# Courses of Study : Mathematics

Operations and Algebraic Thinking
Use the four operations with whole numbers to solve problems.
 Mathematics (2016) Grade(s): 4 All Resources: 0
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. [4-OA1]

NAEP Framework
NAEP Statement::
8NPO3a: Perform computations with rational numbers.

NAEP Statement::
8NPO5b: Recognize, find, or use factors, multiples, or prime factorization.

 Mathematics (2016) Grade(s): 4 All Resources: 0
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. (See Appendix A, Table 2.) [4-OA2]

NAEP Framework
NAEP Statement::
4NPO3f: Solve application problems involving numbers and operations.

NAEP Statement::
8NPO3a: Perform computations with rational numbers.

 Mathematics (2016) Grade(s): 4 All Resources: 0
3 ) Solve multistep word problems posed with whole numbers and having whole-number answers using the four operations, including problems in which remainders must be interpreted. Represent these problems using equations with a letter standing for the unknown quantity. Assess the reasonableness of answers using mental computation and estimation strategies including rounding. [4-OA3]

NAEP Framework
NAEP Statement::
4NPO2c: Verify solutions or determine the reasonableness of results in meaningful contexts.

NAEP Statement::
4NPO3f: Solve application problems involving numbers and operations.

NAEP Statement::
8NPO2c: Verify solutions or determine the reasonableness of results in a variety of situations, including calculator and computer results.

NAEP Statement::
8NPO3a: Perform computations with rational numbers.

NAEP Statement::
8NPO5d: Use divisibility or remainders in problem settings.

Alabama Alternate Achievement Standards
AAS Standard:
M.AAS.4.3- Solve one-step real-world problems using addition, multiplication, or subtraction (within forty; no regrouping); select the appropriate method of computation (limited to addition or subtraction) when problem solving.

Gain familiarity with factors and multiples.
 Mathematics (2016) Grade(s): 4 All Resources: 5 Learning Activities: 3 Lesson Plans: 2
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. [4-OA4]

NAEP Framework
NAEP Statement::
4NPO5b: Identify factors of whole numbers.

NAEP Statement::
4NPO5e: Apply basic properties of operations.

NAEP Statement::
8NPO3a: Perform computations with rational numbers.

NAEP Statement::
8NPO5b: Recognize, find, or use factors, multiples, or prime factorization.

NAEP Statement::
8NPO5c: Recognize or use prime and composite numbers to solve problems.

Alabama Alternate Achievement Standards
AAS Standard:
M.AAS.4.4- Arrange, match, and/or recognize factor pairs limited to ones, twos, threes, fours, fives, and tens to their products using models or tools.

Generate and analyze patterns.
 Mathematics (2016) Grade(s): 4 All Resources: 3 Learning Activities: 3
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. [4-OA5]

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.

NAEP Framework
NAEP Statement::
4A1b: Given a pattern or sequence, construct or explain a rule that can generate the terms of the pattern or sequence.

NAEP Statement::
8A1a: Recognize, describe, or extend numerical and geometric patterns using tables, graphs, words, or symbols.

NAEP Statement::
8A1b: Generalize a pattern appearing in a numerical sequence, table, or graph using words or symbols.

NAEP Statement::
8NPO3a: Perform computations with rational numbers.

NAEP Statement::
8NPO5a: Describe odd and even integers and how they behave under different operations.

Number and Operations in Base Ten
(Grade 4 expectations in this domain are limited to whole numbers less than or equal to 1,000,000.)
Generalize place value understanding for multi-digit whole numbers.
 Mathematics (2016) Grade(s): 4 All Resources: 0
6 ) 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. [4-NBT1]

Example: Recognize that 700 ÷ 70 = 10 by applying concepts of place value and division.

NAEP Framework
NAEP Statement::
4NPO1a: Identify place value and actual value of digits in whole numbers.

NAEP Statement::
8NPO3a: Perform computations with rational numbers.

Alabama Alternate Achievement Standards
AAS Standard:
M.AAS.4.6- Compose and decompose numbers from 11 to 50 into a number of tens and a number of ones.

