3-5

3-5 M03.A-T.1.1.1 Round two- and three-digit whole numbers to the nearest ten or hundred, respectively.
 * __Grade 3__**
 * Content Currently Taught || Currently Missing || New Content ||
 * **Numbers & Operations in Base Ten **

M03.A-T.1.1.2 Add two- and three-digit whole numbers (limit sums from 100 through 1,000) and/or subtract two- and three-digit numbers from three-digit whole numbers.

M03.A-T.1.1.3 Multiply one-digit whole numbers by two-digit multiples of 10 (from 10 through 90).

M03.A-T.1.1.4 Order a set of whole numbers from least to greatest or greatest to least (up through 9,999, and limit sets to no more than four numbers).

M03.A-F.1.1.1 Demonstrate that when a whole or set is <span style="font-family: 'Arial','sans-serif'; font-size: 13.3333px;">partitioned into y equal parts, the fraction 1/y <span style="font-family: 'Arial','sans-serif'; font-size: 13.3333px;">represents 1 part of the whole and/or the fraction x/y represents x <span style="font-family: 'Arial','sans-serif'; font-size: 13.3333px;">equal parts of the whole (limit <span style="font-family: 'Arial','sans-serif'; font-size: 13.3333px;">denominators to 2, 3, 4, <span style="font-family: 'Arial','sans-serif'; font-size: 13.3333px;">6, and 8; limit numerators <span style="font-family: 'Arial','sans-serif'; font-size: 13.3333px;">to whole numbers less than the denominator; and no simplification necessary).

<span style="font-family: 'Arial','sans-serif'; font-size: 13.3333px;">M03.A-F.1.1.2 <span style="font-family: 'Arial','sans-serif'; font-size: 13.3333px;">Represent fractions on a number line (limit <span style="font-family: 'Arial','sans-serif'; font-size: 13.3333px;">denominators to 2 and 4; limit numerators <span style="font-family: 'Arial','sans-serif'; font-size: 13.3333px;">to whole numbers less than the denominator; and no simplification necessary).

<span style="font-family: 'Arial','sans-serif'; font-size: 13.3333px;">M03.A-F.1.1.3 <span style="font-family: 'Arial','sans-serif'; font-size: 13.3333px;">Recognize and generate simple equivalent <span style="font-family: 'Arial','sans-serif'; font-size: 13.3333px;">fractions (limit the denominators to 1, 2, 3, 4, 6, <span style="font-family: 'Arial','sans-serif'; font-size: 13.3333px;">and 8 and limit numerators to whole numbers less <span style="font-family: 'Arial','sans-serif'; font-size: 13.3333px;">than the denominator). <span style="font-family: 'Arial','sans-serif'; font-size: 13.3333px;">Example 1: <span style="font-family: 'Arial','sans-serif'; font-size: 13.3333px;">1/2 = 2/4 <span style="font-family: 'Arial','sans-serif'; font-size: 13.3333px;">Example 2: <span style="font-family: 'Arial','sans-serif'; font-size: 13.3333px;">4/6 = 2/3

<span style="font-family: 'Arial','sans-serif'; font-size: 13.3333px;">M03.A-F.1.1.4 <span style="font-family: 'Arial','sans-serif'; font-size: 13.3333px;">Express whole numbers as fractions, and/or <span style="font-family: 'Arial','sans-serif'; font-size: 13.3333px;">generate fractions that are equivalent to whole <span style="font-family: 'Arial','sans-serif'; font-size: 13.3333px;">numbers (limit denominators to 1, 2, 3, 4, 6, and <span style="font-family: 'Arial','sans-serif'; font-size: 13.3333px;">8). <span style="font-family: 'Arial','sans-serif'; font-size: 13.3333px;">Example 1: <span style="font-family: 'Arial','sans-serif'; font-size: 13.3333px;">Express 3 in the form 3 = 3/1. <span style="font-family: 'Arial','sans-serif'; font-size: 13.3333px;">Example 2: <span style="font-family: 'Arial','sans-serif'; font-size: 13.3333px;">Recognize that 6/1 = 6.

<span style="font-family: 'Arial','sans-serif'; font-size: 13.3333px;">M03.A-F.1.1.5 <span style="font-family: 'Arial','sans-serif'; font-size: 13.3333px;">Compare two fractions with the same denominator (limit denominators to 1, 2, 3, 4, 6, and 8), using the symbols >, =, or <, and/or justify the conclusions. ||  || Fractions on a number line with a denominator of 3, 6, and 8 || <span style="font-family: 'Arial','sans-serif'; font-size: 13.3333px;">M03.B-O.1.1.1 <span style="font-family: 'Arial','sans-serif'; font-size: 13.3333px;">Interpret and/or describe products of whole <span style="font-family: 'Arial','sans-serif'; font-size: 13.3333px;">numbers (up to and including 10 × 10). <span style="font-family: 'Arial','sans-serif'; font-size: 13.3333px;">Example 1: Interpret 35 as the total number of <span style="font-family: 'Arial','sans-serif'; font-size: 13.3333px;">objects in 5 groups, each containing 7 objects. <span style="font-family: 'Arial','sans-serif'; font-size: 13.3333px;">Example 2: Describe a context in which a total <span style="font-family: 'Arial','sans-serif'; font-size: 13.3333px;">number of objects can be expressed as 5 × 7
 * **Operations & Algebraic Thinking**

<span style="font-family: 'Arial','sans-serif'; font-size: 13.3333px;">M03.B-O.1.1.2 <span style="font-family: 'Arial','sans-serif'; font-size: 13.3333px;">Interpret and/or describe whole-number quotients of whole numbers (limit dividends through 50 and limit divisors and quotients through 10). <span style="font-family: 'Arial','sans-serif'; font-size: 13.3333px;">Example 1: <span style="font-family: 'Arial','sans-serif'; font-size: 13.3333px;">Interpret 48 ÷ 8 as the number of <span style="font-family: 'Arial','sans-serif'; font-size: 13.3333px;">objects in each share when 48 objects are <span style="font-family: 'Arial','sans-serif'; font-size: 13.3333px;">partitioned equally into 8 shares, or as a number of <span style="font-family: 'Arial','sans-serif'; font-size: 13.3333px;">shares when 48 objects are partitioned into equal <span style="font-family: 'Arial','sans-serif'; font-size: 13.3333px;">shares of 8 objects each. <span style="font-family: 'Arial','sans-serif'; font-size: 13.3333px;">Example 2: <span style="font-family: 'Arial','sans-serif'; font-size: 13.3333px;">Describe a context in which a number <span style="font-family: 'Arial','sans-serif'; font-size: 13.3333px;">of shares or a number of groups can be expressed as 48 ÷ 8.

<span style="font-family: 'Arial','sans-serif'; font-size: 13.3333px;">M03.B-O.1.2.1 <span style="font-family: 'Arial','sans-serif'; font-size: 13.3333px;">Use multiplication (up to and including 10 × 10) <span style="font-family: 'Arial','sans-serif'; font-size: 13.3333px;">and/or division (limit dividends through 50 and limit divisors and quotients through 10) to solve word problems in situations involving equal groups, arrays, and/or measurement quantities.

<span style="font-family: 'Arial','sans-serif'; font-size: 13.3333px;">M03.B-O.1.2.2 <span style="font-family: 'Arial','sans-serif'; font-size: 13.3333px;">Determine the unknown whole number in a <span style="font-family: 'Arial','sans-serif'; font-size: 13.3333px;">multiplication (up to and including 10 × 10) or <span style="font-family: 'Arial','sans-serif'; font-size: 13.3333px;">division (limit dividends through 50 and limit <span style="font-family: 'Arial','sans-serif'; font-size: 13.3333px;">divisors and quotients through 10) equation <span style="font-family: 'Arial','sans-serif'; font-size: 13.3333px;">relating three whole numbers. <span style="font-family: 'Arial','sans-serif'; font-size: 13.3333px;">Example: <span style="font-family: 'Arial','sans-serif'; font-size: 13.3333px;">Determine the unknown number that <span style="font-family: 'Arial','sans-serif'; font-size: 13.3333px;">makes an equation true.

<span style="font-family: 'Arial','sans-serif'; font-size: 13.3333px;">M03.B-O.2.1.1 <span style="font-family: 'Arial','sans-serif'; font-size: 13.3333px;">Apply the commutative property of multiplication <span style="font-family: 'Arial','sans-serif'; font-size: 13.3333px;">(not identification or definition of the property).

<span style="font-family: 'Arial','sans-serif'; font-size: 13.3333px;">M03.B-O.2.1.2 <span style="font-family: 'Arial','sans-serif'; font-size: 13.3333px;">Apply the associative property of multiplication (not identification or definition of the property).

