Core Content Connectors by Common Core State Standards: Mathematics 4th Grade

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Grade 4 Overview

Operations and Algebraic Thinking

• Use the four operations with whole numbers to solve problems.
• Gain familiarity with factors and multiples.
• Generate and analyze patterns.

Number and Operations in Base Ten

• Generalize place value understanding for multi-digit whole numbers.
• Use place value understanding and properties of operations to perform multi-digit arithmetic.

Numbers and Operations – Fractions

• Extend understanding of fraction equivalence and ordering.
• Build fractions from unit fractions by applying and extending previous understandings of operations on whole numbers.
• Understand decimal notation for fractions, and compare decimal fractions.

Measurement and Data

• Solve problems involving measurement and conversion of measurements from a larger unit to a smaller unit.
• Represent and interpret data.
• Geometric measurement: understand concepts of angle and measure angles.

Geometry

• Draw and identify lines and angles, and classify shapes by properties of their lines and angles.

Operations and Algebraic Thinking	4.OA
Use the four operations with whole numbers to solve problems.
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.
CCCs linked to 4.OA.A.1	4.PRF.1d2 Use objects to model multiplication and division situations involving up to 5 groups with up to 5 objects in each group and interpret the results.
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.
CCCs linked to 4.OA.A.2	4.NO.2d7 Determine how many objects go into each group when given the total number of objects and the number of groups where the number in each group or number of groups is not greater than 10.
	4.PRF.1e3 Solve multiplicative comparisons with an unknown using up to 2-digit numbers with information presented in a graph or word problem (e.g., an orange hat cost $3. A purple hat cost 2 times as much. How much does the purple hat cost? [3 x 2 = p]).
3. Solve multi-step 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.
CCCs linked to 4.0A.A.3	4.NO.2e2 Solve or solve and check one or two step word problems requiring addition, subtraction or multiplication with answers up to 100.
	5.NO.2a1 Solve problems or word problems using up to three digit numbers and addition or subtraction or multiplication.
Gain familiarity with factors and multiples.
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.
CCCs linked to 4.0A.B.4	4.NO.2f1 Identify multiples for a whole number (e.g., 2= 2, 4, 6, 8, 10).
Generate and analyze patterns.
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.
CCCs linked to 4.OA.C.5	4.PRF.2d3 Generate a pattern when given a rule and word problem (I run 3 miles every day, how many miles have I run in 3 days).
	4.PRF.2e1 Extend a numerical pattern when the rule is provided.
	5.PRF.2a1 Generate a pattern that follows the provided rule.

Numbers and Operations in Base Ten	4.NBT
Generalize place value understanding for multi-digit whole numbers.
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.
CCCs linked to 4.NBT.A.1	4.NO.1k1 Compare the value of a number when it is represented in different place values of two 3 digit numbers.
	4.NO.1k1 Compare the value of a number when it is represented in different place values of two 3 digit numbers.
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.
CCCs linked to 4.NBT.A.2	4.NO.1j6 Compare multi-digit numbers using representations and numbers.
	4.NO.1j7 Write or select the expanded form for a multi-digit number.
3. Use place value understanding to round multi-digit whole numbers to any place.
CCCs linked to 4.NBT.A.3	4.NO.1j5 Use place value to round to any place (i.e., ones, tens, hundreds, thousands).
Use place value understanding and properties of operations to perform multi-digit arithmetic.
4. Fluently add and subtract multi-digit whole numbers using the standard algorithm.
CCCs linked to 4.NBT.B.4	4.NO.2c2 Solve multi-digit addition and subtraction problems up to 1000.
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.
CCCs linked to 4.NBT.B.5	4.NO.2f2 Solve multiplication problems up to two digits by one digit.
	4.PRF.1f4 Solve a 2-digit by 1-digit multiplication problem using 2 different strategies.
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.
CCCs linked to 4.NBT.B.6	5.NO.2a2 Separate a group of objects into equal sets when given the number of sets to find the total in each set with the total number less than 50.