 Mathematics (2016) Grade(s): 4 All Resources: 2 Learning Activities: 1 Lesson Plans: 1
7 ) 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. [4-NBT2]

NAEP Framework
NAEP Statement::
4NPO1c: Compose or decompose whole quantities by place value (e.g., write whole numbers in expanded notation using place value: 342 = 300 + 40 + 2).

NAEP Statement::
4NPO1e: Connect model, number word, or number using various models and representations for whole numbers, fractions, and decimals.

NAEP Statement::
4NPO1i: Order or compare whole numbers, decimals, or fractions.

NAEP Statement::
8NPO3a: Perform computations with rational numbers.

Alabama Alternate Achievement Standards
AAS Standard:
M.AAS.4.7- Compare the value of two numbers up to 100 and read a whole number up to 100.

 Mathematics (2016) Grade(s): 4 All Resources: 1 Learning Activities: 1
8 ) Use place value understanding to round multi-digit whole numbers to any place. [4-NBT3]

NAEP Framework
NAEP Statement::
4NPO2b: Make estimates appropriate to a given situation with whole numbers, fractions, or decimals by:
• Knowing when to estimate,
• Selecting the appropriate type of estimate, including overestimate, underestimate, and range of estimate, or
• Selecting the appropriate method of estimation (e.g., rounding).

NAEP Statement::
8NPO3a: Perform computations with rational numbers.

Alabama Alternate Achievement Standards
AAS Standard:
M.AAS.4.8- Round a whole number from 1 to 99 to the nearest ten.

Use place value understanding and properties of operations to perform multi-digit arithmetic.
 Mathematics (2016) Grade(s): 4 All Resources: 3 Learning Activities: 2 Lesson Plans: 1
9 ) Fluently add and subtract multi-digit whole numbers using the standard algorithm. [4-NBT4]

NAEP Framework
NAEP Statement::
8NPO3a: Perform computations with rational numbers.

Alabama Alternate Achievement Standards
AAS Standard:
M.AAS.4.9- Add and subtract one- and two-digit numbers with regrouping.

 Mathematics (2016) Grade(s): 4 All Resources: 1 Learning Activities: 1
10 ) Multiply a whole number of up to four digits by a one-digit whole number, and multiply two two-digit numbers, using strategies based on place value and the properties of operations. Illustrate and explain the calculation by using equations, rectangular arrays, and/or area models. [4-NBT5]

NAEP Framework
NAEP Statement::
8NPO3a: Perform computations with rational numbers.

Alabama Alternate Achievement Standards
AAS Standard:
M.AAS.4.10- Multiply a two-digit number by a one-digit number with no regrouping.

 Mathematics (2016) Grade(s): 4 All Resources: 1 Learning Activities: 1
11 ) 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. [4-NBT6]

NAEP Framework
NAEP Statement::
4NPO3c: Divide whole numbers:
• Up to three digits by one digit with paper and pencil computation, or
• Up to five digits by two digits with use of calculator.

NAEP Statement::
8NPO3a: Perform computations with rational numbers.

Alabama Alternate Achievement Standards
AAS Standard:
M.AAS.4.11- Divide a two-digit number by a one-digit number with no remainder.

Number and Operations — Fractions
(Grade 4 expectations in this domain are limited to fractions with denominations 2, 3, 4, 5, 6, 8, 10, 12, and 100.)
Extend understanding of fraction equivalence and ordering.
 Mathematics (2016) Grade(s): 4 All Resources: 2 Learning Activities: 2
12 ) Explain why a fraction a/b is equivalent to a fraction nxa/nxb by using visual fraction models, with attention to how the number and size of the parts differ even though the two fractions themselves are the same size. Use this principle to recognize and generate equivalent fractions. [4-NF1]

NAEP Framework
NAEP Statement::
4NPO6a: Explain or justify a mathematical concept or relationship (e.g., explain why 15 is an odd number or why 7-3 is not the same as 3-7).

NAEP Statement::
8NPO1d: Write or rename rational numbers.

NAEP Statement::
8NPO1h: Order or compare rational numbers (fractions, decimals, percents, or integers) using various models and representations (e.g., number line).