<span style="font-family: 'Arial','sans-serif'; font-size: 13.3333px;">M03.B-O.2.2.1 <span style="font-family: 'Arial','sans-serif'; font-size: 13.3333px;">Interpret and/or model division as a multiplication <span style="font-family: 'Arial','sans-serif'; font-size: 13.3333px;">equation with an unknown factor. <span style="font-family: 'Arial','sans-serif'; font-size: 13.3333px;">Example: <span style="font-family: 'Arial','sans-serif'; font-size: 13.3333px;">Find 32 ÷ 8 by solving 8 × ? = 32.

<span style="font-family: 'Arial','sans-serif'; font-size: 13.3333px;">M03.B-O.3.1.1 <span style="font-family: 'Arial','sans-serif'; font-size: 13.3333px;">Solve two-step word problems using the four <span style="font-family: 'Arial','sans-serif'; font-size: 13.3333px;">operations (expressions are not explicitly stated). Limit to problems with whole numbers and having whole-number answers.

<span style="font-family: 'Arial','sans-serif'; font-size: 13.3333px;">M03.B-O.3.1.2 <span style="font-family: 'Arial','sans-serif'; font-size: 13.3333px;">Represent two-step word problems using <span style="font-family: 'Arial','sans-serif'; font-size: 13.3333px;">equations with a symbol standing for the unknown quantity. Limit to problems with whole numbers and having whole-number answers.

<span style="font-family: 'Arial','sans-serif'; font-size: 13.3333px;">M03.B-O.3.1.3 <span style="font-family: 'Arial','sans-serif'; font-size: 13.3333px;">Assess the reasonableness of answers. Limit <span style="font-family: 'Arial','sans-serif'; font-size: 13.3333px;">problems posed with whole numbers and having whole-number answers.

<span style="font-family: 'Arial','sans-serif'; font-size: 13.3333px;">M03.B-O.3.1.4 <span style="font-family: 'Arial','sans-serif'; font-size: 13.3333px;">Solve two-step equations using order of operations <span style="font-family: 'Arial','sans-serif'; font-size: 13.3333px;">(equation is explicitly stated with no grouping <span style="font-family: 'Arial','sans-serif'; font-size: 13.3333px;">symbols).

<span style="font-family: 'Arial','sans-serif'; font-size: 13.3333px;">M03.B-O.3.1.7 <span style="font-family: 'Arial','sans-serif'; font-size: 13.3333px;">Identify the missing symbol (+ <span style="font-family: 'Arial','sans-serif'; font-size: 13.3333px;">, –, ×, ÷, <, >, and =) <span style="font-family: 'Arial','sans-serif'; font-size: 13.3333px;">that makes a number sentence true ||  || Students don’t use a symbol for an unknown value.

<span style="font-family: 'Arial','sans-serif'; font-size: 13.3333px;">M03.B-O.3.1.5 <span style="font-family: 'Arial','sans-serif'; font-size: 13.3333px;">Identify arithmetic patterns (including patterns in the addition table or multiplication table) and/or <span style="font-family: 'Arial','sans-serif'; font-size: 13.3333px;">explain them using properties of operations. <span style="font-family: 'Arial','sans-serif'; font-size: 13.3333px;">Example 1: <span style="font-family: 'Arial','sans-serif'; font-size: 13.3333px;">Observe that 4 times a number is <span style="font-family: 'Arial','sans-serif'; font-size: 13.3333px;">always even. <span style="font-family: 'Arial','sans-serif'; font-size: 13.3333px;">Example 2: <span style="font-family: 'Arial','sans-serif'; font-size: 13.3333px;">Explain why 6 times a number can be <span style="font-family: 'Arial','sans-serif'; font-size: 13.3333px;">decomposed into three equal addends.

<span style="font-family: 'Arial','sans-serif'; font-size: 13.3333px;">M03.B-O.3.1.6 <span style="font-family: 'Arial','sans-serif'; font-size: 13.3333px;">Create or match a story to a given combination of <span style="font-family: 'Arial','sans-serif'; font-size: 13.3333px;">symbols (+, –, ×, ÷, <, <span style="font-family: 'Arial','sans-serif'; font-size: 13.3333px;">>, and =) and numbers. <span style="font-family: 'Arial','sans-serif'; font-size: 13.3333px;">. || <span style="font-family: 'Arial','sans-serif'; font-size: 13.3333px;">M03.C-G.1.1.1 <span style="font-family: 'Arial','sans-serif'; font-size: 13.3333px;">Explain that shapes in different categories may <span style="font-family: 'Arial','sans-serif'; font-size: 13.3333px;">share attributes and that the shared attributes can <span style="font-family: 'Arial','sans-serif'; font-size: 13.3333px;">define a larger category. <span style="font-family: 'Arial','sans-serif'; font-size: 13.3333px;">Example 1: <span style="font-family: 'Arial','sans-serif'; font-size: 13.3333px;">A rhombus and a rectangle are both <span style="font-family: 'Arial','sans-serif'; font-size: 13.3333px;">quadrilaterals since they both have exactly four <span style="font-family: 'Arial','sans-serif'; font-size: 13.3333px;">sides. <span style="font-family: 'Arial','sans-serif'; font-size: 13.3333px;">Example 2: <span style="font-family: 'Arial','sans-serif'; font-size: 13.3333px;">A triangle and a pentagon are both <span style="font-family: 'Arial','sans-serif'; font-size: 13.3333px;">polygons since they are both multi-sided plane <span style="font-family: 'Arial','sans-serif'; font-size: 13.3333px;">figures.
 * **<span style="font-family: 'Arial','sans-serif'; font-size: 13.3333px;">Geometry **

<span style="font-family: 'Arial','sans-serif'; font-size: 13.3333px;">M03.C-G.1.1.2 <span style="font-family: 'Arial','sans-serif'; font-size: 13.3333px;">Recognize rhombi, rectangles, and squares as <span style="font-family: 'Arial','sans-serif'; font-size: 13.3333px;">examples of quadrilaterals and/or draw examples <span style="font-family: 'Arial','sans-serif'; font-size: 13.3333px;">of quadrilaterals that do not belong to any of these <span style="font-family: 'Arial','sans-serif'; font-size: 13.3333px;">subcategories.

<span style="font-family: 'Arial','sans-serif'; font-size: 13.3333px;">M03.C-G.1.1.3 <span style="font-family: 'Arial','sans-serif'; font-size: 13.3333px;">Partition shapes into parts with equal areas. <span style="font-family: 'Arial','sans-serif'; font-size: 13.3333px;">Express the area of each part as a unit fraction of <span style="font-family: 'Arial','sans-serif'; font-size: 13.3333px;">the whole. <span style="font-family: 'Arial','sans-serif'; font-size: 13.3333px;">Example 1: <span style="font-family: 'Arial','sans-serif'; font-size: 13.3333px;">Partition a shape into 4 parts with <span style="font-family: 'Arial','sans-serif'; font-size: 13.3333px;">equal areas. <span style="font-family: 'Arial','sans-serif'; font-size: 13.3333px;">Example 2: <span style="font-family: 'Arial','sans-serif'; font-size: 13.3333px;">Describe the area of each of 8 equal <span style="font-family: 'Arial','sans-serif'; font-size: 13.3333px;">parts as 1/8 of the area of the shape. ||  ||   || <span style="font-family: 'Arial','sans-serif'; font-size: 13.3333px;">M03.D-M.1.1.1 <span style="font-family: 'Arial','sans-serif'; font-size: 13.3333px;">Tell, show, and/or write time (analog) to the <span style="font-family: 'Arial','sans-serif'; font-size: 13.3333px;">nearest minute.
 * **Measurement & Data**

<span style="font-family: 'Arial','sans-serif'; font-size: 13.3333px;">M03.D-M.1.1.2 <span style="font-family: 'Arial','sans-serif'; font-size: 13.3333px;">Calculate elapsed time to the minute in a given <span style="font-family: 'Arial','sans-serif'; font-size: 13.3333px;">situation (total elapsed time limited to 60 minutes <span style="font-family: 'Arial','sans-serif'; font-size: 13.3333px;">or less).

<span style="font-family: 'Arial','sans-serif'; font-size: 13.3333px;">M03.D-M.1.2.1 <span style="font-family: 'Arial','sans-serif'; font-size: 13.3333px;">Measure and estimate liquid volumes and masses <span style="font-family: 'Arial','sans-serif'; font-size: 13.3333px;">of objects using standard units (cups [c], pints [pt], <span style="font-family: 'Arial','sans-serif'; font-size: 13.3333px;">quarts [qt], gallons [gal <span style="font-family: 'Arial','sans-serif'; font-size: 13.3333px;">], ounces [oz.], and <span style="font-family: 'Arial','sans-serif'; font-size: 13.3333px;">pounds [lb]) and metric units (liters [l], grams [g], <span style="font-family: 'Arial','sans-serif'; font-size: 13.3333px;">and kilograms [kg]).

