Standards for Mathematical Content Grade 4
Operations and Algebraic Thinking
Use the four operations with whole numbers to solve problems.
4.OA.1. Interpret a multiplication equation as a comparison (e.g., interpret 35 = 5 × 7 as a statement that 35 is 5 groups of 7 and 7 groups of 5). (Commutative property) 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 or missing numbers in an array). Distinguish multiplicative comparison from additive comparison.
4.OA.3. Solve multistep word problems posed with whole numbers and having whole-number answers using the four operations, including problems in which remainders must be interpreted. Represent these problems using equations with a letter standing for the unknown quantity. Assess the reasonableness of answers using mental computation and estimation strategies including rounding.
Gain familiarity with factors and multiples.
4.OA.4.
- Find all factor pairs for a whole number in the range 1--100.
- Explain the correlation/differences between multiples and 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.
Generate and analyze patterns.
4.OA.5. Generate a number, shape pattern, table, t-chart, or input/output function that follows a given rule. Identify apparent features of the pattern that were not explicit in the rule itself. Be able to express the pattern in algebraic terms. 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.
4.OA.6 Extend patterns that use addition, subtraction, multiplication, division or symbols, up to 10 terms, represented by models (function machines), tables, sequences, or in problem situations (L)
Numbers and Operations in Base Ten
Generalize place value understanding for multi-digit whole numbers.
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.
4.NBT.2. Read and write multi-digit whole numbers using base-ten numerals, number names, and expanded form. Compare two multi-digit numbers based on the value of the digits in each place, using >, =, and < symbols to record the results of comparisons.
4.NBT.3. Use place value understanding to round multi-digit whole numbers to any place using a variety of estimation methods; be able to describe, compare, and contrast solutions.
Use place value understanding and properties of operations to perform multi-digit arithmetic.
4.NBT.4. Fluently add and subtract multi-digit whole numbers using any algorithm. Verify the reasonableness of the results.
4.NBT.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.
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.
Number and Operations---Fractions
(limited in this grade to fractions with denominators 2, 3, 4, 5, 6, 8, 10, 12, and 100)
Extend understanding of fraction equivalence and ordering.
4.NF.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.
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 ½). 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).
Build fractions from units by applying and extending understandings of operations on whole numbers.
4.NF.3. 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 = 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).
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). Check for the reasonableness of the answer. 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?
Understand decimal notation for fractions, and compare decimal fractions.
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.
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.
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).
Measurement and Data
Solve problems of measurement and conversions from a larger unit to smaller units, involving time.
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 measurement quantities using diagrams such as number line diagrams that feature a measurement scale.
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.
4.MD.4. Solve real-world problems involving elapsed time between U.S. time zones (including Alaska Standard time) (L)
Represent and interpret data.
4.MD.5. 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.
4.MD.6. Explain the classification of data from real-world problems shown in graphical representations including the use of terms range and mode with a given set of data. (L)
Geometric measurement: understand concepts of angle and measure angles.
4.MD.7. Recognize angles as geometric shapes that are formed wherever two rays share a common endpoint, and understand the following 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.
4.MD.8. Measure and draw angles in whole-number degrees using a protractor. Estimate and sketch angles of specified measure.
4.MD.9. Recognize angle measure as additive. When an angle is divided 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).
Geometry
Draw and identify lines and angles, and classify shapes by properties of their lines and angles.
4.G.1. Draw points, lines, line segments, rays, angles (right, acute, obtuse), and perpendicular, parallel, and intersecting line segments. Identify these in two-dimensional (plane) figures.
4.G.2. Classify two-dimensional (plane) 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.G.3. Recognize a line of symmetry for a two-dimensional (plane) 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.
Standards for Mathematical Practice
Instruction around the Standards of Mathematical Practices is delivered across all grades K-12. These eight standards define experiences that build understanding of mathematics and ways of thinking through which students develop, apply, and assess their knowledge.
1. Make sense of problems and persevere in solving them.
explain correspondences between equations, verbal descriptions, tables, and graphs
draw diagrams of important features and relationships, graph data, and search for regularity or trends
use concrete objects or pictures to help conceptualize and solve a problem
understand the approaches of others to solving complex problems
identify correspondences between different approaches
check if the solution makes sense
2. Reason abstractly and quantitatively.
represent a situation symbolically
create a coherent representation of the problem
have the ability to show how problem has a realistic meaning
reflect during the manipulation process in order to probe into the meanings for the symbols involved
use units consistently
3. Construct viable arguments and critique the reasoning of others.
construct arguments using concrete referents such as objects, drawings, diagrams, and actions
justify conclusions, communicate conclusions, listen and respond to arguments, decide whether the argument makes sense, and ask questions to clarify the argument
reason inductively about data, making plausible arguments that take into account the context from which the data arose
4. Model with Mathematics.
apply mathematics to solve problems arising in everyday life
identify important quantities in a practical situation and model the situation using such tools as manipulatives, diagrams, two-way tables, graphs or pictures
interpret mathematical results in the context of the situation and reflect on whether the results make sense
apply mathematical knowledge, make assumptions and approximations to simplify a complicated situation
5. Use appropriate tools strategically.
select the available tools (such as pencil and paper, manipulatives, rulers, calculators, a spreadsheet, and available technology) when solving a mathematical problem
be familiar with tools appropriate for their grade level to make sound decisions about when each of these tools might be helpful
identify relevant external mathematical resources and use them to pose or solve problems
use technological tools to explore and deepen their understanding of concepts
detect possible errors by strategically using estimation and other mathematical knowledge
know that technology can enable them to visualize the results of varying assumptions, explore consequences, and compare predictions with data
6. Attend to precision.
give carefully formulated explanations to each other
use clear definitions and reasoning in discussion with others
state the meaning of symbols, including using the equal sign consistently and appropriately
specify units of measure, and label axes to clarify the correspondence with quantities in a problem
calculate accurately and efficiently
express numerical answers with a degree of precision appropriate for the problem context
7. Look for and make use of structure.
discern a pattern or structure
understand complex structures as single objects or as being composed of several objects
check if the answer is reasonable
8. Look for and express regularity in repeated reasoning.
identify if calculations or processes are repeated
use alternative and traditional methods to solve problems
evaluate the reasonableness of their intermediate results, while attending to the details