NAEP Statement::
8NPO3a: Perform computations with rational numbers.

NAEP Statement::
8NPO3d: Describe the effect of multiplying and dividing by numbers including the effect of multiplying or dividing a rational number by:
• Zero, or
• A number less than zero, or
• A number between zero and one,
• One, or
• A number greater than one.

 Mathematics (2016) Grade(s): 4 All Resources: 0
13 ) 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-NF2]

NAEP Framework
NAEP Statement::
8NPO1d: Write or rename rational numbers.

NAEP Statement::
8NPO1h: Order or compare rational numbers (fractions, decimals, percents, or integers) using various models and representations (e.g., number line).

NAEP Statement::
8NPO3a: Perform computations with rational numbers.

NAEP Statement::
8NPO3d: Describe the effect of multiplying and dividing by numbers including the effect of multiplying or dividing a rational number by:
• Zero, or
• A number less than zero, or
• A number between zero and one,
• One, or
• A number greater than one.

Alabama Alternate Achievement Standards
AAS Standard:
M.AAS.4.13- Using models, identify a fraction that is greater than, less than, or equal to a given fraction (limited to halves, thirds, and fourths).

Build fractions from unit fractions by applying and extending previous understandings of operations on whole numbers.
 Mathematics (2016) Grade(s): 4 All Resources: 0
14 ) Understand a fraction a/b with a > 1 as a sum of fractions 1/b. [4-NF3]

a. Understand addition and subtraction of fractions as joining and separating parts referring to the same whole. [4-NF3a]

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. [4-NF3b]

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. [4-NF3c]

d. Solve word problems involving addition and subtraction of fractions referring to the same whole and having like denominators, e.g., by using visual fraction models and equations to represent the problem. [4-NF3d]

NAEP Framework
NAEP Statement::
• Whole numbers, or
• Fractions with like denominators, or
• Decimals through hundredths.

NAEP Statement::
8NPO1d: Write or rename rational numbers.

NAEP Statement::
8NPO1h: Order or compare rational numbers (fractions, decimals, percents, or integers) using various models and representations (e.g., number line).

NAEP Statement::
8NPO3a: Perform computations with rational numbers.

NAEP Statement::
8NPO3d: Describe the effect of multiplying and dividing by numbers including the effect of multiplying or dividing a rational number by:
• Zero, or
• A number less than zero, or
• A number between zero and one,
• One, or
• A number greater than one.

 Mathematics (2016) Grade(s): 4 All Resources: 1 Learning Activities: 1
15 ) Apply and extend previous understandings of multiplication to multiply a fraction by a whole number. [4-NF4]

a. Understand a fraction a/b as a multiple of 1/b. [4-NF4a]

Example: Use a visual fraction model to represent 5/4 as the product 5 x (1/4), recording the conclusion by the equation 5/4 = 5 x (1/4).

b. Understand a multiple of a/b as a multiple of 1/b, and use this understanding to multiply a fraction by a whole number. [4-NF4b]

Example: Use a visual fraction model to express 3 x (2/5) as 6 x (1/5), recognizing this product as 6/5. (In general, n x (a/b) = (nxa)/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. [4-NF4c]

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 which two whole numbers does your answer lie'

NAEP Framework
NAEP Statement::
4NPO3f: Solve application problems involving numbers and operations.

NAEP Statement::
8NPO1b: Model or describe rational numbers or numerical relationships using number lines and diagrams.

NAEP Statement::
8NPO1d: Write or rename rational numbers.

NAEP Statement::
8NPO1h: Order or compare rational numbers (fractions, decimals, percents, or integers) using various models and representations (e.g., number line).

NAEP Statement::
8NPO3d: Describe the effect of multiplying and dividing by numbers including the effect of multiplying or dividing a rational number by:
• Zero, or
• A number less than zero, or
• A number between zero and one,
• One, or
• A number greater than one.

NAEP Statement::
8NPO5b: Recognize, find, or use factors, multiples, or prime factorization.

Alabama Alternate Achievement Standards
AAS Standard:
M.AAS.4.15- Multiply a one-digit whole number by a unit fraction (limited to whole numbers to 1 to 5 and fractions of halves, fourths, and thirds).