<span style="font-family: 'Arial','sans-serif'; font-size: 13.3333px;">M03.D-M.1.2.2 <span style="font-family: 'Arial','sans-serif'; font-size: 13.3333px;">Add, subtract, multiply, and divide to solve one- <span style="font-family: 'Arial','sans-serif'; font-size: 13.3333px;">step word problems involving masses or liquid <span style="font-family: 'Arial','sans-serif'; font-size: 13.3333px;">volumes that are given in the same units.

<span style="font-family: 'Arial','sans-serif'; font-size: 13.3333px;">M03.D-M.1.2.3 <span style="font-family: 'Arial','sans-serif'; font-size: 13.3333px;">Use a ruler to measure lengths to the nearest <span style="font-family: 'Arial','sans-serif'; font-size: 13.3333px;">quarter inch or centimeter

<span style="font-family: 'Arial','sans-serif'; font-size: 13.3333px;">M03.D-M.1.3.1 <span style="font-family: 'Arial','sans-serif'; font-size: 13.3333px;">Compare total values of combinations of coins <span style="font-family: 'Arial','sans-serif'; font-size: 13.3333px;">(penny, nickel, dime, and quarter) and/or dollar <span style="font-family: 'Arial','sans-serif'; font-size: 13.3333px;">bills less than $5.00.

<span style="font-family: 'Arial','sans-serif'; font-size: 13.3333px;">M03.D-M.1.3.2 <span style="font-family: 'Arial','sans-serif'; font-size: 13.3333px;">Make change for an amount up to $5.00 with no <span style="font-family: 'Arial','sans-serif'; font-size: 13.3333px;">more than $2.00 change given (penny, nickel, <span style="font-family: 'Arial','sans-serif'; font-size: 13.3333px;">dime, quarter, and dollar).

<span style="font-family: 'Arial','sans-serif'; font-size: 13.3333px;">M03.D-M.1.3.3 <span style="font-family: 'Arial','sans-serif'; font-size: 13.3333px;">Round amounts of money to the nearest dollar <span style="font-family: 'Arial','sans-serif'; font-size: 13.3333px;">M03.D-M.2.1.1 <span style="font-family: 'Arial','sans-serif'; font-size: 13.3333px;">Complete a scaled pictograph and a scaled bar <span style="font-family: 'Arial','sans-serif'; font-size: 13.3333px;">graph to represent a data set with several <span style="font-family: 'Arial','sans-serif'; font-size: 13.3333px;">categories (scales limited to 1, 2, 5, and 10).

<span style="font-family: 'Arial','sans-serif'; font-size: 13.3333px;">M03.D-M.2.1.2 <span style="font-family: 'Arial','sans-serif'; font-size: 13.3333px;">Solve one- and two-step problems using <span style="font-family: 'Arial','sans-serif'; font-size: 13.3333px;">information to interpret data presented in scaled <span style="font-family: 'Arial','sans-serif'; font-size: 13.3333px;">pictographs and scaled bar graphs (scales limited <span style="font-family: 'Arial','sans-serif'; font-size: 13.3333px;">to 1, 2, 5, and 10). <span style="font-family: 'Arial','sans-serif'; font-size: 13.3333px;">Example 1: <span style="font-family: 'Arial','sans-serif'; font-size: 13.3333px;">(One-step) “Which category is the <span style="font-family: 'Arial','sans-serif'; font-size: 13.3333px;">largest?” <span style="font-family: 'Arial','sans-serif'; font-size: 13.3333px;">Example 2: <span style="font-family: 'Arial','sans-serif'; font-size: 13.3333px;">(Two-step) “How many more are in <span style="font-family: 'Arial','sans-serif'; font-size: 13.3333px;">category A than in category B?”

<span style="font-family: 'Arial','sans-serif'; font-size: 13.3333px;">M03.D-M.2.1.3 <span style="font-family: 'Arial','sans-serif'; font-size: 13.3333px;">Generate measurement data by measuring lengths <span style="font-family: 'Arial','sans-serif'; font-size: 13.3333px;">using rulers marked with halves and fourths of an <span style="font-family: 'Arial','sans-serif'; font-size: 13.3333px;">inch. Display the data by making a line plot, where <span style="font-family: 'Arial','sans-serif'; font-size: 13.3333px;">the horizontal scale is marked in appropriate <span style="font-family: 'Arial','sans-serif'; font-size: 13.3333px;">units—whole numbers, halves, or quarters.

<span style="font-family: 'Arial','sans-serif'; font-size: 13.3333px;">M03.D-M.2.1.4 <span style="font-family: 'Arial','sans-serif'; font-size: 13.3333px;">Translate information from one type of display to <span style="font-family: 'Arial','sans-serif'; font-size: 13.3333px;">another. Limit to pictographs, tally charts, bar <span style="font-family: 'Arial','sans-serif'; font-size: 13.3333px;">graphs, and tables. <span style="font-family: 'Arial','sans-serif'; font-size: 13.3333px;">Example: <span style="font-family: 'Arial','sans-serif'; font-size: 13.3333px;">Convert a tally chart to a bar graph.

<span style="font-family: 'Arial','sans-serif'; font-size: 13.3333px;">M03.D-M.3.1.1 <span style="font-family: 'Arial','sans-serif'; font-size: 13.3333px;">Measure areas by counting unit squares <span style="font-family: 'Arial','sans-serif'; font-size: 13.3333px;">(square cm, square m, square in., square ft, and <span style="font-family: 'Arial','sans-serif'; font-size: 13.3333px;">non-standard square units).

<span style="font-family: 'Arial','sans-serif'; font-size: 13.3333px;">M03.D-M.3.1.2 <span style="font-family: 'Arial','sans-serif'; font-size: 13.3333px;">Multiply side lengths to find areas of rectangles with <span style="font-family: 'Arial','sans-serif'; font-size: 13.3333px;">whole-number side lengths in the context of solving <span style="font-family: 'Arial','sans-serif'; font-size: 13.3333px;">real-world and mathematical problems, and <span style="font-family: 'Arial','sans-serif'; font-size: 13.3333px;">represent whole-number products as rectangular <span style="font-family: 'Arial','sans-serif'; font-size: 13.3333px;">areas in mathematical reasoning.

<span style="font-family: 'Arial','sans-serif'; font-size: 13.3333px;">M03.D-M.4.1.1 <span style="font-family: 'Arial','sans-serif'; font-size: 13.3333px;">Solve real-world and mathematical problems <span style="font-family: 'Arial','sans-serif'; font-size: 13.3333px;">involving perimeters of polygons, including finding <span style="font-family: 'Arial','sans-serif'; font-size: 13.3333px;">the perimeter given the side lengths, finding an <span style="font-family: 'Arial','sans-serif'; font-size: 13.3333px;">unknown side length, exhibiting rectangles with the <span style="font-family: 'Arial','sans-serif'; font-size: 13.3333px;">same perimeter and different areas, and exhibiting <span style="font-family: 'Arial','sans-serif'; font-size: 13.3333px;">rectangles with the same area and different <span style="font-family: 'Arial','sans-serif'; font-size: 13.3333px;">perimeters. Use the same units throughout the <span style="font-family: 'Arial','sans-serif'; font-size: 13.3333px;">problem. ||  ||   ||


 * __Grade 4__**

<span style="font-family: 'Arial','sans-serif'; font-size: 13.3333px;">M04.A-T.1.1.1 <span style="font-family: 'Arial','sans-serif'; font-size: 13.3333px;">Demonstrate an understanding that in a multi-digit <span style="font-family: 'Arial','sans-serif'; font-size: 13.3333px;">whole number (through 1,000,000), a digit in one <span style="font-family: 'Arial','sans-serif'; font-size: 13.3333px;">place represents ten times what it represents in <span style="font-family: 'Arial','sans-serif'; font-size: 13.3333px;">the place to its right. <span style="font-family: 'Arial','sans-serif'; font-size: 13.3333px;">Example: <span style="font-family: 'Arial','sans-serif'; font-size: 13.3333px;">Recognize that in the number 770, the 7 <span style="font-family: 'Arial','sans-serif'; font-size: 13.3333px;">in the hundreds place is ten times the 7 in the tens <span style="font-family: 'Arial','sans-serif'; font-size: 13.3333px;">place.
 * Numbers and Operations in Base Ten**

<span style="font-family: 'Arial','sans-serif'; font-size: 13.3333px;">M04.A-T.1.1.2 <span style="font-family: 'Arial','sans-serif'; font-size: 13.3333px;">Read and write whole numbers in expanded, <span style="font-family: 'Arial','sans-serif'; font-size: 13.3333px;">standard, and word form through 1,000,000.

