# Gain familiarity with factors and multiples. Use place value understanding and properties of operations to perform multi-digit arithmetic.

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1 Prairie-Hills Elementary School District th Grade ~ MATH Curriculum Map Quarter 1 Month: August, September, October Domain(s): Operations and Algebraic Thinking Number Base Ten (NBT) Cluster(s): Use the four operations with whole numbers to solve problems. Generalize place value understanding for multi-digit whole numbers Gain familiarity with factors and multiples. Use place value understanding and properties of operations to perform multi-digit arithmetic. Use the four operations with whole numbers to solve problems. Standard(s): 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. 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. Generalize place value understanding for multi-digit whole numbers. 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 = 10 by applying concepts of place value and division. 4.NBT.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. Gain familiarity with factors and multiples. 4.OA.4 Find all factor pairs for a whole number in the range Recognize that a whole number is a multiple of each of its factors. Determine whether a given whole number in the range is a multiple of a given one-digit number. Determine whether a given whole number in the range is prime or composite. CCSS.MATH.CONTENT.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.

2 Use place value understanding and properties of operations to perform multi-digit arithmetic. 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 arrays, and/or area models. 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 calculation by using equations, rectangular arrays, and/or area models. Use the four operations with whole numbers to solve problems. 4.OA.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. 4.OA.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. Mathematical Practices Standards 1 Make sense of problems and persevere in solving them 2 Reason abstractly and quantitatively 3 Construct viable arguments and critique the reasoning of others 4 Model with mathematics 5 Use appropriate tools strategically 6 Attend to precision 7 Look for and make use of structure. 8 Look for an express regularity in repeated reasoning

3 Targeted Skills: Count, read and write numbers through 1,000,000 Compare and order whole numbers Identify the four steps in a problem solving process Round whole number and money amounts through millions Make a table to organize data and solve a problem Count coins and bills to find money amounts and make change Analyze data and make decisions Use addition properties to solve problems Form conclusions about whether to estimate or find an exact answer Add and subtract whole numbers up to1,000,000 Review subtracting whole numbers and money Subtracting numbers across zero Write a number sentence to solve a problem Solving word problems using pictures Estimate difference of up to 6-digit numbers Understand factors to 11 Identify properties of operation Know multiplication strategies Interpret a multiplication equation as a comparison (e.g. 18= 3 times as many as 6.) Define prime and composite numbers Generate a number or shape pattern that follows a given rule Identify a number or shape pattern Recognize that a whole number is a multiple of each of its factors Determine if a given whole number (1-100) is a multiple of a given one-digit number Key Vocabulary: Critical Terms: Supplemental Terms: Factor Multiple Area Model Array Prime Composite Product Equation Standard Form Written Form Expanded Form Multiplicative comparison

4 Prairie-Hills Elementary School District th Grade ~ MATH Curriculum Map Quarter 2 Month: October, November, December Domain(s): Number Fractions (NF) Measurement & Data (MD) Number Base Ten (NBT) Cluster(s): Extend understanding of fraction equivalence and ordering. Build fractions from unit fractions by applying and extending previous understandings of operations on whole numbers. Solve problems involving measurement and conversion of measurement from a larger unit to a smaller unit. Represent and interpret data. Use place value understanding and properties of operations to perform multi-digit arithmetic. Standard(s): Extend understanding of fraction equivalence and ordering. 4.NF.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 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. 4.NF.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 ½. 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. Build fractions from unit fractions by applying and extending previous understandings of operations on whole numbers. 4.NF.3 Understand a fraction a/b with a > 1 as a sum of fractions 1/b. a. Understand addition and subtraction of fractions as joining and separating parts referring to the same whole. 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 = /8 = 8/8 + 8/8 + 1/8. 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. 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. 4.NF.4 Apply and extend previous understandings of multiplication to multiply a fraction by a whole number. a. Understand a fraction a/b as a multiple of 1/b. For example, use a visual fraction model to represent 5/4 and the product 5 x (1/4), recording the conclusion by the equation 5/4 = 5 x (1/4). 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 x (2/5) as 6 x (1/5), recognizing this product as 6/5. (In general, n x (a/b) = (n x a)/b.) 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?

5 Solve problems involving measurement and conversion of measurement 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 equivalents in a two-column table. For example, know that if 1 ft is 12 times as long as 1 in. Express the length of a 4 ft snake as 48 in. Generate conversion table for feet and inches listing the number pairs (1, 12), (2,24), (3, 36), Represent and interpret data. 4.MD.4 Make a line plot to display a data set of measurements in fractions of a unit (1/2, 1/4, 1/8). Solve problems involving addition and subtraction of fractions by using information presented in line plots. For example, from a line plot find and interpret the difference in length between the longest and shortest specimens in an insect collection. Use place value understanding and properties of operations to perform multi-digit arithmetic. 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 calculation by using equations, rectangular arrays, and/or area models.