Understand decimal notation for fractions, and compare decimal fractions.
 Mathematics (2016) Grade(s): 4 All Resources: 0
16 ) 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. (Students who can generate equivalent fractions can develop strategies for adding fractions with unlike denominators in general. But addition and subtraction with unlike denominators in general is not a requirement at this grade.) [4-NF5]

Example: Express 3/10 as 30/100, and add 3/10 + 4/100 = 34/100.

NAEP Framework
NAEP Statement::
8NPO1h: Order or compare rational numbers (fractions, decimals, percents, or integers) using various models and representations (e.g., number line).

NAEP Statement::
8NPO3a: Perform computations with rational numbers.

 Mathematics (2016) Grade(s): 4 All Resources: 0
17 ) Use decimal notation for fractions with denominators 10 or 100. [4-NF6]

Example: Rewrite 0.62 as 62/100; describe a length as 0.62 meters; locate 0.62 on a number line diagram.

NAEP Framework
NAEP Statement::
8NPO1h: Order or compare rational numbers (fractions, decimals, percents, or integers) using various models and representations (e.g., number line).

NAEP Statement::
8NPO3a: Perform computations with rational numbers.

Alabama Alternate Achievement Standards
AAS Standard:
M.AAS.4.17- Use decimal notation for a fraction with a denominator of 10.

 Mathematics (2016) Grade(s): 4 All Resources: 0
18 ) 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. [4-NF7]

NAEP Framework
NAEP Statement::
8NPO1h: Order or compare rational numbers (fractions, decimals, percents, or integers) using various models and representations (e.g., number line).

NAEP Statement::
8NPO3a: Perform computations with rational numbers.

Measurement and Data
Solve problems involving measurement and conversion of measurements from a larger unit to a smaller unit.
 Mathematics (2016) Grade(s): 4 All Resources: 0
19 ) Know relative sizes of measurement units within one system of units, including km, m, cm; kg, g; lb, oz; l, ml; and 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. [4-MD1]

Examples: 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), ...

NAEP Framework
NAEP Statement::
4M2b: Solve problems involving conversions within the same measurement system such as conversions involving inches and feet or hours and minutes.

NAEP Statement::
4M2d: Determine appropriate size of unit of measurement in problem situation involving such attributes as length, time, capacity, or weight.

NAEP Statement::
8M2a: Select or use an appropriate type of unit for the attribute being measured such as length, area, angle, time, or volume.

NAEP Statement::
8M2b: Solve problems involving conversions within the same measurement system such as conversions involving square inches and square feet.

NAEP Statement::
8M2c: Estimate the measure of an object in one system given the measure of that object in another system and the approximate conversion factor. For example:
• Distance conversion: 1 kilometer is approximately 5/8 of a mile.
• Money conversion: U.S. dollars to Canadian dollars.
• Temperature conversion: Fahrenheit to Celsius.

Alabama Alternate Achievement Standards
AAS Standard:
M.AAS.4.19- Identify the smaller measurement unit that comprises a larger unit within a measurement system (inches/feet, minutes/hours, feet/yards).

 Mathematics (2016) Grade(s): 4 All Resources: 1 Lesson Plans: 1
20 ) 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. [4-MD2]

NAEP Framework
NAEP Statement::
4NPO3f: Solve application problems involving numbers and operations.

Alabama Alternate Achievement Standards
AAS Standard:
M.AAS.4.20- Tell time to the half-hour; identify the hour before or after a given time; measure weight using standard units; recognize the value of coins in cents.

 Mathematics (2016) Grade(s): 4 All Resources: 0
21 ) Apply the area and perimeter formulas for rectangles in real-world and mathematical problems. [4-MD3]

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.

NAEP Framework
NAEP Statement::
4M1f: Solve problems involving perimeter of plane figures.

NAEP Statement::
4M1g: Solve problems involving area of squares and rectangles.

NAEP Statement::
8M1f: Solve mathematical or real-world problems involving perimeter or area of plane figures such as triangles, rectangles, circles, or composite figures.

