Domain: Operations and Algebraic Thinking

Strand: Use the four operations with whole numbers to solve problems.

Standard:

• • • (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 (e.g., by using drawings and equations with a symbol for the unknown number to represent the problem or missing numbers in an array).

    • (4.OA.2) Multiply or divide to solve word problems involving multiplicative comparison. 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.

Examples & Resources:

Literature Connections:

• The I Hate Mathematics! Book by Marilyn Burns

• The Everything Kids' Joke Book: Side-Splitting, Rib-Tickling Fun by Michael Dahl

Strand: Gain familiarity with factors and multiples.

Standard:

• • • (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.

Examples & Resources:

Literature Connections:

• • • The History of Counting by Denise Schmandt-Besserat

    • 12 Ways to Get to 11 by Eve Merriam

Strand: Generate and analyze patterns.

Standard:

• • • (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.

    • (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.

Examples & Resources:

• (4.OA.5) 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.

Domain: Number and Operations - Fractions

(Limited in this grade to fractions with denominators 2, 3, 4, 5, 6, 8, 10, 12, and 100.)

Strand: Extend understanding of fraction equivalence and ordering.

Standard:

• • • (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).

Strand: Build fractions from unit fractions by applying and extending previous understandings of operations on whole numbers.

Standard:

• (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).

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.

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.

• 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.

Examples & Resources:

• • • (4.NF.3b) 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.

    • (4.NF.4a) 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).

    • (4.NF.4b) 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.).

    • (4.NF.4c) 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?

Literature Connections:

• Fannie in the Kitchen: The Whole Story from Soup to Nuts of How Fannie Farmer Invented Recipes with Precise Measurements by Deborah Hopkinson

Strand: Understand decimal notation for fractions, and compare decimal fractions.

Standard:

• • • (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.

    • (4.NF.6) Use decimal notation for fractions with denominators 10 or 100.

    • (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).

Examples & Resources:

• (4.NF.5) Express 3/10 as 30/100, and add 3/10 + 4/100 = 34/100.

• (4.NF.6) Rewrite 0.62 as 62/100; describe a length as 0.62 meters; locate 0.62 on a number line diagram.

Domain: Geometry

Strand: Draw and identify lines and angles, and classify shapes by properties of their lines and angles.

Standard:

• (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.

Examples & Resources:

Literature Connections:

• • • Reflections by Ann Jonas

    • Sea Squares by Joy N. Hulme

    • Shadows and Reflections by Tana Hoban

    • Mummy Math: An Adventure in Geometry by Cindy Neuschwander

    • My Full Moon Is Square by Elinor J. Pinczes

Strand: Draw and identify lines and angles, and classify shapes by properties of their lines and angles.

Standard:

• (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.