4 th Grade Math - Year at a Glance

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1 4 th Grade Math - Year at a Glance Quarters Q1 Q2 Q3 Q4 *4.1.1 (4.NBT.2) *4.1.2 (4.NBT.1) *4.1.3 (4.NBT.3) *4.1.4 (4.NBT.1) (4.NBT.2) *4.1.5 (4.NF.3) Bundles Read and write whole numbers up to 1,000,000. a. Read (orally) whole numbers up to 1,000,000. b. Write whole numbers up to 1,000,000 in standard form. c. Write whole numbers up to 1,000,000 in word form. d. Write whole numbers up to 1,000,000 in expanded form. 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. (Note: The CCSS includes expanded form and comparison of numbers less than or equal to 1,000,000.) Identify and write whole numbers up to 1,000,000, given a place-value model. a. Write whole numbers up to 1,000,000 given a place-value model. b. Represent whole numbers with base ten blocks and place-value charts. Round whole numbers up to 10,000 to the nearest ten, hundred, and thousand. a. Round whole numbers up to 10,000 to the nearest ten. b. Round whole numbers up to 10,000 to the nearest hundred. c. Round whole numbers up to 10,000 to the nearest thousand. Use place value understanding to round multi-digit whole numbers to any place. (Note: The CCSS includes rounding numbers less than or equal to 1,000,000 to any place.) Order and compare whole numbers using symbols for less than (<), equal to (=), and greater than (>). a. Compare whole numbers up to 100,000 using >, <, =. b. Order whole numbers from least to greatest up to 100,000 on a number line. c. Order whole numbers up to 100,000 from greatest to least on a number line. d. Order a series of whole numbers up to 100,000 from both greatest to least and least to greatest. 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. (Note: The CCSS includes expanded form and comparison of numbers less than or equal to 1,000,000.) Rename and write whole numbers as fractions. 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. Big Idea Place Value Multiplication Division Fractions/Decimals Lines, Rays, Angles Area/Perimeter Measurement Algebra/Data

2 *4.1.6 (4.NF.3) *4.1.7 (4.NF.3) *4.1.8 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. Name and write mixed numbers, using objects or pictures. a. Define and explain mixed numbers as whole numbers and a fraction. b. Name and write mixed numbers, using objects or pictures. 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. Name and write mixed numbers as improper fractions, using objects or pictures. a. Describe an improper fraction as larger than a whole number. b. Write an improper fraction using objects or pictures. Understand a fraction a/b with a > 1 as a sum of fractions 1/ 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. Write tenths and hundredths in decimal and fraction notations. Know the fraction and decimal equivalents for halves and fourths. a. Write tenths in decimal and fraction notations. b. Write hundredths in decimal and fraction notations. c. Name and write the fraction and decimal equivalents for halves and fourths. 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. (4.NF.6) *4.1.9 Round two-place decimals to tenths or to the nearest whole number. a. Round two-place decimals to tenths. b. Round two-place decimals to the nearest whole number. *4.2.1 Understand and use standard algorithms for addition and subtraction. a. Define standard algorithm. b. Calculate by using addition a group of (2 or more) multi-digit whole numbers, without regrouping, using the

