MATHEMATICS FOURTH GRADE Common Curricular Goal: 4.1 NUMBER AND OPERATIONS: Develop an understanding of decimals, including the connections between fractions and decimals. State Standard Task Analysis Vocabulary Assessments Resources Common Core MA.4.1.1 Extend the baseten system to read, write, and represent decimal numbers (to the hundredths) between 0 and 1, between 1 and 2, etc. Recite/identify place value from millions to hundredths Write numbers in standard form from millions to hundredths Use base ten blocks to model numbers from millions to hundredths Use a place-value chart to illustrate numbers from millions to hundredths Apply expanded notation from millions to hundredths Represent numbers in a variety of ways (drawings, models, words, standard form) Read decimals correctly, using and to denote the decimal point Standard form Expanded notation Symbol Value Place Base ten Decimal -ths and CC.4.NF.5 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 100.4 CC.4.NF.6 6. Use decimal notation for fractions with denominators 10 or 100. MA.4.1.2 Use models to connect and compare equivalent fractions and decimals. Use manipulatives to model tenths and hundredths Create numbers using base ten blocks and compare Read and locate numbers on a number line Know distance between 0 and 1 can be divided into fractional parts and can be named as fractions or decimals Determine the name of fractions and/or decimals that are modeled on a number line Use <, >, = to compare Greater than Less than Equal Compare Order Least Greatest CC.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
and/or two numbers from millions to hundredths Use models to create an equivalent fraction or decimal to a given fraction or decimal generate equivalent fractions. CC.4.NF.5 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 100.4 CC.4.NF.6 6. Use decimal notation for fractions with denominators 10 or 100. MA.4.1.3 Determine decimal equivalents or approximations of common fractions. Write an equivalent fraction or decimal to represent a given fraction or decimal 4/10 = 40/100 0.4 = 0.40 Equivalent fraction Approximate Common fraction Common decimal CC.4.NF.6 6. Use decimal notation for fractions with denominators 10 or 100. MA.4.1.4 Compare and order fractions and decimals. Read and locate fractions and decimals on a number line to see tenths and hundredths Demonstrate that there are ten ticks between 0 and 1 that represents tenths. Demonstrate that there are ten ticks between 0 and 0.1 that represents hundredths. Ticks CC.4.NF.7 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. MA.4.1.5 Estimate decimal or fractional amounts in problem solving. MA.4.1.6 Represent money amounts to $10.00 in dollars and cents, and apply to situations involving purchasing ability and making change. Metric measure? Measure objects to the nearest centimeter Contextual situations Round decimals to the nearest hundredth, tenth, whole numbers Round fractions to the nearest whole or half Demonstrate that our monetary system uses place value Represent money amounts in fractions to their equivalent decimal (1/10 = $0.10, ¼ of a dollar = $ 0.25, ½ of a dollar = $ 0.50, ¾ of a dollar = $0.75, 4/4 = $1.00) Combinations of all coins and bills to equal $5 and $10 Use currency from $0.01 to $10.00 to represent all different combinations Compare prices and determine the better buy Determine the correct amount of change with the least amount of currency Currency Change Bills Deposit Withdrawl CC.4.MD.2 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 measurements given in a larger unit in terms of a smaller unit. Represent measurement quantities using diagrams such as number line diagrams that feature a measurement scale. Common Curricular Goal: 4.2 NUMBER AND OPERATIONS AND ALGEBRA: Develop fluency with multiplication facts and related division facts, and with multi-digit whole number multiplication. State Standard Task Analysis Vocabulary Assessments Resources Common Core MA.4.2.1 Apply with fluency multiplication facts Memorize multiplication Fact family Patterns
to 10 times 10 and related division facts. MA.4.2.2 Apply understanding of models for multiplication (e.g., equalsized groups, arrays, area models, equal intervals on the number line), place value, and properties of operations (commutative, associative, and distributive). facts 0-10 Memorize division facts 0-10 Identify combinations of factors that equal the same product Solve problems with factors that are multiples of 10 Solve more complex, related multiplication and division problems using knowledge of basic facts (use 3 x 5 to determine 30 x 50 and 12 / 3 to determine 120 / 30) Identify inverse operations Perform operations in more than one way (examples for multiplication-repeated addition, partial products, arrays with base 10 blocks, array/grid paper; division: repeated subtraction, partial quotients, put in groups, arrays with base 10 blocks, array/grid paper) Understand and generalize patterns involving multiplying by 10s, 100s, and 1000s. Order of operations Identify that parentheses means to complete first Identify commutative property as the order property Identify associative property as the grouping property Illustrate and model examples of the properties using objects Recognize and discover that the products are the same Factors Commutative Multiples Multiplication symbols, *, #(#), x Digit Product Square numbers Dividend Divisor quotient Arrays Equal size groups Area models Equal intervals Partial Product Commutative Associative Distributive CC.4.NBT.5 5. Multiply a whole number of up to four digits by a one-digit whole number, and multiply two twodigit 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.
