4th Grade Math (Massachusetts Curriculum Frameworks)

Operations and Algebraic Thinking (4.OA)

• 4.OA.A.1 Interpret a multiplication equation as comparing two amounts (e.g. 35 is five times as many as 7) and write such comparisons as equations.
• 4.OA.A.2 Solve multiplicative comparison word problems with drawings and equations; tell them apart from additive comparisons.
• 4.OA.A.3 Solve multi-step whole-number word problems with all four operations, interpret remainders, and check with estimation.
  • a. Know times-table facts and matching division facts up to 12 × 12.
• 4.OA.B.4 Find all factor pairs of numbers 1–100, recognize multiples, and say whether a number is prime or composite.
• 4.OA.C.5 Make a number or shape pattern from a rule and explain features of the pattern not stated in the rule.

Number and Operations in Base Ten (4.NBT)

• 4.NBT.A.1 Know a digit in any place is worth ten times what it would be one place to the right (whole numbers to 1,000,000).
• 4.NBT.A.2 Read, write and compare whole numbers to 1,000,000 in numerals, words and expanded form using >, = and <.
• 4.NBT.A.3 Round whole numbers up to 1,000,000 to any place.
• 4.NBT.B.4 Add and subtract multi-digit whole numbers accurately and efficiently with the standard algorithm.
• 4.NBT.B.5 Multiply up to four digits by one digit and two two-digit numbers using place value; explain with equations, arrays or area models.
• 4.NBT.B.6 Divide up to four-digit numbers by one-digit divisors, with remainders, using place value; explain with equations, arrays or area models.

Number and Operations—Fractions (4.NF)

• 4.NF.A.1 Explain with models why a/b = (n×a)/(n×b), including fractions greater than 1 (denominators 2, 3, 4, 5, 6, 8, 10, 12, 100).
• 4.NF.A.2 Compare two fractions with different numerators and denominators using common denominators or benchmarks like 1/2; justify.
• 4.NF.B.3 See a fraction a/b with a > 1 as a total of several 1/b pieces.
  • a. See adding and subtracting fractions as joining and separating parts of the same whole.
  • b. Split a fraction into a sum of same-denominator fractions in more than one way and justify with models.
  • c. Add and subtract mixed numbers that share a denominator.
  • d. Solve word problems adding and subtracting fractions with like denominators.
• 4.NF.B.4 Multiply a fraction by a whole number.
  • a. See a/b as a copies of 1/b.
  • b. See n × (a/b) as (n × a) copies of 1/b and use this to multiply.
  • c. Solve word problems multiplying a fraction by a whole number.
• 4.NF.C.5 Write a fraction in tenths as an equal fraction in hundredths and add fractions with denominators 10 and 100.
• 4.NF.C.6 Write fractions with denominators 10 or 100 as decimals and place them on a number line.
• 4.NF.C.7 Compare decimals to the hundredths place by thinking about their size, for decimals of the same whole; justify.

Measurement and Data (4.MD)

• 4.MD.A.1 Know relative sizes of units within one system and convert larger units to smaller ones in a table.
• 4.MD.A.2 Solve word problems on distance, time, liquid volume, mass and money, including fractions and decimals.
• 4.MD.A.3 Use rectangle area (square units) and perimeter (linear units) formulas in real and math problems.
• 4.MD.B.4 Make a line plot (dot plot) of measurements in halves, quarters and eighths and solve add/subtract problems with it.
• 4.MD.C.5 Understand angles as shapes made by two rays and how they are measured.
  • a. An angle is measured by the fraction of a circle its rays cut off; one degree is 1/360 of a turn.
  • b. An angle made of n one-degree angles measures n degrees.
• 4.MD.C.6 Measure and sketch angles in whole degrees with a protractor.
• 4.MD.C.7 Know angle measures add and find unknown angles with addition and subtraction equations.

Geometry (4.G)

• 4.G.A.1 Draw and identify points, lines, segments, rays, right, acute and obtuse angles, and perpendicular and parallel lines.
• 4.G.A.2 Classify 2D shapes by parallel or perpendicular lines and by angle types; recognize right triangles.
• 4.G.A.3 Recognize line-symmetric shapes and draw their lines of symmetry.