3 standard algorithm. c. Add any multi-digit whole numbers, with regrouping, using properties of the number system. d. Subtract any multi-digit whole numbers, without regrouping, using properties of the number system. e. Subtract any multi-digit whole numbers, with regrouping, using properties of the number system. f. Select and describe an appropriate method for addition and subtraction for any group of whole numbers. (4.NBT.4) Fluently add and subtract multi-digit whole numbers using the standard algorithm. *4.2.2 Represent as multiplication any situation involving repeated addition. *4.2.3 Represent as division any situation involving the sharing of objects or the number of groups of shared objects *4.2.4 Demonstrate mastery of the multiplication tables for numbers between 1 and 10 and of the corresponding division facts. a. Recite and write multiplication facts for numbers between 1 and 10. b. Recite and write division facts that have whole number quotients between 1 and 10. c. Demonstrate mastery of multiplication facts 1 through10 and corresponding division facts. *4.2.5 Multiply numbers up to 100 by numbers up to 10 using a standard algorithm, using relevant properties of the number system. Multiply a whole number of up to four digits by a one-digit whole number, and multiply two two-digit (4.NBT.5) 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. (Notes: The expectation increase from multiplying numbers up to 100 by numbers up to 10 to multiplying numbers up to 4 digits by 1-digit numbers, and also multiplying two 2-digit numbers.) *4.2.6 Use a standard algorithm to divide numbers up to 100 by numbers up to 10 without remainders, using relevant properties of the number system. a. Demonstrate and explain the steps (standard algorithm) used to divide numbers up to 100 by numbers up to 10 without remainders. (The expectation increases from dividing numbers up to 100 by numbers up to 10 without remainders to dividing up to 4-digit numbers by one-digit numbers with remainders.) b. Solve division problems up to 100 by numbers up to 10 without remainders (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. (The expectation increases from dividing numbers up to 100 by numbers up to 10 without remainders to dividing up to 4-digit numbers by one-digit numbers with remainders Understand the special properties of 0 and 1 in multiplication and division. a. Explain why a number cannot be divided by 0. b. Apply the identity property of multiplication in both multiplication and division. c. Apply the zero property of multiplication in both multiplication and division. d. Solve multiplication problems involving the identity and zero properties. e. Solve division problems involving the identity and zero properties. *4.2.8 Add and subtract simple fractions with different denominators, using objects or pictures. a. Explain the need for a common denominator when adding and subtracting fractions. b. Add simple fractions with different denominators using objects or pictures. c. Subtract simple fractions with different denominators, using objects or pictures. Understand a fraction a/b with a > 1 as a sum of fractions 1/b. (4.NF.3) 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

4 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 Add and subtract decimals (to hundredths), using objects or pictures. a. Add decimals (to hundredths), using objects or pictures. b. Subtract decimals (to hundredths), using objects or pictures. * Use a standard algorithm to add and subtract decimals (to hundredths). a. Use a standard algorithm to add decimals (to hundredths). b. Use a standard algorithm to subtract decimals (to hundredths). c. Represent an unknown number in an equation or expression as a variable using letters, boxes, or other symbols. d. Solve unknown variable when given a simple expression, equations, or inequalities Identify and apply strategies used to estimate results of any whole-number computation. a. Calculate by using addition any multi-digit whole numbers rounded to hundreds or thousands using mental (4.OA.3) math. b. Use mental mathematics to subtract numbers rounded to hundreds or thousands Use mental arithmetic to add or subtract numbers rounded to hundreds or thousands. (4.OA.3) *4.3.1 (4.OA.2) (4.OA.3) Use letters, boxes, or other symbols to represent any number in simple expressions, equations, or inequalities (i.e., demonstrate an understanding of and the use of the concept of a variable). 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. *4.3.2 Use and interpret formulas to answer questions about quantities and their relationships. *4.3.3 Understand that multiplication and division are performed before addition and subtraction in expressions without parentheses. a. Recognize that multiplication and division are performed before addition and subtraction in expressions without parentheses. b. Write expressions without parentheses including multiplication, division, addition, and subtraction. c. Solve expressions without parentheses that include multiplication, division, addition, and subtraction. *4.3.4 (4.OA.5) *4.3.5 (4.OA.5) *4.3.6 (4.OA.2) Understand that in an equation such as y=3x+5 is a rule for finding a second number when a first number is given. a. Identify a rule for finding a second number when a first number is given. b. Solve equations to find a second number when a first number is given. Complete number patterns using multiplication and division. Recognize and apply the relationships between addition and multiplication, between subtraction and division, and the inverse relationship between multiplication and division to solve problems. a. Identify and apply relationships between addition and multiplication. b. Identify and apply relationships between subtraction and division. c. Identify and apply the inverse relationship between multiplication and division to solve problems.