Numbers and Operations--Fractions	4.NF
Extend understanding of fraction equivalence and ordering.
1. Explain why a fraction a/b is equivalent to a fraction (n × a)/(n × b) by using visual fraction models, with attention to how the number and size of the parts differ even though the two fractions themselves are the same size. Use this principle to recognize and generate equivalent fractions.
CCCs linked to 4.NF.A.1	4.NO.1m1 Determine equivalent fractions.
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.
CCCs linked to 4.NF.A.2	4.SE.1g2 Use =, <, or > to compare 2 fractions (fractions with a denominator or 10 or less).
	4.NO.1n2 Compare up to 2 given fractions that have different denominators.
Build fractions from unit fractions by applying and extending previous understandings of operations on whole numbers.
3. Understand a fraction a/b with a > 1 as a sum of fractions 1/b.
1. 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 = 1 + 1 + 1/8 = 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.
CCCs linked to 4.NF.B.3	4.NO.2g1 Using a representation, decompose a fraction into multiple copies of a unit fraction (e.g., ¾ = ¼ + ¼ + ¼ ).
	4.NO.2h1 Add and subtract fractions with like denominators of (2, 3, 4, or 8.)
	4.NO.2h2 Add and subtract fractions with like denominators (2, 3, 4, or 8) using representations.
	4.NO.2h3 Solve word problems involving addition and subtraction of fractions with like denominators (2, 3, 4, or 8).
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?
CCCs linked to 4.NF.B.4	5.NO.2b3 Multiply a fraction by a whole or mixed number
Understand decimal notation for fractions, and compare decimal fractions.
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.
CCCs linked to 4.NF.C.5	4.NO.1o2 Find the equivalent decimal for a given fraction.
Generate and analyze patterns.
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.
CCCs linked to 4.NF.C.6	4.SE.1h2 Identify the equivalent decimal for a fraction
	4.NO.1o1 Match a fraction with a denominator of 10 or 100 as a decimal (5/10 = .5).
	4.NO.1p1 Read, write or select decimals to the tenths place.
	4.NO.1p2 Read, write or select decimals to the hundredths place.
	5.NO.1c1 Rewrite a fraction as a decimal.
	5.NO.1c2 Rewrite a decimal as a fraction.
Generate and analyze patterns.
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.
CCCs linked to 4.NF.C.7	4.SE.1g3 Use =, <, or > to compare 2 decimals (decimals in multiples of 10).
	4.NO.1q1 Compare two decimals to the tenths place with a value of less than 1.
	4.NO.1q2 Compare two decimals to the hundredths place with a value of less than 1.

Measurement and Data	4.MD
Solve problems involving measurement and conversion of measurements from a larger unit to a smaller unit.
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), ...
CCCs linked to 4.MD.A.1	4.ME.2f1 Complete a conversion table for length and mass within a single system.
	5.ME.1a1 Identify the appropriate units of measurement for different purposes in a real life context (e.g., measure a wall using feet, not inches).
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.
CCCs linked to 4.MD.A.2	4.ME.1g2 Solve word problems using perimeter and area where changes occur to the dimensions of a figure.
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.
CCCs linked to 4.MD.3	4.ME.1g2 Solve word problems using perimeter and area where changes occur to the dimensions of a figure.
Represent and interpret data.
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.
CCCs linked to 4.MD.B.4	4.ME.2e7 Make a line plot to display a data set of measurements in fractions of a unit (1/2, 1/4, 1/8).
	4.ME.2e8 Solve problems involving addition and subtraction of fractions with like denominators by using information presented in line plots.
Geometric measurement: Understand concepts of angle and measure angles.
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 n one-degree angles is said to have an angle measure of n degrees.
CCCs linked to 4.MD.C.5	4.GM.1j3 Recognize an angle in two-dimensional figures.
6. Measure angles in whole-number degrees using a protractor. Sketch angles of specified measure.
CCCs linked to 4.MD.C.6	4.ME.2e4 Select appropriate tool for measurement: mass, length, angles.
	4.ME.2e5 Construct a given angle
	4.ME.2e6 Measure right angles using a tool (e.g., angle ruler, protractor).
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.
CCCs linked to 4.MD.C.7	None

Geometry	4.G
Draw and identify lines and angles, and classify shapes by properties of their lines and angles.
1. Draw points, lines, line segments, rays, angles (right, acute, obtuse), and perpendicular and parallel lines. Identify these in two-dimensional figures.
CCCs linked to 4.G.A.1	4.GM.1j1 Recognize a point, line and line segment, rays in two-dimensional figures.
	4.GM.1j2 Recognize perpendicular and parallel lines in two-dimensional figure.
	4.GM.1j3 Recognize an angle in two-dimensional figures.
	5.GM.1j1 Recognize parallel and perpendicular lines within the context of two-dimensional figures.
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.
CCCs linked to 4.G.A.2	4.GM.1h2 Classify two-dimensional shapes based on attributes (# of angles).
	4.GM.1j4 Categorize angles as right, acute, or obtuse.
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.
CCCs linked to 4.G.A.3	4.GM.1k1 Recognize a line of symmetry in a figure.