MA.4.2.3 Select and use appropriate estimation strategies for multiplication (e.g., use benchmarks, overestimate, underestimate, round) to calculate mentally based on the problem situation when computing with whole numbers. MA.4.2.4 Develop and use accurate, efficient, and generalizable methods to multiply multi-digit whole numbers. MA.4.2.5 Develop fluency with efficient procedures for multiplying multi-digit whole numbers and justify why the procedures work on the basis of place value and number properties. when using the commutative and the associative properties Recognize and discover that the product is always 0 when multiplying by 0. Understand and generalize patterns involving multiplying by 10s, 100s, and 1000s. Understanding of rounding to the nearest 10, 100, 1000, etc. Estimation strategies (benchmarks) to verify reasonableness of answers in multiplication problems Perform operations in more than one way (examples for multiplication: repeated addition, partial products, arrays with base 10 blocks) Identify vocabulary needed to solve multiplication contextual problems Use calculator Multiply two-digit number by two-digit number Estimation strategies (benchmarks) to verify reasonableness of answers in multiplication problems Overestimate Underestimate Round Benchmarks Verify Reasonable CC.4.NBT.5 5. Multiply a whole number of up to four digits by a one-digit whole number, and multiply two twodigit 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. Common Curricular Goal: 4.3 MEASUREMENT: Develop an understanding of area and determine the areas of two-dimensional shapes. State Standard Task Analysis Vocabulary Assessments Resources Common Core
MA.4.3.1 Recognize area as an attribute of twodimensional regions. MA.4.3.2 Determine area by finding the total number of same-sized units of area that cover a shape without gaps or overlaps. MA.4.3.3 Recognize a square that is one unit on a side as the standard unit for measuring area. MA.4.3.4 Determine the appropriate units, strategies, and tools to solving problems that involve estimating or measuring area. MA.4.3.5 Connect area measure to the area model used to represent multiplication and use this to justify the formula for area of a rectangle. MA.4.3.6 Find the areas of complex shapes that can be subdivided into rectangles. MA.4.3.7 Solve problems involving perimeters and areas of rectangles and squares. Define area as a flat surface Model/identify twodimensional figures Recognize that the area of a shape, in square units, is the number of a 1 unit by 1 unit squares needed to cover the shape Distinguish between the application of square units of measure and linear units of measure Select the appropriate unit of measure to apply to a situation described in a contextual problem (square unit, square mile, square feet, square inches) Apply strategies and tools to solve a problem, including covering with squares and half squares and using a formula. Use arrays to develop formula of a rectangle Area formula for rectangle is A = l * w Identify rectangles in complex shapes. Apply area strategies to determine the area of complex shapes Distinguish between the application of square units of measure and linear units of measure. Justify and explain answers to single and multi-step problems involving perimeters of plane figures Area Two-dimensional Formula Length of base Width (Height) Dimension Complex shapes Square units Linear units Plane figures CC.4.MD.3 3. Apply the area and perimeter formulas for rectangles in real world and mathematical problems.