<span style="font-family: 'Arial','sans-serif'; font-size: 13.3333px;">M04.A-T.1.1.3 <span style="font-family: 'Arial','sans-serif'; font-size: 13.3333px;">Compare two multi-digit numbers through <span style="font-family: 'Arial','sans-serif'; font-size: 13.3333px;">1,000,000 based on meanings of the digits in each <span style="font-family: 'Arial','sans-serif'; font-size: 13.3333px;">place, using >, =, and < symbols.

<span style="font-family: 'Arial','sans-serif'; font-size: 13.3333px;">M04.A-T.1.1.4 <span style="font-family: 'Arial','sans-serif'; font-size: 13.3333px;">Round multi-digit whole numbers (through <span style="font-family: 'Arial','sans-serif'; font-size: 13.3333px;">1,000,000) to any place.

<span style="font-family: 'Arial','sans-serif'; font-size: 13.3333px;">M04.A-T.2.1.1 <span style="font-family: 'Arial','sans-serif'; font-size: 13.3333px;">Add and subtract multi-digit whole numbers (limit <span style="font-family: 'Arial','sans-serif'; font-size: 13.3333px;">sums and subtrahends up to and including <span style="font-family: 'Arial','sans-serif'; font-size: 13.3333px;">1,000,000).

<span style="font-family: 'Arial','sans-serif'; font-size: 13.3333px;">M04.A-T.2.1.2 <span style="font-family: 'Arial','sans-serif'; font-size: 13.3333px;">Multiply a whole number of up to four digits by a <span style="font-family: 'Arial','sans-serif'; font-size: 13.3333px;">one-digit whole number and multiply 2 two-digit <span style="font-family: 'Arial','sans-serif'; font-size: 13.3333px;">numbers.

<span style="font-family: 'Arial','sans-serif'; font-size: 13.3333px;">M04.A-T.2.1.3 <span style="font-family: 'Arial','sans-serif'; font-size: 13.3333px;">Divide up to four-digit dividends by one-digit <span style="font-family: 'Arial','sans-serif'; font-size: 13.3333px;">divisors with answers written as whole-number <span style="font-family: 'Arial','sans-serif'; font-size: 13.3333px;">quotients and remainders.

<span style="font-family: 'Arial','sans-serif'; font-size: 13.3333px;">M04.A-T.2.1.4 <span style="font-family: 'Arial','sans-serif'; font-size: 13.3333px;">Estimate the answer to addition, subtraction, and <span style="font-family: 'Arial','sans-serif'; font-size: 13.3333px;">multiplication problems using whole numbers <span style="font-family: 'Arial','sans-serif'; font-size: 13.3333px;">through six digits (for multiplication, no more than <span style="font-family: 'Arial','sans-serif'; font-size: 13.3333px;">2 digits × 1 digit, excluding powers of 10)

<span style="font-family: 'Arial','sans-serif'; font-size: 13.3333px;">M04.A-F.1.1.1 <span style="font-family: 'Arial','sans-serif'; font-size: 13.3333px;">Recognize and generate equivalent fractions.

<span style="font-family: 'Arial','sans-serif'; font-size: 13.3333px;">M04.A-F.1.1.2 <span style="font-family: 'Arial','sans-serif'; font-size: 13.3333px;">Compare two fractions with different numerators <span style="font-family: 'Arial','sans-serif'; font-size: 13.3333px;">and different denominators (denominators limited <span style="font-family: 'Arial','sans-serif'; font-size: 13.3333px;">to 2, 3, 4, 5, 6, 8, 10, 12, and 100) using the <span style="font-family: 'Arial','sans-serif'; font-size: 13.3333px;">symbols >, =, or < and justify the conclusions. || || || <span style="font-family: 'Arial','sans-serif'; font-size: 13.3333px;">M04.A-F.1.1.1 <span style="font-family: 'Arial','sans-serif'; font-size: 13.3333px;">Recognize and generate equivalent fractions.
 * **<span style="font-family: 'Arial','sans-serif'; font-size: 13.3333px;">Numbers & Operations - Fractions **

<span style="font-family: 'Arial','sans-serif'; font-size: 13.3333px;">M04.A-F.1.1.2 <span style="font-family: 'Arial','sans-serif'; font-size: 13.3333px;">Compare two fractions with different numerators <span style="font-family: 'Arial','sans-serif'; font-size: 13.3333px;">and different denominators (denominators limited <span style="font-family: 'Arial','sans-serif'; font-size: 13.3333px;">to 2, 3, 4, 5, 6, 8, 10, 12, and 100) using the <span style="font-family: 'Arial','sans-serif'; font-size: 13.3333px;">symbols >, =, or < and justify the conclusions <span style="font-family: 'Arial','sans-serif'; font-size: 13.3333px;">M04.A-F.2.1.1 <span style="font-family: 'Arial','sans-serif'; font-size: 13.3333px;">Add and subtract fractions with a common <span style="font-family: 'Arial','sans-serif'; font-size: 13.3333px;">denominator (denominators limited to 2, 3, 4, 5, 6, <span style="font-family: 'Arial','sans-serif'; font-size: 13.3333px;">8, 10, 12, and 100; answers do not need to be <span style="font-family: 'Arial','sans-serif'; font-size: 13.3333px;">simplified; and no improper fractions as the <span style="font-family: 'Arial','sans-serif'; font-size: 13.3333px;">final answer).

<span style="font-family: 'Arial','sans-serif'; font-size: 13.3333px;">M04.A-F.2.1.2 <span style="font-family: 'Arial','sans-serif'; font-size: 13.3333px;">Decompose a fraction or a mixed number into a <span style="font-family: 'Arial','sans-serif'; font-size: 13.3333px;">sum of fractions with the same denominator <span style="font-family: 'Arial','sans-serif'; font-size: 13.3333px;">(denominators limited to 2, 3, 4, 5, 6, 8, 10, 12, and <span style="font-family: 'Arial','sans-serif'; font-size: 13.3333px;">100), recording the decomposition by an equation. <span style="font-family: 'Arial','sans-serif'; font-size: 13.3333px;">Justify decompositions (e.g., by using a visual <span style="font-family: 'Arial','sans-serif'; font-size: 13.3333px;">fraction model). <span style="font-family: 'Arial','sans-serif'; font-size: 13.3333px;">Example 1: <span style="font-family: 'Arial','sans-serif'; font-size: 13.3333px;">3/8 = 1/8 + 1/8 + 1/ <span style="font-family: 'Arial','sans-serif'; font-size: 13.3333px;">8 OR 3/8 = 1/8 + 2/8 <span style="font-family: 'Arial','sans-serif'; font-size: 13.3333px;">Example 2: <span style="font-family: 'Arial','sans-serif'; font-size: 13.3333px;">2 1/12 = 1 + 1 + 1/12 = <span style="font-family: 'Arial','sans-serif'; font-size: 13.3333px;">12/12 + 12/12 + 1/12

<span style="font-family: 'Arial','sans-serif'; font-size: 13.3333px;">M04.A-F.2.1.3 <span style="font-family: 'Arial','sans-serif'; font-size: 13.3333px;">Add and subtract mixed numbers with a common <span style="font-family: 'Arial','sans-serif'; font-size: 13.3333px;">denominator (denominators limited to 2, 3, 4, 5, 6, <span style="font-family: 'Arial','sans-serif'; font-size: 13.3333px;">8, 10, 12, and 100; no regrouping with subtraction; <span style="font-family: 'Arial','sans-serif'; font-size: 13.3333px;">fractions do not need to be simplified; and no <span style="font-family: 'Arial','sans-serif'; font-size: 13.3333px;">improper fractions as the final answers).

<span style="font-family: 'Arial','sans-serif'; font-size: 13.3333px;">M04.A-F.2.1.4 <span style="font-family: 'Arial','sans-serif'; font-size: 13.3333px;">Solve word problems involving addition and <span style="font-family: 'Arial','sans-serif'; font-size: 13.3333px;">subtraction of fractions referring to the same whole <span style="font-family: 'Arial','sans-serif'; font-size: 13.3333px;">or set and having like denominators (denominators <span style="font-family: 'Arial','sans-serif'; font-size: 13.3333px;">limited to 2, 3, 4, 5, 6, 8, 10, 12, and 100).

