Grade 4 Math: Learn It by Talking It Through

A taste of a lesson on Equivalent fractions with visual models

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The 26 topics in Grade 4 Math

Each topic builds on the ones before it. The tutor checks what you already know and starts there.

1. Multiplicative comparison and multiplication/division word problems

   Interpret a multiplication equation like 35 = 5 x 7 as a comparison (35 is 5 times as many as 7). Represent verbal comparison statements as equations with a letter for the unknown, and solve multiplicative comparison problems using drawings and equations. Distinguish multiplicative comparison ('3 times as many') from additive comparison ('3 more than').

2. Factor pairs, multiples, and divisibility

   Find all factor pairs of whole numbers from 1 to 100 by systematic search, and recognize that a number is a multiple of each of its factors. Determine whether a number from 1 to 100 is a multiple of a given one-digit number, and determine whether a whole number from 1 to 100 is prime or composite. Use the idea that factors come in pairs to check completeness.

   Builds on Multiplicative comparison and multiplication/division word problems

3. Number and shape patterns

   Generate a number or shape pattern from a given rule (e.g., add 3 starting at 1), and identify features of the pattern not stated in the rule, such as whether terms alternate odd and even or whether all terms are multiples of a number. Explain why such features hold.

   Builds on Factor pairs, multiples, and divisibility

4. Place value, reading, writing, and comparing multi-digit numbers

   Recognize that a digit in one place is ten times the value of the same digit one place to its right (e.g., 700 is 10 times 70, so 700 divided by 70 is 10). Read and write whole numbers up to one million in base-ten numerals, number names, and expanded form. Compare multi-digit numbers by the meaning of digits in each place and record results with >, =, and <.

5. Rounding multi-digit whole numbers

   Round multi-digit whole numbers to any place (thousands, ten-thousands, hundred-thousands, and so on) using place value understanding and the number line, deciding whether to round up or down by looking at the digit to the right of the rounding place. Apply rounding to estimate answers in context.

   Builds on Place value, reading, writing, and comparing multi-digit numbers

6. Multi-digit addition and subtraction with the standard algorithm

   Add and subtract multi-digit whole numbers fluently using the standard algorithm, including regrouping (carrying and borrowing) across multiple places and across zeros. Check answers by estimation or by the inverse operation.

   Builds on Place value, reading, writing, and comparing multi-digit numbers

7. Multiplying multi-digit whole numbers

   Multiply a whole number of up to four digits by a one-digit number, and multiply two two-digit numbers, using place value strategies (partial products, area models) and the distributive property. Illustrate each calculation with equations and area diagrams, and explain why partial products add to the total.

   Builds on Multiplicative comparison and multiplication/division word problems, Place value, reading, writing, and comparing multi-digit numbers

8. Division with remainders using place value strategies

   Find whole-number quotients and remainders with up to four-digit dividends and one-digit divisors, using strategies such as breaking the dividend into place-value parts, using multiples of the divisor, and the relationship between multiplication and division. Check each answer with the equation dividend = divisor x quotient + remainder, and explain what a remainder means in context.

   Builds on Factor pairs, multiples, and divisibility, Place value, reading, writing, and comparing multi-digit numbers, Multiplying multi-digit whole numbers

9. Multistep word problems with the four operations

   Solve multistep word problems with whole numbers and whole-number answers using all four operations. Include problems where remainders must be interpreted (e.g., 23 students in vans seating 5 needs 5 vans). Represent each problem with an equation using a letter for the unknown, and check that the answer makes sense in context.

   Builds on Factor pairs, multiples, and divisibility, Multi-digit addition and subtraction with the standard algorithm, Multiplying multi-digit whole numbers, Division with remainders using place value strategies

10. Equivalent fractions with visual models

    Explain why a/b equals (n x a)/(n x b) using visual fraction models, noting that the number and size of the parts change while the total amount stays the same. Generate equivalent fractions by multiplying numerator and denominator by the same number, and recognize simplest form.

    Builds on Multiplicative comparison and multiplication/division word problems

11. Comparing fractions with different numerators and denominators

    Compare two fractions with different numerators and denominators by creating common denominators or numerators, or by comparing to the benchmark 1/2. Record results with >, =, <, and justify each comparison. Recognize that comparisons are valid only when both fractions refer to the same whole.

    Builds on Equivalent fractions with visual models

12. Fractions greater than one as sums of unit fractions

    Understand a fraction a/b with a greater than 1 as a sum of 1/b fractions (for example, 5/4 = 1/4 + 1/4 + 1/4 + 1/4 + 1/4). Use visual models of fraction strips and number lines to show this, and connect mixed numbers to these sums.

    Builds on Equivalent fractions with visual models

13. Adding and subtracting fractions with like denominators

    Understand addition and subtraction of fractions as joining and separating parts of the same whole. Decompose a fraction into a sum of fractions with the same denominator in more than one way, recording each decomposition as an equation and justifying it with a model. Add and subtract fractions with like denominators, including mixed numbers (by converting to improper fractions or by adding whole and fractional parts), and solve word problems using models and equations.