MA.4.3.8 Recognize that rectangles with the same area can have different perimeters and that rectangles with the same perimeter can have different areas. Justify and explain answers to single and multi-step problems involving area of rectangles Label answers with appropriate unit of measure (units squared vs. units) Using concrete and pictorial models such as grid paper and square tiles, students will demonstrate the relationship of a rectangle s area to its perimeter. Create rectangle models with the same area but with different perimeters Create rectangle models with the same perimeter but with different areas Perimeter Common Core Not Associated with 4 th Grade ODE Standards CC.4.OA.1 Interpret a multiplication equation as a comparison, e.g., interpret 35 = 5 x 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. CC.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 CC.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. CC.4.OA.4 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 Task Analysis or Other ODE Standard Demonstrate ability to represent verbal statements of mult. Comparisons as equations and vice versa. Represent comparison situations with drawing or scale models Understand that variables are solutions to the equation. MTH.5.2.3 MTH.5.2.6 Given a rule, equation, or formula, develop or create a number or shape pattern. Analyze patterns to find features that do not fit the rules.
multiple of a given one-digit number. Determine whether a given whole number in the range 1 100 is prime or composite. CC.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. CC.4.NBT.3 3. Use place value understanding to round multi-digit whole numbers to any place. CC.4.NBT.4 4. Fluently add and subtract multi-digit whole numbers using the standard algorithm. CC.4.NBT.6 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. CC.4.NF.3 3. Understand a fraction a/b with a > 1 as a sum of fractions 1/b. CC.4.NF.3a a. Understand addition and subtraction of fractions as joining and separating parts referring to the same whole. CC.4.NF.3b 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. CC.4.NF.3c 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. CC.4.NF.3d d. Solve word problems involving addition and Construct Numbers using place value mats Identify and apply the concept of place value using hundreds, tens, and ones Use physical objects to represent a whole number using Base 10 blocks, cubes, coins) Understand multi-digit place value Rounding whole numbers Solve multi-digit word problems which require addition and subtraction of multi-digit numbers Solve multi-step problems, using addition or subtraction, that arise from real world/ mathematical context Identify and apply the concept of place value using hundreds, tens, and ones Understand and apply the concepts of carrying and borrowing Explain carrying and borrowing by using different models (manipulatives, verbally, models) MTH.5.2.1 MTH.5.2.2 MTH.5.2.4 MTH.5.2.5 MTH.3.1.6 MTH.3.1.6 MTH.3.1.6 MTH.3.1.6 MTH.3.1.6
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. CC.4.NF.4 4. Apply and extend previous understandings of multiplication to multiply a fraction by a whole number. CC.4.NF.4b 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. CC.4.NF.4c 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. CC.4.NF.5 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 100.4 CC.4.NF.6 6. Use decimal notation for fractions with denominators 10 or 100. CC.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. CC.4.MD.4 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. CC.4.MD.5 5. Recognize angles as geometric shapes that are formed wherever two rays share a common endpoint, and understand concepts of angle measurement: CC.4.MD.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 onedegree angle, and can be used to measure angles. CC.4.MD.5 b. An angle that turns through n one-degree angles is said to have an angle measure of n degrees. MTH.6.1.2 MTH.6.1.2 MTH.6.1.2 MTH.5.1.1 MTH.5.1.4 MTH.6.1.7 MTH.6.1.7 Analyze line plot to solve problems involving addition and subtraction of fractions Create line plot graphs from data sets Create multiple line plot graphs with the fractional units (1/2, 1/4, 1/8) as the axis increments. MTH.3.3.1 Using a circle to represent or determine the measurement of an angle Using the fraction of the circle w. total degrees of the circle as the denominator to find angle measure understand the identity property (i.e., any number multiplied by 1 is the number)
CC.4.MD.6 6. Measure angles in whole-number degrees using a protractor. Sketch angles of specified measure. measure various angles with protractors angles of specified measurements Draw a variety of CC.4.MD.7 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. CC.4.G.1 1. Draw points, lines, line segments, rays, angles (right, acute, obtuse), and perpendicular and parallel lines. Identify these in twodimensional figures. CC.4.G.3 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. Decompose angles understand that angles are additive, the angle measure of the whole is the sum of the parts Solve one-step algebraic problems involving addition and subtraction where the variable represents an unknown angle measure MTH.3.3.1 MTH.3.3.2 MTH.3.3.6 MTH.3.3.8 MTH.5.3.1 MTH.1.3.2