---
title: "Math 4"
url: "https://books.hrgrvs.net/2/standards/52/math-4"
---

# 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