Title Math Grade 4 Type Essential Document Map Authors Melissa Cosgrove, Sara Pascarella, Madeleine Tarleton Subject Mathematics Course Math Grade 4 Grade(s) 04 Location District Curriculum Writing History Notes Attachments Page: 1 of 15
September/Week 1 - October/Week 7 September October November December January February March April May June 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 Use the Four Operations with Whole Numbers to Solve Problems October/Week 8 - December/Week 14 Compute with Multi-Digit Whole Numbers and Define Equivalent Fractions December/Week 15 - February/Week 21 Properties of Operations with Multi-Digit Arithmetic, Fraction Addition, and Subtraction February/Week 22 - March/Week 28 Extend Understanding of Fractions, Solve Word Problems, and Introduce Decimals April/Week 29 - May/Week 35 Compare Decimals and Measure and Classify Geometric Figures Page: 2 of 15
Duration: September/Week 1 - October/Week 7 UNIT NAME: Use the Four Operations with Whole Numbers to Solve Problems Enduring Understandings Essential Questions Knowledge Skills Standards Place value is based on How does the position of a groups of ten. digit in a number affect its For any number, the place value? of a digit tells how many What are strategies to ones, tens, hundreds, and make a reasonable so forth are represented by estimate? that digit. What are different models Each place value to the left of and models for of another is ten times multiplication and division? greater than the one to the What questions can be right (e.g., 100 = 10 x 10). answered using Numbers can be compared multiplication and division? using greater than, less than, or equal. Whole numbers can be compared by analyzing corresponding place values. Estimation is a way to get an approximate answer. Some real-world problems involving joining equal groups, separating equal groups, comparison, or combinations can be solved using multiplication; others can be solved using division. Vocabulary: digit, ten times, compare, <, >, =, comparison, round, multiplication equation, multiply, divide, unknown In multiplicative comparison, the underlying question is what factor would multiply one quantity in order to result in the other. In additive comparison, the underlying question is what amount would be added to one quantity in order to result in the other. Explain the quantitative relationship between places of a multi-digit whole number up to one million when moving from left to right. Compare two multi-digit numbers up to one million (presented as base ten numerals, number names, or expanded form). Use <, >, and = to compare numbers. Round multi-digit whole numbers up to one million to any place. Write multiplication equations from multiplicative comparisons given in words (e.g., 35 is 5 times as many as 7 and 7 times as many as 5). Describe a multiplication equation in words. Multiply or divide to solve word problems involving multiplicative comparisons. Write an equation to identify the arithmetic operation written in a word problem (without solving). 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 700 70 = 10 by applying concepts of place value and division. (04) 4.NBT.2-Read and write multidigit whole numbers using baseten 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. (04)[State:New 4.NBT.3-Use place value understanding to round multidigit whole numbers to any place. (04)[State:New Jersey 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. (04)[State:New 4.OA.2-Multiply or divide to solve word problems involving multiplicative comparison, e.g., by using drawings and Page: 3 of 15
Plans: equations with a symbol for the unknown number to represent the problem, distinguishing multiplicative comparison from additive comparison.* (04) Page: 4 of 15
Duration: October/Week 8 - December/Week 14 UNIT NAME: Compute with Multi-Digit Whole Numbers and Define Equivalent Fractions Enduring Understandings Essential Questions Knowledge Skills Standards Place value is based on groups of ten. Computation involves taking apart and combining numbers using a variety of approaches. Flexible methods of computation involve grouping numbers in strategic ways. Proficieny with basic facts aids estimation and computation of larger and smaller numbers. When you divide whole numbers sometimes there is a remainder; the remainder must be less than the divisor. The real-world situation determines how a remainder needs to be interpreted when solving a problem. Properties of whole numbers apply to certain operations but not others (e.g., The commutative property applies to addition and multiplication but not subtraction and division). Fractions express a relationship between two numbers. A fraction describes the division of a whole (region, set, segment) into equal parts. How does the position of a digit in a number affect its value? How can place value properties aid computation? What are efficient methods for finding sums and differences? What are different models of and models for multiplication and division? What are efficient methods for finding products and quotients? How are the four operations related to one another? How can fractions be modeled and compared? Vocabulary: add, subtract, multiply, factor, product, factor pair, multiple, prime, composite, equation, rectangular array, area model, properties (rules about how numbers work), quotient, remainder, dividend, divisor, multiplication, division, fraction, equivalent Prime numbers have exactly two factors, the number one and their own number. Composite numbers have more than two factors. The number one is neither prime nor composite. Fluently add and subtract 4.NBT.4-Fluently add and multi-digit whole numbers subtract multi-digit whole using the standard numbers using the standard