    Builds on Comparing fractions with different numerators and denominators, Fractions greater than one as sums of unit fractions

14. Multiplying a fraction by a whole number

    Understand a fraction a/b as a multiple of 1/b, so a/b = a x (1/b). Use this to multiply a fraction by a whole number, for example 3 x (2/5) = 6 x (1/5) = 6/5. Solve word problems such as sharing 3/8 pound of roast beef per person among several people, using visual models and equations.

    Builds on Adding and subtracting fractions with like denominators

15. Decimal notation for fractions with denominators 10 and 100

    Rewrite fractions with denominators 10 or 100 in decimal form (for example, 62/100 = 0.62) and back. Locate decimals on number line diagrams, and describe lengths or amounts in decimal form (0.62 meter). Express a fraction with denominator 10 as an equivalent fraction with denominator 100, and add two fractions with denominators 10 and 100 (for example, 3/10 + 27/100 = 57/100). Use place value of digits in tenths and hundredths positions.

    Builds on Place value, reading, writing, and comparing multi-digit numbers, Equivalent fractions with visual models, Adding and subtracting fractions with like denominators

16. Comparing decimals to hundredths

    Compare two decimals to hundredths by reasoning about their size using tenths and hundredths place values and models such as grids or number lines. Record comparisons with >, =, or < and justify each conclusion. Recognize that the comparison is valid only when both decimals refer to the same whole.

    Builds on Comparing fractions with different numerators and denominators, Decimal notation for fractions with denominators 10 and 100

17. Measurement units and conversions within a system

    Know the relative sizes of units within one system: km, m, cm; kg, g; lb, oz; l, ml; hr, min, sec; and the US customary length units (ft, in, yd, mi), weight, capacity, and time units. Express a measurement in a larger unit in terms of a smaller unit (for example, 3 m = 300 cm), record measurement equivalents in a two-column table, and recognize the pattern in the table.

    Builds on Multiplying multi-digit whole numbers

18. Measurement word problems with the four operations

    Use the four operations to solve word problems involving distances, intervals of time, liquid volumes, masses of objects, and money, including problems with simple fractions or decimals (for example, adding 2 1/2 hours and 45 minutes) and problems requiring conversion between units within a system.

    Builds on Multi-digit addition and subtraction with the standard algorithm, Adding and subtracting fractions with like denominators, Decimal notation for fractions with denominators 10 and 100, Measurement units and conversions within a system

19. Line plots with fractional measurements

    Make a line plot to display a data set of measurements in fractions of a unit (1/2, 1/4, 1/8). Read the plot and solve addition and subtraction problems with fractions using information from the line plot, such as finding the total length of all objects or the difference between the longest and shortest.

    Builds on Adding and subtracting fractions with like denominators

20. Area and perimeter of rectangles

    Apply the area formula (length x width) and perimeter formula for rectangles in real-world and mathematical problems. View area as multiplication by tiling with unit squares, and solve problems such as finding the unknown width of a rectangular room given its area and length. Explain why area formulas are multiplication of side lengths.

    Builds on Multiplying multi-digit whole numbers

21. Points, lines, rays, angles, and perpendicular and parallel lines

    Draw and name points, lines, line segments, and rays, and identify these in two-dimensional figures. Define right, acute, and obtuse angles by comparison with a right angle (square corner). Identify perpendicular lines (meeting at right angles) and parallel lines (never meeting) in figures.

22. Classifying two-dimensional figures by parallel, perpendicular, and angle features

    Classify two-dimensional figures based on the presence or absence of parallel or perpendicular lines, or angles of a specified size (for example, a quadrilateral with 4 right angles, a trapezoid with one pair of parallel sides). Recognize right triangles as a category and identify them among other triangles.

    Builds on Points, lines, rays, angles, and perpendicular and parallel lines

23. Lines of symmetry

    Recognize a line of symmetry for a two-dimensional figure as a line across the figure such that folding along it produces matching parts. Identify line-symmetric figures, determine how many lines of symmetry a figure has, and draw lines of symmetry for given figures.

    Builds on Points, lines, rays, angles, and perpendicular and parallel lines

24. Angle measure and the degree unit

    Recognize angles as shapes formed where two rays share a common endpoint. Understand that an angle is measured by reference to a circle centered at the common endpoint, with the arc between the rays divided into equal parts; a one-degree angle is 1/360 of a full circle, and an angle that turns through n one-degree angles has measure n degrees.

    Builds on Points, lines, rays, angles, and perpendicular and parallel lines

25. Measuring and sketching angles with a protractor

    Measure angles in whole-number degrees using a protractor, aligning the center and a ray with the zero line, and reading the correct scale. Sketch angles of a specified measure (for example, a 75-degree angle) and estimate whether an angle is acute, right, or obtuse before measuring.

    Builds on Angle measure and the degree unit

26. Angle addition and unknown angles

    Recognize that angle measure is additive: when an angle is split into non-overlapping parts, the measure of the whole equals the sum of the parts. Solve addition and subtraction equations to find unknown angles on a diagram, such as a missing angle on a straight line (180 degrees) or around a point (360 degrees).

    Builds on Multistep word problems with the four operations, Angle measure and the degree unit, Measuring and sketching angles with a protractor

Practice questions in Grade 4 Math

A few of the kinds of questions you will work through, with answers.