6 Targeted Skills: Round multi-digit whole numbers to any place using place value Divide whole numbers including division with remainders. Represent verbal statements of multiplicative comparisons as multiplication equations. Determine and use a variety of representations to model a problem involving multiplicative comparison. Access the reasonableness of an answer in solving a multistep word problem using mental math and estimation strategies (including rounding). Create a line plot to display a data set of measurement given in fractions of a unit. Use strategies based on place value and the properties of operations to multiply whole numbers. Recognize the relationship with multiplication and division Understand the function of equivalent fractions. Understand comparing and ordering fractions. Identify fractions on number lines. Use visual equivalent models to show why fractions are equivalent (ex. 3/4 = 6/8). Recognize that two fractions with unlike denominators can be equivalent. Add and subtract mixed numbers by replacing each mixed number with an equivalent fraction. Understand improper fractions and mixed numbers. Recognize fractions as being greater than, less than, or equal to other fractions. Multiply two two-digit numbers. Multiply or divide to solve word problems. Identify a number or shape pattern. Find and use elapsed time. Understand and use coordinate graphing. Critical Terms: Benchmark fractions Common denominators Improper fraction Mixed numbers Visual fraction model Range Divisor Dividend Quotient Remainder Supplemental Terms: Unit fractions Decompose Compose Equivalent Numerator Denominator Symbols Number line Line plot Quarters Halves Distances (inches and feet) Intervals (of time) Elapsed time (seconds, minutes, hours, days, etc.) Liquid volume (fluid ounce, cup, pint, quart, gallon) Weight (ounce, pound, ton)

7 Prairie-Hills Elementary School District th Grade ~ MATH Curriculum Map Quarter 3 Months: December, January, February, March Domain(s): Number Fractions (NF) Operations & Algebraic Thinking (OA) Number Base Ten (NBT) Cluster(s): Understand decimal notation for fractions, and compare decimal fractions. Generate and analyze patterns. Use place value understanding and properties of operations to perform multi-digit arithmetic. Use the four operations with whole numbers to solve problems. Solve problems involving measurement and conversion of measurements from a larger unit to a smaller unit. Standard(s): 4.NF.3 Understand a fraction a/b with a > 1 as a sum of fractions 1/b. a. Understand addition and subtraction of fractions as joining and separating parts referring to the same whole. 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 = /8 = 8/8 + 8/8 + 1/8. 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. 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. 4.NF.4 Apply and extend previous understandings of multiplication to multiply a fraction by a whole number. a. Understand a fraction a/b as a multiple of 1/b. For example, use a visual fraction model to represent 5/4 and the product 5 x (1/4), recording the conclusion by the equation 5/4 = 5 x (1/4). 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 x (2/5) as 6 x (1/5), recognizing this product as 6/5. (In general, n x (a/b) = (n x a)/b.) 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? Understand decimal notation for fractions, and compare decimal fractions. 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/ NF.6 Use decimal notation for fractions with denominators 10 or 100. For example, rewrite 0.62 as 62/100; describe a length of 0.62 meters; locate 0.62 on a number line diagram.

8 Standard(s): Use the four operations with whole numbers to solve problems. 4.OA.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. Represent and interpret data. 4.MD.5 Recognize angles as geometric shapes that are formed wherever two rays share a common endpoint, and understand concepts of angle measurement: CCSS.MATH.CONTENT.4.MD.C.5.A An angle is measured 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. CCSS.MATH.CONTENT.4.MD.C.5.B An angle that turns through n one-degree angles is said to have an angle measure ofn degrees. CCSS.MATH.CONTENT.4.MD.C.6 Measure angles in whole-number degrees using a protractor. Sketch angles of specified measure. CCSS.MATH.CONTENT.4.MD.C.7 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. Solve addition and subtraction problems to find unknown angles on a diagram in real world and mathematical problems, e.g., by using an equation with a symbol for the unknown angle measure. 4.MD.5 Recognize angles as geometric shapes that are formed wherever two rays share a common endpoint, and understand concepts of angle measurement: a. An angle is measured 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. b. An angle that turns through none-degree angles is said to have an angle measure of n degrees. Mathematical Practices Standards 1 Make sense of problems and persevere in solving them 2 Reason abstractly and quantitatively 3 Construct viable arguments and critique the reasoning of others 4 Model with mathematics 5 Use appropriate tools strategically 6 Attend to precision 7 Look for and make use of structure. 8 Look for an express regularity in repeated reasoning