algorithm. algorithm. (04)[State:New Determine if a number between 1 and 100 is a 4.NBT.5-Multiply a whole prime or composite number. number of up to four digits by a Find all factor pairs for a one-digit whole number, and whole number up to 100. multiply two two-digit numbers, Determine if a number is a using strategies based on place multiple of a given 1-digit value and the properties of whole number. operations. Illustrate and Multiply multi-digit numbers explain the calculation by using using a variety of strategies equations, rectangular arrays, (up to 4-digits by 1-digit or 2- and/or area models. (04) digits by 2-digits). Explain the answers to 4.NBT.6-Find whole-number multi-digit multiplication quotients and remainders with problems using equations, up to four-digit dividends and rectangular arrays, and one-digit divisors, using area models (up to 4-digits strategies based on place value, by 1-digit or 2-digits by 2- the properties of operations, digits). and/or the relationship between Divide multi-digit dividends multiplication and division. by one-digit divisors using a Illustrate and explain the variety of strategies (up to 4- calculation by using equations, digit dividends). rectangular arrays, and/or area Explain the answers to models. (04)[State:New Jersey multi-digit division problems using equations, 4.NF.1-Explain why a fraction a/ rectangular arrays, and b is equivalent to a fraction (n area models (up to 4-digit a)/(n b) by using visual dividends). fraction models, with attention to Recognize and generate how the number and size of the equivalent fractions. parts differ even though the two Explain why fractions are fractions themselves are the equivalent using visual same size. Use this principle to fraction models. recognize and generate Page: 5 of 15
The bottom number of a fraction tells how many equal parts the whole or unit is divided into. The top number tells how many equal parts are indicated. A fraction is relative to the size of the whole or unit. A fraction can be associated with a unique point on the number line. Letters are used in mathematics to represent unknowns in equations. Plans: Explain why a fraction a/b is equivalent to a fraction (n x a)/(n x b) using visual fraction models. Compose equations from information supplied in word problems (with all 4 operations) using letters to represent unknowns (without solving). equivalent fractions. (04) 4.OA.3-Solve multistep word problems posed with whole numbers and having wholenumber 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. (04)[State:New Jersey 4.OA.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. (04) Page: 6 of 15
Duration: December/Week 15 - February/Week 21 UNIT NAME: Properties of Operations with Multi-Digit Arithmetic, Fraction Addition, and Subtraction Enduring Understandings Essential Questions Knowledge Skills Standards Patterns can grow and What is the repeating and/ repeat. or increasing unit in the Patterns can be generalized. pattern? Number patterns and What strategies can be relationships can be used to continue a represented using variables. sequence? Fractions express a How does finding patterns relationship between two help in counting and/or numbers. computation? A fraction describes the How can fractions be division of a whole (region, modeled and compared? set, segment) into equal What are tools of parts. measurement and how are The bottom number in a they used? fraction tells how many What is the purpose of equal parts the whole or standard units of unit is divided into. The top measurement? number tells how many How do units within a parts are indicated. system relate to each A fraction is relative to the other? (e.g., time, length, size of the whole or unit. volume, weight) Each fraction can be What questions can be associated with a unique answered using addition point on the number line. and/or subtraction? Objects have distinct What are efficient methods attributes that can be for finding sums and measured. differences? Standard units provide What are different models common language for of and models for addition communication measures. and subtraction? The choice of measurement tools depends on the measureable attribute and the degree of precision desired. The longer the unit of measure, the few units it takes to measure the object. Vocabulary: number pattern, shape pattern, rule, fraction, addition, subtraction, joining parts, separating parts, decompose, mixed numbers, numerator, denominator, unknown Arithmetic patterns are patterns that change by the same rate, such as adding the same number. Comparison of two fractions is only valid when the two fractions refer to the same whole. Fractions can be composed from unit fractions and decomposed into unit fractions. Vocabulary Measurement: km, m, cm; kg, g; lb., oz.; l, ml; hr, min, sec; in. ft, yd, mi (mile); cup (c), pint (pt), quart (qt), equivalent Larger units can be subdivided into equivalent units (partition). The same unit can be repeated to determine the measure (iteration). Generate number or shape patterns by using rules including words, models or graphs. Describe features of an arithmetic number pattern or shape pattern by identifying the rule and features that are not explicit in the rule. (e.g., Given the rule "Add 3" and the starting number 1 observe that the terms in the resulting sequence appear to alternate between odd and even numbers.) Compare two fractions with different numerators and different denominators using <, >, and =. Justify the comparison by using visual fraction models. Decompose a fraction into a sum of fractions with the same denominator in more than one way and record each decomposition as an equation (e.g., 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). Justify their breaking apart (decomposing) of fractions using visual fraction models. 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. 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. (04) 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 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. (04) 4.NF.3-Understand a fraction a/ b with a > 1 as a sum of fractions 1/b. (04)[State:New 4.NF.3.a-Understand addition and subtraction of fractions as joining and separating parts referring to the same whole. (04) Page: 7 of 15