<span style="font-family: 'Arial','sans-serif'; font-size: 13.3333px;">M04.A-F.3.1.2 <span style="font-family: 'Arial','sans-serif'; font-size: 13.3333px;">Use decimal notation for fractions with <span style="font-family: 'Arial','sans-serif'; font-size: 13.3333px;">denominators 10 or 100. <span style="font-family: 'Arial','sans-serif'; font-size: 13.3333px;">Example: <span style="font-family: 'Arial','sans-serif'; font-size: 13.3333px;">Rewrite 0.62 as 62/100 and vice versa.

<span style="font-family: 'Arial','sans-serif'; font-size: 13.3333px;">M04.A-F.3.1.3 <span style="font-family: 'Arial','sans-serif'; font-size: 13.3333px;">Compare two decimals to hundredths using the <span style="font-family: 'Arial','sans-serif'; font-size: 13.3333px;">symbols >, =, or <, and justify the conclusions. || || <span style="font-family: 'Arial','sans-serif'; font-size: 13.3333px;">M04.A-F.2.1.5 <span style="font-family: 'Arial','sans-serif'; font-size: 13.3333px;">Multiply a whole number by a unit fraction <span style="font-family: 'Arial','sans-serif'; font-size: 13.3333px;">(denominators limited to 2, 3, 4, 5, 6, 8, 10, 12, and <span style="font-family: 'Arial','sans-serif'; font-size: 13.3333px;">100 and final answers do not need to be <span style="font-family: 'Arial','sans-serif'; font-size: 13.3333px;">simplified or written as a mixed number). <span style="font-family: 'Arial','sans-serif'; font-size: 13.3333px;">Example: <span style="font-family: 'Arial','sans-serif'; font-size: 13.3333px;">5 × (1/4) = 5/4

<span style="font-family: 'Arial','sans-serif'; font-size: 13.3333px;">M04.A-F.2.1.6 <span style="font-family: 'Arial','sans-serif'; font-size: 13.3333px;">Multiply a whole number by a non-unit fraction <span style="font-family: 'Arial','sans-serif'; font-size: 13.3333px;">(denominators limited to 2, 3, 4, 5, 6, 8, 10, 12, and <span style="font-family: 'Arial','sans-serif'; font-size: 13.3333px;">100 and final answers do not need to be <span style="font-family: 'Arial','sans-serif'; font-size: 13.3333px;">simplified or written as a mixed number). <span style="font-family: 'Arial','sans-serif'; font-size: 13.3333px;">Example: <span style="font-family: 'Arial','sans-serif'; font-size: 13.3333px;">3 × (5/6) = 15/6

<span style="font-family: 'Arial','sans-serif'; font-size: 13.3333px;">M04.A-F.2.1.7 <span style="font-family: 'Arial','sans-serif'; font-size: 13.3333px;">Solve word problems involving multiplication of a <span style="font-family: 'Arial','sans-serif'; font-size: 13.3333px;">whole number by a fraction (denominators limited <span style="font-family: 'Arial','sans-serif'; font-size: 13.3333px;">to 2, 3, 4, 5, 6, 8, 10, 12, and 100).

<span style="font-family: 'Arial','sans-serif'; font-size: 13.3333px;">M04.A-F.3.1.1 <span style="font-family: 'Arial','sans-serif'; font-size: 13.3333px;">Add two fractions with respective denominators 10 <span style="font-family: 'Arial','sans-serif'; font-size: 13.3333px;">and 100. <span style="font-family: 'Arial','sans-serif'; font-size: 13.3333px;">Example: <span style="font-family: 'Arial','sans-serif'; font-size: 13.3333px;">Express 3/10 as 30/100, and add <span style="font-family: 'Arial','sans-serif'; font-size: 13.3333px;">3/10 + 4/100 = 30/100 + 4/100 = 34/100. || <span style="font-family: 'Arial','sans-serif'; font-size: 13.3333px;">M04.B-O.1.1.1 <span style="font-family: 'Arial','sans-serif'; font-size: 13.3333px;">Interpret a multiplication equation as a comparison. <span style="font-family: 'Arial','sans-serif'; font-size: 13.3333px;">Represent verbal statements of multiplicative <span style="font-family: 'Arial','sans-serif'; font-size: 13.3333px;">comparisons as multiplication equations. <span style="font-family: 'Arial','sans-serif'; font-size: 13.3333px;">Example 1: <span style="font-family: 'Arial','sans-serif'; font-size: 13.3333px;">Interpret 35 = 5 × 7 as a statement that <span style="font-family: 'Arial','sans-serif'; font-size: 13.3333px;">35 is 5 times as many as 7 and 7 times as many <span style="font-family: 'Arial','sans-serif'; font-size: 13.3333px;">as 5. <span style="font-family: 'Arial','sans-serif'; font-size: 13.3333px;">Example 2: <span style="font-family: 'Arial','sans-serif'; font-size: 13.3333px;">Know that the statement 24 is 3 times <span style="font-family: 'Arial','sans-serif'; font-size: 13.3333px;">as many as 8 can be represented by the equation <span style="font-family: 'Arial','sans-serif'; font-size: 13.3333px;">24 = 3 × 8 or 24 = 8 × 3.
 * **Operations & Algebraic Thinking**

<span style="font-family: 'Arial','sans-serif'; font-size: 13.3333px;">M04.B-O.1.1.2 <span style="font-family: 'Arial','sans-serif'; font-size: 13.3333px;">Multiply or divide to solve word problems involving <span style="font-family: 'Arial','sans-serif'; font-size: 13.3333px;">multiplicative comparison, distinguishing <span style="font-family: 'Arial','sans-serif'; font-size: 13.3333px;">multiplicative comparison from additive <span style="font-family: 'Arial','sans-serif'; font-size: 13.3333px;">comparison. <span style="font-family: 'Arial','sans-serif'; font-size: 13.3333px;">Example: <span style="font-family: 'Arial','sans-serif'; font-size: 13.3333px;">Know that 3 × 4 can be used to <span style="font-family: 'Arial','sans-serif'; font-size: 13.3333px;">represent that Student A has 4 objects and <span style="font-family: 'Arial','sans-serif'; font-size: 13.3333px;">Student B has 3 times as many <span style="font-family: 'Arial','sans-serif'; font-size: 13.3333px;">objects not just <span style="font-family: 'Arial','sans-serif'; font-size: 13.3333px;">3 more objects.

<span style="font-family: 'Arial','sans-serif'; font-size: 13.3333px;">M04.B-O.1.1.3 <span style="font-family: 'Arial','sans-serif'; font-size: 13.3333px;">Solve multi-step word problems posed with whole <span style="font-family: 'Arial','sans-serif'; font-size: 13.3333px;">numbers using the four op <span style="font-family: 'Arial','sans-serif'; font-size: 13.3333px;">erations. Answers will be <span style="font-family: 'Arial','sans-serif'; font-size: 13.3333px;">either whole numbers or have remainders that <span style="font-family: 'Arial','sans-serif'; font-size: 13.3333px;">must be interpreted yielding a final answer that is a <span style="font-family: 'Arial','sans-serif'; font-size: 13.3333px;">whole number. Represent these problems using <span style="font-family: 'Arial','sans-serif'; font-size: 13.3333px;">equations with a symbol or letter standing for the <span style="font-family: 'Arial','sans-serif'; font-size: 13.3333px;">unknown quantity.

<span style="font-family: 'Arial','sans-serif'; font-size: 13.3333px;">M04.B-O.1.1.4 <span style="font-family: 'Arial','sans-serif'; font-size: 13.3333px;">Identify the missing symbol (+ <span style="font-family: 'Arial','sans-serif'; font-size: 13.3333px;">, –, ×, ÷, =, <, and >) <span style="font-family: 'Arial','sans-serif'; font-size: 13.3333px;">that makes a number sentence true (single-digit <span style="font-family: 'Arial','sans-serif'; font-size: 13.3333px;">divisor only).

