flash Cards, Worksheet, Game & Study Guide Patterns

Quiz, Flash Cards, Worksheet, Game & Study Guide Patterns

Mathematical Practices

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

Flip Charts Math Grade 3

Flip Charts Problem Solving Strategies

Flip Charts Problem Solving Strategies

Flip Charts Problem Solving Strategies