Letters are used in mathematics to represent unknowns in equations. Add and subtract mixed numbers with like denominators by replacing each mixed number with an equivalent fraction. 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). Express measurement comparisons within a single system of measurement and record in a two-column chart within a single system of measurement (e.g., know that 1 ft. is 12 times as long as 1 in.). Compose equations from information supplied in word problems using letters to represent unknowns and solve the word problems with addition and subtraction. Fluently add and subtract two multi-digit whole numbers using the standard algorithm. 4.NF.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. (04) 4.NF.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. (04) 4.NF.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. (04)[State:New Jersey 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 1 ft is 12 times as long as 1 in. Express the length Page: 8 of 15
Plans: 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),... (04)[State:New Jersey 4.OA.3-Solve multistep word problems posed with whole numbers and having wholenumber 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. (04)[State:New Jersey 4.NBT.4-Fluently add and subtract multi-digit whole numbers using the standard algorithm. (04)[State:New Page: 9 of 15
Duration: February/Week 22 - March/Week 28 UNIT NAME: Extend Understanding of Fractions, Solve Word Problems, and Introduce Decimals Enduring Understandings Essential Questions Knowledge Skills Standards A fraction describes the division of a whole (region, set, segment) into equal parts. The bottom number in a fraction tells how many equal parts the whole or unit is divided into. The top number tells how many parts are indicated. A fraction is relative to the size of the whole or unit. Each fraction can be associated with a unique point on the number line. Fractions and decimals express a relationship between two numbers. Fractions with unlike denominators are renamed as equivalent fractions with like denominators to add and subtract. Decimal place value is an extension of whole number place value. The base-ten numeration system extends infinitely to very large and very small numbers (e.g., millions and millionths). Objects have distinct attributes that can be measured. How is multiplication of a fraction by a whole number similar and different to whole number multiplication? How can fractions be modeled? How is addition of fractions similar and different to whole number addition and subtraction? How are common fractions and decimals alike and different? How does what I measure influence how I measure? What are tools of measurement and how are they used? What is the purpose of standard units of measurement? How do units within a system relate to each other? (time, money, length, volume, weight) How can data be gathered, recorded and organized? How does the type of data influence the type of display? What aspects of a graph help people understand and interpret the data easily? What kinds of questions can and cannot be answered from a graph? Vocabulary: numerator, denominator, equivalent, decimal, tenths, hundredths, area, perimeter, square unit, line plot, data, distance, time, liquid volume, mass, money, measurement scale A number can be represented as both a fraction and a decimal. Multiply a fraction by a whole number using visual fraction models and equations, demonstrating fraction a/b as a multiple of 1/b. For example, use a visual fraction model to express 3 x (2/5) as 6 x (1/5), recognizing this product as 6/6. (In general n x (a/b) = (n x a)/b.) Use visual fraction models and equations to solve 1- step word problems related to multiplying a whole number by a fraction. Express a fraction with a denominator of 10 as an equivalent fraction with denominator 100. Add two fractions with respective denominators 10 and 100 by writing each fraction as a fraction with denominator 100 (e.g., express 3/10 as 30/100, and add 3/10 + 4/100 = 34/100). Use decimal notation for fractions with denominators of 10 or 100 (e.g., rewrite 0.62 as 62/100, describe a length as 0.62 meters, locate 0.62 on a number line). 4.NF.4-Apply and extend previous understandings of multiplication to multiply a fraction by a whole number. (04) 4.NF.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). (04)[State:New Jersey 4.NF.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.) (04)[State:New Jersey 4.NF.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? (04)[State:New Page: 10 of 15
