M05.A-T.1.1.2: Explain patterns in the number of zeros of the product when multiplying a number by powers of 10 and explain patterns in the placement of the decimal point when a decimal is multiplied or divided by a power of 10. Use whole-number exponents to denote powers of 10.

Example 1: 4 × 10 (to the 2nd power)  = 400

Example 2: 0.05 ÷ 10 (to the 3rd power) = 0.00005 

 

M05.A-T.1.1.3: Read and write decimals to thousandths using base-ten numerals, word form, and expanded form.

Example: 347.392 

300 + 40 + 7 + 0.3 + 0.09 + 0.002

3 × 100 + 4 × 10 + 7 × 1 + 3 × (0.1) + 9 × (0.01) + 2 × (0.001)

 

M05.A-T.1.1.4: Compare two decimals to thousandths based on meanings of the digits in each place using >, =, and < symbols.

 

M05.A-T.1.1.5: Round decimals to any place (limit rounding to ones, tenths, hundredths, or thousandths place). 

 

M05.A-T.2.1.1: Multiply multi-digit whole numbers (not to exceed three-digit by three-digit).

 

M05.A-T.2.1.2: Find whole-number quotients of whole numbers with up to four-digit dividends and two-digit divisors.

 

M05.A-T.2.1.3: Add, subtract, multiply, and divide decimals to hundredths (no divisors with decimals).

 

M05.A-F.1.1.1: Add and subtract fractions (including mixed numbers) with unlike denominators. (May include multiple methods and representations.)

Example: 2/3 + 5/4 = 8/12 + 15/12 = 23/12

 

M05.A-F.2.1.1: Solve word problems involving division of whole numbers leading to answers in the form of fractions (including mixed numbers).

 

M05.A-F.2.1.2: Multiply a fraction (including mixed numbers) by a fraction.

 

M05.A-F.2.1.3: Demonstrate an understanding of multiplication as scaling (resizing).

Example 1: Comparing the size of a product to the size of one factor on the basis of the size of the other factor without performing the indicated multiplication.

Example 2: Explaining why multiplying a given number by a fraction greater than 1 results in a product greater than the given number (recognizing multiplication by whole numbers greater than 1 as a familiar case); explaining why multiplying a given number by a fraction less than 1 results in a product smaller than the given number.

 

M05.A-F.2.1.4: Divide unit fractions by whole numbers and whole numbers by unit fractions.

 

M05.B-O.1.1.1: Use multiple grouping symbols (parentheses, brackets, or braces) in numerical expressions and evaluate expressions containing these symbols.

 

M05.B-O.1.1.2: Write simple expressions that model calculations with numbers and interpret numerical expressions without evaluating them.

Example 1: Express the calculation “add 8 and 7, then multiply by 2” as 2 × (8 + 7).

Example 2: Recognize that 3 × (18,932 + 921) is three times as large as 18,932 + 921 without having to calculate the indicated sum or product.

 

M05.B-O.2.1.1: Generate two numerical patterns using two given rules.

Example: Given the rule “add 3” and the starting number 0 and given the rule “add 6” and the starting number 0, generate terms in the resulting sequences.

 

M05.B-O.2.1.2: Identify apparent relationships between corresponding terms of two patterns with the same starting numbers that follow different rules.

Example: Given two patterns in which the first pattern follows the rule “add 8” and the second pattern follows the rule “add 2,” observe that the terms in the first pattern are 4 times the size of the terms in the second pattern.

 

M05.C-G.1.1.1: Identify parts of the coordinate plane (x-axis, y-axis, and the origin) and the ordered pair (x-coordinate and y-coordinate). Limit the coordinate plane to quadrant I.

 

M05.C-G.1.1.2: Represent real-world and mathematical problems by plotting points in quadrant I of the coordinate plane and interpret coordinate values of points in the context of the situation.

 

M05.C-G.2.1.1: Classify two-dimensional figures in a hierarchy based on properties.

Example 1: All polygons have at least three sides, and pentagons are polygons, so all pentagons have at least three sides.

Example 2: A rectangle is a parallelogram, which is a quadrilateral, which is a polygon; so, a rectangle can be classified as a parallelogram, as a quadrilateral, and as a polygon.

 

M05.D-M.1.1.1: Convert between different-sized measurement units within a given measurement system. A table of equivalencies will be provided.

Example: Convert 5 cm to meters.

 

M05.D-M.2.1.1: Solve problems involving computation of fractions by using information presented in line plots.

 

M05.D-M.2.1.2: Display and interpret data shown in tallies, tables, charts, pictographs, bar graphs, and line graphs, and use a title, appropriate scale, and labels. A grid will be provided to display data on bar graphs or line graphs.

 

M05.D-M.3.1.1: Apply the formulas V = l × w × h and V = B × h for rectangular prisms to find volumes of right rectangular prisms with whole-number edge lengths in the context of solving real-world and mathematical problems. Formulas will be provided.

 

M05.D-M.3.1.2: Find volumes of solid figures composed of two non-overlapping right rectangular prisms.