5 *4.3.7 (4.OA.2) *4.3.8 (4.MD.4) *4.4.1 (4.G.1) 4.MD.5 4.MD.6 4.MD.7 *4.4.2 (4.G.1) Relate problem situations to number sentences involving multiplication and division. Plot and label whole numbers on a number line up to 100. Estimate positions on the number line. a. Plot whole numbers on a number line up to 100. b. Plot whole numbers on a number line up to 10,000. Identify, describe, and draw rays, right angles, acute angles, obtuse angles, and straight angles using appropriate mathematical tools and technology. a. Identify, describe, and draw rays using appropriate mathematical tools and technology. b. Identify, describe, and draw right angles using appropriate mathematical tools and technology. c. Identify, describe, and draw obtuse angles using appropriate mathematical tools and technology. d. Identify, describe, and draw straight angles using appropriate mathematical tools and technology. e. Identify, describe, and draw acute angles using appropriate mathematical tools and technology. 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 n one-degree angles is said to have an angle measure of n degrees. Measure angles in whole-number degrees using a protractor. Sketch angles of specified measure. 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. Identify, describe, and draw parallel, perpendicular, and oblique lines using appropriate mathematical tools and technology. a. Identify, describe, and draw parallel lines using appropriate mathematical tools and technology. b. Identify, describe, and draw perpendicular lines using appropriate mathematical tools and technology. c. Identify, describe, and draw oblique lines using appropriate mathematical tools and technology. *4.4.3 Identify, describe, and draw parallelograms, rhombuses, and trapezoids, using appropriate mathematical tools and technology. a. Identify, describe, and draw parallelograms using appropriate mathematical tools and technology. b. Identify, describe and draw rhombuses using appropriate mathematical tools and technology. c. Identify, describe, and draw trapezoids using appropriate mathematical tools and technology. *4.4.4 Identify congruent quadrilaterals and give reasons for congruence using sides, angles, parallels, and perpendiculars. a. Identify congruent quadrilaterals by using attributes, such as sides, angles, parallels, and perpendiculars. b. Classify and explain congruent quadrilaterals by using attributes (properties), such as sides, angles, parallels, and perpendiculars. *4.4.5 Identify and draw lines of symmetry in polygons. (4.G.3) Construct cubes and prisms and describe their attributes. a. Describe (orally and in writing) the attributes (faces, edges, and vertices) of cubes. b. Describe (orally and in writing) the attributes (faces, edges, and vertices) of prisms. c. Construct cubes and prisms.

6 *4.5.1 Measure length to the nearest quarter-inch, eighth-inch, and millimeter. a. Measure length to the nearest quarter-inch. b. Measure length to the nearest eighth-inch. c. Measure length to the nearest millimeter. *4.5.2 Subtract units of length that may require renaming of feet to inches or meters to centimeters. a. Convert units of length that may require renaming of feet to inches. b. Convert units of length that may require renaming of meters to centimeters. c. Solve subtraction problems involving converting units of length. (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 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),... (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 *4.5.3 (4.MD.3) *4.5.4 (4.MD.3) (4.MD.3) *4.5.6 (4.MD.3) measurement quantities using diagrams such as number line diagrams that feature a measurement scale. Know and use formulas for finding the perimeters of rectangles and squares. a. Derive the formula for perimeter of a square by modeling multiplication as repeated addition. b. Calculate the perimeter of rectangles and squares by adding all sides. c. Calculate the perimeter of rectangles and squares using standard formulas. d. Select appropriate units of measurement for finding perimeter (in, ft, yd, cm, m). e. Memorize and calculate formula for perimeter of rectangles and squares. Know and use formulas for finding the areas of rectangles and squares. a. Calculate the area of rectangles and squares using standard formulas. b. Select appropriate units for measurement of area. c. Memorize and calculate area formula for rectangles and squares. Estimate and calculate the area of rectangular shapes using appropriate units, such as square centimeter (cm 2 ), square meter (m 2 ), square inch (in 2 ), or square yard (yd 2 ). a. Estimate the area of rectangular shapes using appropriate units, such as square centimeter (cm2), square meter (m2), square inch (in2), or square yard (yd2). b. Calculate the area of rectangular shapes using appropriate units, such as square centimeter (cm2), square meter (m2), square inch (in2), or square yard (yd2). Understand that rectangles with the same area can have different perimeters and that rectangles with the same perimeter can have different areas. a. Demonstrate and explain why rectangles with the same area can have different perimeters. b. Recognize and show that rectangles with the same perimeter can have different areas. c. Explain why rectangles with the same perimeters can have different areas. *4.5.7 Find areas of shapes by dividing them into basic shapes such as rectangles. a. Subdivide shapes into basic shapes. b. Calculate area of subdivided shapes, such as rectangles, to find the area of the complete shape Use volume and capacity as different ways of measuring the space inside a shape. a. Compare the difference between volume and capacity. b. Identify and measure volume and capacity as different ways of measuring the space inside a shape.