<span style="font-family: 'Arial','sans-serif'; font-size: 13.3333px;">M04.B-O.2.1.1 <span style="font-family: 'Arial','sans-serif'; font-size: 13.3333px;">Find all factor pairs for a whole number in the <span style="font-family: 'Arial','sans-serif'; font-size: 13.3333px;">interval 1 through 100. Recognize that a whole <span style="font-family: 'Arial','sans-serif'; font-size: 13.3333px;">number is a multiple of each of its factors. <span style="font-family: 'Arial','sans-serif'; font-size: 13.3333px;">Determine whether a given whole number in the <span style="font-family: 'Arial','sans-serif'; font-size: 13.3333px;">interval 1 through 100 is a multiple of a given one- <span style="font-family: 'Arial','sans-serif'; font-size: 13.3333px;">digit number. Determine whether a given whole <span style="font-family: 'Arial','sans-serif'; font-size: 13.3333px;">number in the interval 1 through 100 is prime or <span style="font-family: 'Arial','sans-serif'; font-size: 13.3333px;">composite. <span style="font-family: 'Arial','sans-serif'; font-size: 13.3333px;">M04.B-O.3.1.1 <span style="font-family: 'Arial','sans-serif'; font-size: 13.3333px;">Generate a number or shape pattern that follows a <span style="font-family: 'Arial','sans-serif'; font-size: 13.3333px;">given rule. Identify apparent features of the pattern <span style="font-family: 'Arial','sans-serif'; font-size: 13.3333px;">that were not explicit in the rule itself. <span style="font-family: 'Arial','sans-serif'; font-size: 13.3333px;">Example 1: <span style="font-family: 'Arial','sans-serif'; font-size: 13.3333px;">Given the rule “add 3” and the starting <span style="font-family: 'Arial','sans-serif'; font-size: 13.3333px;">number 1, generate terms in the resulting <span style="font-family: 'Arial','sans-serif'; font-size: 13.3333px;">sequence and observe that the terms alternate <span style="font-family: 'Arial','sans-serif'; font-size: 13.3333px;">between odd and even numbers. <span style="font-family: 'Arial','sans-serif'; font-size: 13.3333px;">Example 2: <span style="font-family: 'Arial','sans-serif'; font-size: 13.3333px;">Given the rule “increase the number of <span style="font-family: 'Arial','sans-serif'; font-size: 13.3333px;">sides by 1” and starting with a triangle, observe <span style="font-family: 'Arial','sans-serif'; font-size: 13.3333px;">that the tops of the shapes alternate between a <span style="font-family: 'Arial','sans-serif'; font-size: 13.3333px;">side and a vertex.

<span style="font-family: 'Arial','sans-serif'; font-size: 13.3333px;">M04.B-O.3.1.2 <span style="font-family: 'Arial','sans-serif'; font-size: 13.3333px;">Determine the missing elements in a function table <span style="font-family: 'Arial','sans-serif'; font-size: 13.3333px;">(limit to +, –, or × and to whole numbers or <span style="font-family: 'Arial','sans-serif'; font-size: 13.3333px;">money).

<span style="font-family: 'Arial','sans-serif'; font-size: 13.3333px;">M04.B-O.3.1.3 <span style="font-family: 'Arial','sans-serif'; font-size: 13.3333px;">Determine the rule for a function given a table <span style="font-family: 'Arial','sans-serif'; font-size: 13.3333px;">(limit to +, –, or × <span style="font-family: 'Arial','sans-serif'; font-size: 13.3333px;">and to whole numbers). || || || <span style="font-family: 'Arial','sans-serif'; font-size: 13.3333px;">M04.C-G.1.1.1 <span style="font-family: 'Arial','sans-serif'; font-size: 13.3333px;">Draw points, lines, line segments, rays, angles <span style="font-family: 'Arial','sans-serif'; font-size: 13.3333px;">(right, acute, and obtuse), and perpendicular <span style="font-family: 'Arial','sans-serif'; font-size: 13.3333px;">and parallel lines. Identify these in two- <span style="font-family: 'Arial','sans-serif'; font-size: 13.3333px;">dimensional figures.
 * **Geometry**

<span style="font-family: 'Arial','sans-serif'; font-size: 13.3333px;">M04.C-G.1.1.2 <span style="font-family: 'Arial','sans-serif'; font-size: 13.3333px;">Classify two-dimensional figures based on the <span style="font-family: 'Arial','sans-serif'; font-size: 13.3333px;">presence or absence of parallel or perpendicular <span style="font-family: 'Arial','sans-serif'; font-size: 13.3333px;">lines or the presence or absence of angles of a <span style="font-family: 'Arial','sans-serif'; font-size: 13.3333px;">specified size. Recognize right triangles as a <span style="font-family: 'Arial','sans-serif'; font-size: 13.3333px;">category, and identify right triangles.

<span style="font-family: 'Arial','sans-serif'; font-size: 13.3333px;">M04.C-G.1.1.3 <span style="font-family: 'Arial','sans-serif'; font-size: 13.3333px;">Recognize a line of symmetry for a two- <span style="font-family: 'Arial','sans-serif'; font-size: 13.3333px;">dimensional figure as a line across the figure such <span style="font-family: 'Arial','sans-serif'; font-size: 13.3333px;">that the figure can be folded along the line into <span style="font-family: 'Arial','sans-serif'; font-size: 13.3333px;">mirroring parts. Identify line-symmetric figures and <span style="font-family: 'Arial','sans-serif'; font-size: 13.3333px;">draw lines of symmetry <span style="font-family: 'Arial','sans-serif'; font-size: 13.3333px;">(up to two lines of <span style="font-family: 'Arial','sans-serif'; font-size: 13.3333px;">symmetry). || || || <span style="font-family: 'Arial','sans-serif'; font-size: 13.3333px;">M04.D-M.1.1.1 <span style="font-family: 'Arial','sans-serif'; font-size: 13.3333px;">Know relative sizes of measurement units within <span style="font-family: 'Arial','sans-serif'; font-size: 13.3333px;">one system of units including standard units (in., <span style="font-family: 'Arial','sans-serif'; font-size: 13.3333px;">ft, yd, mi; oz., lb; and c, pt, qt, gal), metric units <span style="font-family: 'Arial','sans-serif'; font-size: 13.3333px;">(cm, m, km; g, kg; and mL, L), and time (sec, min, <span style="font-family: 'Arial','sans-serif'; font-size: 13.3333px;">hr, day, wk, mo, and yr). Within a single system of <span style="font-family: 'Arial','sans-serif'; font-size: 13.3333px;">measurement, express measurements in a larger <span style="font-family: 'Arial','sans-serif'; font-size: 13.3333px;">unit in terms ofa smaller unit. <span style="font-family: 'Arial','sans-serif'; font-size: 13.3333px;">A table of <span style="font-family: 'Arial','sans-serif'; font-size: 13.3333px;">equivalencies will be provided. <span style="font-family: 'Arial','sans-serif'; font-size: 13.3333px;">Example 1: <span style="font-family: 'Arial','sans-serif'; font-size: 13.3333px;">Know that 1 kg is 1,000 times as <span style="font-family: 'Arial','sans-serif'; font-size: 13.3333px;">heavy as 1 g. <span style="font-family: 'Arial','sans-serif'; font-size: 13.3333px;">Example 2: <span style="font-family: 'Arial','sans-serif'; font-size: 13.3333px;">Express the length of a 4-foot snake <span style="font-family: 'Arial','sans-serif'; font-size: 13.3333px;">as 48 in. <span style="font-family: 'Arial','sans-serif'; font-size: 13.3333px;">M04.D-M.1.1.2 <span style="font-family: 'Arial','sans-serif'; font-size: 13.3333px;">Use the four operations to solve word problems <span style="font-family: 'Arial','sans-serif'; font-size: 13.3333px;">involving distances, intervals of time (such as <span style="font-family: 'Arial','sans-serif'; font-size: 13.3333px;">elapsed time), liquid volumes, masses of objects; <span style="font-family: 'Arial','sans-serif'; font-size: 13.3333px;">money, including problems involving simple <span style="font-family: 'Arial','sans-serif'; font-size: 13.3333px;">fractions or decimals; and problems that require <span style="font-family: 'Arial','sans-serif'; font-size: 13.3333px;">expressing measurements given in a larger unit in <span style="font-family: 'Arial','sans-serif'; font-size: 13.3333px;">terms of a smaller unit.
 * **Measurement & Data**

<span style="font-family: 'Arial','sans-serif'; font-size: 13.3333px;">M04.D-M.1.1.3 <span style="font-family: 'Arial','sans-serif'; font-size: 13.3333px;">Apply the area and perimeter formulas for <span style="font-family: 'Arial','sans-serif'; font-size: 13.3333px;">rectangles in real-world and mathematical <span style="font-family: 'Arial','sans-serif'; font-size: 13.3333px;">problems (may include finding a missing side <span style="font-family: 'Arial','sans-serif'; font-size: 13.3333px;">length). Whole numbers only. <span style="font-family: 'Arial','sans-serif'; font-size: 13.3333px;">The formulas will <span style="font-family: 'Arial','sans-serif'; font-size: 13.3333px;">be provided.