Alabama Alternate Achievement Standards
AAS Standard:
M.AAS.4.21- Given a drawing of a square or rectangle on a grid, determine the area or perimeter (sum or product limited to 40).

Represent and interpret data.
 Mathematics (2016) Grade(s): 4 All Resources: 0
22 ) 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. [4-MD4]

Example: From a line plot find and interpret the difference in length between the longest and shortest specimens in an insect collection.

Alabama Alternate Achievement Standards
AAS Standard:
M.AAS.4.22- Interpret data on a pictograph or bar graph to solve a problem.

Geometric measurement: understand concepts of angle and measure angles.
 Mathematics (2016) Grade(s): 4 All Resources: 1 Learning Activities: 1
23 ) Recognize angles as geometric shapes that are formed wherever two rays share a common endpoint, and understand concepts of angle measurement. [4-MD5]

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. [4-MD5a]

b. An angle that turns through n one-degree angles is said to have an angle measure of n degrees. [4-MD5b]

Alabama Alternate Achievement Standards
AAS Standard:
M.AAS.4.23- Identify an angle in a given shape (square, rectangle, triangle).

 Mathematics (2016) Grade(s): 4 All Resources: 2 Learning Activities: 1 Lesson Plans: 1
24 ) Measure angles in whole-number degrees using a protractor. Sketch angles of specified measure. [4-MD6]

 Mathematics (2016) Grade(s): 4 All Resources: 1 Learning Activities: 1
25 ) 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 or mathematical problems, e.g., by using an equation with a symbol for the unknown angle measure. [4-MD7]

NAEP Framework
NAEP Statement::
4NPO3f: Solve application problems involving numbers and operations.

Geometry
Draw and identify lines and angles, and classify shapes by properties of their lines and angles.
 Mathematics (2016) Grade(s): 4 All Resources: 3 Learning Activities: 2 Lesson Plans: 1
26 ) Draw points, lines, line segments, rays, angles (right, acute, obtuse), and perpendicular and parallel lines. Identify these in two-dimensional figures. [4-G1]

NAEP Framework
NAEP Statement::
4G1a: Explore properties of paths between points.

NAEP Statement::
4G1c: Identify or draw angles and other geometric figures in the plane.

NAEP Statement::
4G4a: Describe relative positions of points and lines using the geometric ideas of parallelism or perpendicularity.

NAEP Statement::
8G3g: Describe or analyze properties and relationships of parallel or intersecting lines.

Alabama Alternate Achievement Standards
AAS Standard:
M.AAS.4.26- Recognize angles, parallel and perpendicular lines, and intersecting lines.

 Mathematics (2016) Grade(s): 4 All Resources: 1 Learning Activities: 1
27 ) Classify two-dimensional figures based on the presence or absence of parallel or perpendicular lines or the presence or absence of angles of a specified size. Recognize right triangles as a category, and identify right triangles. [4-G2]

NAEP Framework
NAEP Statement::
4G3f: Describe and compare properties of simple and compound figures composed of triangles, squares, and rectangles.

NAEP Statement::
4G4a: Describe relative positions of points and lines using the geometric ideas of parallelism or perpendicularity.

NAEP Statement::
8G1b: Identify a geometric object given a written description of its properties.

NAEP Statement::
8G3g: Describe or analyze properties and relationships of parallel or intersecting lines.

 Mathematics (2016) Grade(s): 4 All Resources: 2 Learning Activities: 2
28 ) Recognize a line of symmetry for a two-dimensional figure as a line across the figure such that the figure can be folded along the line into matching parts. Identify line-symmetric figures and draw lines of symmetry. [4-G3]

NAEP Framework
NAEP Statement::
4G2a: Identify whether a figure is symmetrical or draw lines of symmetry.

NAEP Statement::
4G2d: Recognize which attributes (such as shape and area) change or do not change when plane figures are cut up or rearranged.

NAEP Statement::
8G2a: Identify lines of symmetry in plane figures or recognize and classify types of symmetries of plane figures.

Alabama Alternate Achievement Standards
AAS Standard:
M.AAS.4.28- Given a drawing of a shape with a line drawn across the shape, identify if it is divided symmetrically.