7 *4.5.9 (4.MD.2) * (4.MD.2) *4.6.1 (4.MD.4) *4.6.2 (4.MD.4) Add time intervals involving hours and minutes. a. Add time intervals involving hours and minutes. b. Convert minutes to hours when solving problems involving time intervals. c. Convert minutes to hours when calculating problems that involve time intervals. 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. Calculate the amount of change from a purchase. 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. Represent data on a number line and in tables, including frequency tables. a. Plot data on a number line. b. Display data in a table. c. Represent data on a line plot. Interpret data graphs to answer questions about a situation. a. Interpret data graphs (line plots, frequency tables) to answer questions about a situation using the words most, few, and none. b. Analyze and describe data patterns using the words most, few, and none on a line plot. *4.6.3 Summarize and display the results of probability experiments in a clear and organized way. a. Display the results of a probability experiment. b. Summarize data results of probability experiments. c. Produce graphs from data collected to display results. *4.7.1 Analyze problems by identifying relationships, telling relevant from irrelevant information, sequencing and prioritizing information, and observing patterns. a. Analyze problems by identifying relationships. b. Analyze problems by telling relevant from irrelevant information. c. Analyze problems by sequencing and prioritizing information. d. Analyze problems by observing patterns. *4.7.2 Decide when and how to break a problem into simpler parts. *4.7.3 Apply strategies and results from simpler problems to solve more complex problems. *4.7.4 Solve problems, justify arguments, and make conjectures by using a variety of methods, such as words, numbers, symbols, charts, graphs, tables, diagrams, tools, and models. *4.7.5 Express solutions clearly and logically by using the appropriate mathematical terms and notation. Support solutions with evidence in both verbal and symbolic work. a. Express solutions clearly and logically by using the appropriate mathematical terms and notation. b. Provide verbal and/or symbolic evidence to support solutions Recognize the relative advantages of exact and approximate solutions to problems and give answers to a specified degree of accuracy. a. Name the relative advantages of exact and approximate solutions to problems. b. Give answers to a specified degree of accuracy.

8 4.7.7 Know and use appropriate methods for estimating results of whole-number computations. a. Know and use appropriate methods for estimating results of whole-number computations. b. Identify appropriate methods for estimating results of whole-number computations. *4.7.8 Make precise calculations and check the validity of the results in the context of the problem. *4.7.9 Explain whether a solution is reasonable in the context of the original situation Note the method of finding the solution and show a conceptual understanding of the method by solving similar 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. (Limit whole numbers less than or equal to 1,000,000) 4.OA.4 4.OA.5 4.NBT.1 4.NF.1 4.NF.2 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 onedigit number. Determine whether a given whole number in the range is prime or composite. 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. 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. 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. 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. 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 as the product 5 (1/4), recording the conclusion by the equation 5/4 = 5 (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 (2/5) as 6 (1/5), recognizing this product as 6/5. (In general, n (a/b) = (n 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? 4.NF.5 4.NF.7 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. 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.