<span style="font-family: 'Arial','sans-serif'; font-size: 13.3333px;">M04.D-M.1.1.4 <span style="font-family: 'Arial','sans-serif'; font-size: 13.3333px;">Identify time (analog or digital) as the amount of <span style="font-family: 'Arial','sans-serif'; font-size: 13.3333px;">minutes before or after the hour. <span style="font-family: 'Arial','sans-serif'; font-size: 13.3333px;">Example 1: <span style="font-family: 'Arial','sans-serif'; font-size: 13.3333px;">2:50 is the same as 10 minutes before <span style="font-family: 'Arial','sans-serif'; font-size: 13.3333px;">3:00. <span style="font-family: 'Arial','sans-serif'; font-size: 13.3333px;">Example 2: <span style="font-family: 'Arial','sans-serif'; font-size: 13.3333px;">Quarter past six is the same as 6:15.

<span style="font-family: 'Arial','sans-serif'; font-size: 13.3333px;">M04.D-M.2.1.3 <span style="font-family: 'Arial','sans-serif'; font-size: 13.3333px;">Translate information from one type of display to <span style="font-family: 'Arial','sans-serif'; font-size: 13.3333px;">another (table, chart, bar graph, or pictograph).

<span style="font-family: 'Arial','sans-serif'; font-size: 13.3333px;">M04.D-M.3.1.1 <span style="font-family: 'Arial','sans-serif'; font-size: 13.3333px;">Measure angles in whole-number degrees using a <span style="font-family: 'Arial','sans-serif'; font-size: 13.3333px;">protractor. With the aid of a protractor, sketch <span style="font-family: 'Arial','sans-serif'; font-size: 13.3333px;">angles of specified measure. <span style="font-family: 'Arial','sans-serif'; font-size: 13.3333px;">M04.D-M.3.1.2 <span style="font-family: 'Arial','sans-serif'; font-size: 13.3333px;">Solve addition and subtraction problems to find <span style="font-family: 'Arial','sans-serif'; font-size: 13.3333px;">unknown angles on a diagram in real-world and <span style="font-family: 'Arial','sans-serif'; font-size: 13.3333px;">mathematical problems. (Angles must be adjacent <span style="font-family: 'Arial','sans-serif'; font-size: 13.3333px;">and non-overlapping.) || || <span style="font-family: 'Arial','sans-serif'; font-size: 13.3333px;">M04.D-M.2.1.1 <span style="font-family: 'Arial','sans-serif'; font-size: 13.3333px;">Make a line plot to display a data set of <span style="font-family: 'Arial','sans-serif'; font-size: 13.3333px;">measurements in fractions of a unit (e.g., intervals <span style="font-family: 'Arial','sans-serif'; font-size: 13.3333px;">of 1/2, 1/4, or 1/8).

<span style="font-family: 'Arial','sans-serif'; font-size: 13.3333px;">M04.D-M.2.1.2 <span style="font-family: 'Arial','sans-serif'; font-size: 13.3333px;">Solve problems involving addition and subtraction <span style="font-family: 'Arial','sans-serif'; font-size: 13.3333px;">of fractions by using information presented in line <span style="font-family: 'Arial','sans-serif'; font-size: 13.3333px;">plots (line plots must be labeled with common <span style="font-family: 'Arial','sans-serif'; font-size: 13.3333px;">denominators, such as 1/4, 2/4, 3/4). ||

<span style="font-family: 'Arial','sans-serif'; font-size: 13.3333px;">M05.A-T.1.1.1 <span style="font-family: 'Arial','sans-serif'; font-size: 13.3333px;">Demonstrate an understanding that in a multi-digit <span style="font-family: 'Arial','sans-serif'; font-size: 13.3333px;">number, a digit in one place represents 1/10 of <span style="font-family: 'Arial','sans-serif'; font-size: 13.3333px;">what it represents in the place to its left. <span style="font-family: 'Arial','sans-serif'; font-size: 13.3333px;">Example: <span style="font-family: 'Arial','sans-serif'; font-size: 13.3333px;">Recognize that in the number 770, the <span style="font-family: 'Arial','sans-serif'; font-size: 13.3333px;">7 in the tens place is 1/10 the 7 in the hundreds <span style="font-family: 'Arial','sans-serif'; font-size: 13.3333px;">place.
 * __Grade 5__**
 * **Numbers & Operations in Base Ten**

<span style="font-family: 'Arial','sans-serif'; font-size: 13.3333px;">M05.A-T.1.1.2 <span style="font-family: 'Arial','sans-serif'; font-size: 13.3333px;">Explain patterns in the number of zeros of the <span style="font-family: 'Arial','sans-serif'; font-size: 13.3333px;">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. <span style="font-family: 'Arial','sans-serif'; font-size: 13.3333px;">Example 1: <span style="font-family: 'Arial','sans-serif'; font-size: 13.3333px;">4 × 10 <span style="font-family: 'Arial','sans-serif'; font-size: 8.66667px;">2 <span style="font-family: 'Arial','sans-serif'; font-size: 13.3333px;">= 400 <span style="font-family: 'Arial','sans-serif'; font-size: 13.3333px;">Example 2: <span style="font-family: 'Arial','sans-serif'; font-size: 13.3333px;">0.05 ÷ 10 <span style="font-family: 'Arial','sans-serif'; font-size: 8.66667px;">3 <span style="font-family: 'Arial','sans-serif'; font-size: 13.3333px;">= 0.00005

<span style="font-family: 'Arial','sans-serif'; font-size: 13.3333px;">M05.A-T.1.1.3 <span style="font-family: 'Arial','sans-serif'; font-size: 13.3333px;">Read and write decimals to thousandths using <span style="font-family: 'Arial','sans-serif'; font-size: 13.3333px;">base-ten numerals, word form, and expanded <span style="font-family: 'Arial','sans-serif'; font-size: 13.3333px;">form. <span style="font-family: 'Arial','sans-serif'; font-size: 13.3333px;">Example: <span style="font-family: 'Arial','sans-serif'; font-size: 13.3333px;">347.392 = 300 + 40 + 7 + 0.3 + 0.09 + <span style="font-family: 'Arial','sans-serif'; font-size: 13.3333px;">0.002 = 3 × 100 + 4 × 10 + 7 × 1 + 3 × (0.1) + <span style="font-family: 'Arial','sans-serif'; font-size: 13.3333px;">9 × (0.01) + 2 × (0.001)

<span style="font-family: 'Arial','sans-serif'; font-size: 13.3333px;">M05.A-T.1.1.4 <span style="font-family: 'Arial','sans-serif'; font-size: 13.3333px;">Compare two decimals to thousandths based on <span style="font-family: 'Arial','sans-serif'; font-size: 13.3333px;">meanings of the digits in each place using >, =, <span style="font-family: 'Arial','sans-serif'; font-size: 13.3333px;">and < symbols.

<span style="font-family: 'Arial','sans-serif'; font-size: 13.3333px;">M05.A-T.1.1.5 <span style="font-family: 'Arial','sans-serif'; font-size: 13.3333px;">Round decimals to any place (limit rounding to <span style="font-family: 'Arial','sans-serif'; font-size: 13.3333px;">ones, tenths, hundredths, or thousandths place).

<span style="font-family: 'Arial','sans-serif'; font-size: 13.3333px;">M05.A-T.2.1.1 <span style="font-family: 'Arial','sans-serif'; font-size: 13.3333px;">Multiply multi-digit whole numbers (not to exceed three-digit by three-digit).

<span style="font-family: 'Arial','sans-serif'; font-size: 13.3333px;">M05.A-T.2.1.2 <span style="font-family: 'Arial','sans-serif'; font-size: 13.3333px;">Find whole-number quotients of whole numbers with up to four-digit dividends and two-digit divisors.

<span style="font-family: 'Arial','sans-serif'; font-size: 13.3333px;">M05.A-T.2.1.3 <span style="font-family: 'Arial','sans-serif'; font-size: 13.3333px;">Add, subtract, multiply, and divide decimals to <span style="font-family: 'Arial','sans-serif'; font-size: 13.3333px;">hundredths (no divisors with decimals). ||  ||   || <span style="font-family: 'Arial','sans-serif'; font-size: 13.3333px;">M05.A-F.1.1.1 <span style="font-family: 'Arial','sans-serif'; font-size: 13.3333px;">Add and subtract fractions (including mixed <span style="font-family: 'Arial','sans-serif'; font-size: 13.3333px;">numbers) with unlike denominators. (May include <span style="font-family: 'Arial','sans-serif'; font-size: 13.3333px;">multiple methods and representations.) <span style="font-family: 'Arial','sans-serif'; font-size: 13.3333px;">Example: <span style="font-family: 'Arial','sans-serif'; font-size: 13.3333px;">2/3 + 5/4 = 8/12 + 15/12 = 23/12
 * **Numbers & Operations – Fractions**

<span style="font-family: 'Arial','sans-serif'; font-size: 13.3333px;">M05.A-F.2.1.1 <span style="font-family: 'Arial','sans-serif'; font-size: 13.3333px;">Solve word problems involving division of whole <span style="font-family: 'Arial','sans-serif'; font-size: 13.3333px;">numbers leading to answers in the form of fractions <span style="font-family: 'Arial','sans-serif'; font-size: 13.3333px;">(including mixed numbers).