Standard units provide common language for communication measurements. The choice of measurement tools depends on the measureable attribute and the degree of precision desired. Graphs convey data in a concise way. Letters are used in mathematics to represent unknowns in equations. The real-world situation determines how a remainder needs to be interpreted when solving a problem. Estimation can be used to check the reasonableness of exact answers found by paper/pencil or calculator methods. What questions can be answered using addition and subtraction? What are efficient methods for finding sums and differences? What questions can be answered using multiplication and division? What are efficient methods for finding products and quotients? Apply area and perimeter formulas for rectangles in real world math problems (whole numbers). Measure objects to the nearest 1/2, 1/4, and 1/8 inch. Make a line plot to display a data set of measurements in fractions of a unit (1/2, 1/4, 1/8). Use the line plot to solve problems involving addition and subtraction of fractions with like denominators. Compose equations from information solved in word problems, using letters to represent unknowns in formulas, and solve the word problems (all four operations). Assess the reasonableness of answers using mental computation and estimation strategies including rounding. Express measurements given in a larger unit in terms of a smaller unit (e.g., feet to inches, meters to centimeters, dollars to cents). Solve word problems involving simple fractions or decimals that incorporate measurement comparisons of like units. 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. (04)[State:New 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. (04) 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. (04)[State:New 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. (04) Page: 11 of 15
Plans: Represent measurement quantities using diagrams such as number line diagrams that feature a measurement scale. 4.OA.3-Solve multistep word problems posed with whole numbers and having wholenumber 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. (04)[State:New Jersey 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 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. (04) 4.NF.4-Apply and extend previous understandings of multiplication to multiply a fraction by a whole number. (04) Page: 12 of 15
Duration: April/Week 29 - May/Week 35 UNIT NAME: Compare Decimals and Measure and Classify Geometric Figures Enduring Understandings Essential Questions Knowledge Skills Standards Mathematical expressions represent relationships. Numbers can be compared using greater than, less than, or equal. Decimal place value is an extension of whole-number place value. The base-ten numeration system extends infinitely to very large and very small numbers (e.g., millions and millionths). Angles can be compared using ideas such as greater than, less than, and equal. A number of degrees can be used to describe the size of an angle's opening. Objects can be described and compared using their geometric attributes. Points, lines, and planes are the foundation of geometry. How can mathematical relationships be expressed symbolically? How can decimals be modeled and compared? How are geometric properties used to solve problems in everyday life? How can plane and solid shapes be described? How are geometric figures constructed? What strategies can be used to verify symmetry and congruency? Vocabulary: <, >, =, decimal, tenths, hundredths, angle, ray, endpoint, circle, one-degree angle, point, line, line segment, right angle, acute angle, obtuse angle, perpendicular lines, parallel lines, protractor, line of symmetry, line-symmetric figures Comparisons between decimals are valid only when the two decimals refer to the same whole. Angles are geometric shapes that are formed whenever two rays share a common endpoint. 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. An angle that turns through n one-degree angles is said to have an angle measure of n degrees. Angle measure is additive. Compare two decimals to hundredths by reasoning about their size. Record the results of comparisons with the symbols <, >, or =. Justify the conclusions of the comparisons (e.g., by using a visual model). Determine the measure of an angle in degrees. Draw points, lines, line segments, rays, angles (right, acute, obtuse), and perpendicular and parallel lines and identify these in two-dimensional figures. Classify two-dimensional figures based on the presence or absence of parallel or perpendicular lines or the presence or absence of angles of a specific size. Recognize right angles as a category. Identify right triangles. Measure angles in wholenumber degrees using a protractor. Sketch angles of specified measure. 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 symbols >, =, or <, and justify the conclusions, e.g., by using a visual model. (04)[State:New 4.MD.5-Recognize angles as geometric shapes that are formed wherever two rays share a common endpoint, and understand concepts of angle measurement: (04)[State:New 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. (04) 4.MD.5.b-An angle that turns through n one-degree angles is said to have an angle measure of n degrees. (04)[State:New 4.G.1-Draw points, lines, line segments, rays, angles (right, acute, obtuse), and Page: 13 of 15
Plans: When an angle is decomposed into nonoverlapping parts, the angle measure of the whole is the sum of the angle measure of the parts. A line of symmetry for a twodimensional figure is a line across the figure such that the figure can be folded along the line into matching parts. Solve addition and subtraction problems to find unknown angles on a diagram in real world and mathematical problems using a symbol for an unknown angle measure. Draw lines of symmetry. Identify line-symmetric figures. perpendicular and parallel lines. Identify these in twodimensional figures. (04) 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. (04) 4.MD.6-Measure angles in whole-number degrees using a protractor. Sketch angles of specified measure. (04) 4.MD.7-Recognize angle measure as additive. When an angle is decomposed into nonoverlapping 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. (04) 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 linesymmetric figures and draw lines of symmetry. (04) Page: 14 of 15
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