9 Targeted Skills: Multiply a whole number of up to four digits by a one-digit whole number. Use strategies based on place value and the properties of operations to multiply whole numbers. Illustrate and explain calculations by using written equations, rectangular arrays, and area models. Find whole number quotients and remainders with up to four-digit dividends and one-digit divisors. Assess the reasonableness of an answer in solving a multistep word problem using mental math and estimation strategies. Divide with two-digit numbers with remainders. Define prime and composite numbers. Know strategies to determine whether a whole number is prime or composite. Determine if a given whole number (1-100) is a multiple of a given one-digit number. Identify all factor pairs for any given number Recognize that a whole number is a multiple of each of its factors. Understand the function of equivalent fractions. Understand comparing and ordering fractions. Identify fractions on number lines. Use visual equivalent models to show why fractions are equivalent (ex. 3/4 = 6/8). Recognize that two fractions with unlike denominators can be equivalent. Add and subtract mixed numbers by replacing each mixed number with an equivalent fraction. Understand improper fractions and mixed numbers. Recognize fractions as being greater than, less than, or equal to other fractions. Add, subtract, multiply and divide fractions and decimals. Solve word problems involving measurement that include simple fractions or decimals. Multiplying a fraction by a whole number. Develop an understanding of decimal place value. Explain how decimals and fractions relate. Understand comparing and ordering decimals. Identify decimals on a number line. Understand equivalent decimals. Convert metric and customary units. Measure temperature in degrees Fahrenheit and Celsius. Recognize that an angle is a fraction of a 360-degree circle. 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. Solve addition and subtraction equations to find unknown angle measurements on a diagram. Estimate or determine the perimeter of a polygon. Estimate or determine the area of a shape using a formula.

10 Key Vocabulary: Critical Terms: Decimals Tenths Hundredths Decimal grids Critical Terms: Shape patterns Rules Variable Formula Supplemental Terms: Number patterns Rounding Estimation Metric units of measurement Distance Liquid volume Mass Perimeter Area

11 Prairie-Hills Elementary School District th Grade ~ MATH Curriculum Map Quarter 4 Month: April, May, June Domain(s): Operations and Algebraic Thinking Number Base Ten (NBT) Measurement & Data (MD) Geometry (G) Cluster(s): Generate and analyze patterns. Generalize place value understanding for multi-digit whole numbers. Use place value understanding and properties of operations to perform multi-digit arithmetic. Use the four operations with whole numbers to solve problems. Solve problems involving measurement and conversion of measurements from a larger unit to a smaller unit. Draw and identify lines and angles, and classify shapes by properties of their lines and angles. Geometric measurement: understand concepts of angle and measure angles. Standard(s): Use the four operations with whole numbers to solve problems. 4.OA.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. 4.OA.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.

12 Standard(s): 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 (metric) of units including km, m, cm; kg, g. 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. 4.MD.2 Use the four operations to solve word problems involving distances, intervals of time, liquid volumes, masses of objects, and money, including problems involving simple fractions or decimals, and problems that require expressing measurement quantities using diagrams such as number line diagrams that feature a measurement scale. 4.MD.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. 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), and perpendicular and parallel lines. Identify these in two-dimensional figures. 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 of a specified size. Recognize right triangles as a category, and identify right triangles. 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. 4.MD.7 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. Solve addition and subtraction problems to find unknown angles on a diagram in real world and mathematical problems, e.g., by using an equation with a symbol for the unknown angle measure.

13 4.NF.3 Understand a fraction a/b with a > 1 as a sum of fractions 1/b. 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. 4.NF.4 Apply and extend previous understandings of multiplication to multiply a fraction by a whole number. 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 x (2/5) as 6 x (1/5), recognizing this product as 6/5. (In general, n x (a/b) = (n x a)/b.) 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 calculation by using equations, rectangular arrays, and/or area models. Targeted Skills: Use models to relate fractions and decimals. Read and write tenths and hundredths as decimals and fractions. Understand decimals for tenths and hundredths. Compare and order decimals. Draw diagrams to solve problems. Analyze data and make decisions.

14 Key Vocabulary: Critical Terms: Points End points Lines Line segments Rays Angles (right, acute, obtuse) Central Adjacent angles Perpendicular lines Parallel lines Protractor Degrees Symmetry Right triangle Scalene triangle Isosceles triangle Supplemental Terms: Plane (two-dimensional) figures Quadrilaterals Square Rhombus Rectangle Circle Triangle Additive Mathematical Practices Standards 1 Make sense of problems and persevere in solving them 2 Reason abstractly and quantitatively 3 Construct viable arguments and critique the reasoning of others 4 Model with mathematics 5 Use appropriate tools strategically 6 Attend to precision 7 Look for and make use of structure. 8 Look for an express regularity in repeated reasoning

### Gain familiarity with factors and multiples. Use place value understanding and properties of operations to perform multi-digit arithmetic.

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