<span style="font-family: 'Arial','sans-serif'; font-size: 13.3333px;">M05.A-F.2.1.2 <span style="font-family: 'Arial','sans-serif'; font-size: 13.3333px;">Multiply a fraction (including mixed numbers) by a fraction.

<span style="font-family: 'Arial','sans-serif'; font-size: 13.3333px;">M05.A-F.2.1.3 <span style="font-family: 'Arial','sans-serif'; font-size: 13.3333px;">Demonstrate an understanding of multiplication as <span style="font-family: 'Arial','sans-serif'; font-size: 13.3333px;">scaling (resizing). <span style="font-family: 'Arial','sans-serif'; font-size: 13.3333px;">Example 1: <span style="font-family: 'Arial','sans-serif'; font-size: 13.3333px;">Comparing the size of a product to the <span style="font-family: 'Arial','sans-serif'; font-size: 13.3333px;">size of one factor on the basis of the size of the other factor without performing the indicated multiplication. <span style="font-family: 'Arial','sans-serif'; font-size: 13.3333px;">Example 2: <span style="font-family: 'Arial','sans-serif'; font-size: 13.3333px;">Explaining why multiplying a given <span style="font-family: 'Arial','sans-serif'; font-size: 13.3333px;">number by a fraction greater than 1 results in a <span style="font-family: 'Arial','sans-serif'; font-size: 13.3333px;">product greater than the given number <span style="font-family: 'Arial','sans-serif'; font-size: 13.3333px;">(recognizing multiplication by whole numbers <span style="font-family: 'Arial','sans-serif'; font-size: 13.3333px;">greater than 1 as a familiar case); explaining why multiplying a given number by a fraction less than1 results in a product smaller than the given number.

<span style="font-family: 'Arial','sans-serif'; font-size: 13.3333px;">M05.A-F.2.1.4 <span style="font-family: 'Arial','sans-serif'; font-size: 13.3333px;">Divide unit fractions by whole numbers and whole numbers by unit fractions. ||  ||   || <span style="font-family: 'Arial','sans-serif'; font-size: 13.3333px;">M05.B-O.1.1.1 <span style="font-family: 'Arial','sans-serif'; font-size: 13.3333px;">Use multiple grouping symbols (parentheses, <span style="font-family: 'Arial','sans-serif'; font-size: 13.3333px;">brackets, or braces) in numerical expressions and evaluate expressions containing these symbols.
 * **Operations & Algebraic Thinking**

<span style="font-family: 'Arial','sans-serif'; font-size: 13.3333px;">M05.B-O.1.1.2 <span style="font-family: 'Arial','sans-serif'; font-size: 13.3333px;">Write simple expressions that model calculations <span style="font-family: 'Arial','sans-serif'; font-size: 13.3333px;">with numbers and interpret numerical expressions <span style="font-family: 'Arial','sans-serif'; font-size: 13.3333px;">without evaluating them. <span style="font-family: 'Arial','sans-serif'; font-size: 13.3333px;">Example 1: <span style="font-family: 'Arial','sans-serif'; font-size: 13.3333px;">Express the calculation “add 8 and 7, <span style="font-family: 'Arial','sans-serif'; font-size: 13.3333px;">then multiply by 2” as 2 × (8 + 7). <span style="font-family: 'Arial','sans-serif'; font-size: 13.3333px;">Example 2: <span style="font-family: 'Arial','sans-serif'; font-size: 13.3333px;">Recognize that 3 × (18,932 + 921) is <span style="font-family: 'Arial','sans-serif'; font-size: 13.3333px;">three times as large as 18,932 + 921 without <span style="font-family: 'Arial','sans-serif'; font-size: 13.3333px;">having to calculate the indicated sum or product. ||  || Not brackets or braces <span style="font-family: 'Arial','sans-serif'; font-size: 13.3333px;">M05.B-O.2.1.1 <span style="font-family: 'Arial','sans-serif'; font-size: 13.3333px;">Generate two numerical patterns using two given rules. <span style="font-family: 'Arial','sans-serif'; font-size: 13.3333px;">Example: <span style="font-family: 'Arial','sans-serif'; font-size: 13.3333px;">Given the rule “add 3” and the starting <span style="font-family: 'Arial','sans-serif'; font-size: 13.3333px;">number 0 and given the rule “add 6” and the <span style="font-family: 'Arial','sans-serif'; font-size: 13.3333px;">starting number 0, generate terms in the resulting sequences.

<span style="font-family: 'Arial','sans-serif'; font-size: 13.3333px;">M05.B-O.2.1.2 <span style="font-family: 'Arial','sans-serif'; font-size: 13.3333px;">Identify apparent relationships between <span style="font-family: 'Arial','sans-serif'; font-size: 13.3333px;">corresponding terms of two patterns with the same starting numbers that follow different rules. <span style="font-family: 'Arial','sans-serif'; font-size: 13.3333px;">Example: <span style="font-family: 'Arial','sans-serif'; font-size: 13.3333px;">Given two patterns in which the first <span style="font-family: 'Arial','sans-serif'; font-size: 13.3333px;">pattern follows the rule “add 8” and the second <span style="font-family: 'Arial','sans-serif'; font-size: 13.3333px;">pattern follows the rule “add 2,” observe that the <span style="font-family: 'Arial','sans-serif'; font-size: 13.3333px;">terms in the first pattern are 4 times the size of the <span style="font-family: 'Arial','sans-serif'; font-size: 13.3333px;">terms in the second pattern. || <span style="font-family: 'Arial','sans-serif'; font-size: 13.3333px;">M05.C-G.1.1.1 <span style="font-family: 'Arial','sans-serif'; font-size: 13.3333px;">Identify parts of the coordinate plane ( <span style="font-family: 'Arial','sans-serif'; font-size: 13.3333px;">x-axis, y-axis, <span style="font-family: 'Arial','sans-serif'; font-size: 13.3333px;">and the origin) and the ordered pair (x-coordinate and y-coordinate). Limit the coordinate plane to <span style="font-family: 'Arial','sans-serif'; font-size: 13.3333px;">quadrant I.
 * **Geometry**

<span style="font-family: 'Arial','sans-serif'; font-size: 13.3333px;">M05.C-G.2.1.1 <span style="font-family: 'Arial','sans-serif'; font-size: 13.3333px;">Classify two-dimensional figures in a hierarchy <span style="font-family: 'Arial','sans-serif'; font-size: 13.3333px;">based on properties. <span style="font-family: 'Arial','sans-serif'; font-size: 13.3333px;">Example 1: <span style="font-family: 'Arial','sans-serif'; font-size: 13.3333px;">All polygons have at least three sides, <span style="font-family: 'Arial','sans-serif'; font-size: 13.3333px;">and pentagons are polygons, so all pentagons <span style="font-family: 'Arial','sans-serif'; font-size: 13.3333px;">have at least three sides. <span style="font-family: 'Arial','sans-serif'; font-size: 13.3333px;">Example 2: <span style="font-family: 'Arial','sans-serif'; font-size: 13.3333px;">A rectangle is a parallelogram, which is <span style="font-family: 'Arial','sans-serif'; font-size: 13.3333px;">a quadrilateral, which is a polygon; so, a rectangle <span style="font-family: 'Arial','sans-serif'; font-size: 13.3333px;">can be classified as a parallelogram, as a <span style="font-family: 'Arial','sans-serif'; font-size: 13.3333px;">quadrilateral, and as a polygon ||  || <span style="font-family: 'Arial','sans-serif'; font-size: 13.3333px;">M05.C-G.1.1.2 <span style="font-family: 'Arial','sans-serif'; font-size: 13.3333px;">Represent real-world and mathematical problems <span style="font-family: 'Arial','sans-serif'; font-size: 13.3333px;">by plotting points in quadrant I of the coordinate <span style="font-family: 'Arial','sans-serif'; font-size: 13.3333px;">plane and interpret coordinate values of points in <span style="font-family: 'Arial','sans-serif'; font-size: 13.3333px;">the context of the situation. || <span style="font-family: 'Arial','sans-serif'; font-size: 13.3333px;">M05.D-M.1.1.1 <span style="font-family: 'Arial','sans-serif'; font-size: 13.3333px;">Convert between different-sized measurement <span style="font-family: 'Arial','sans-serif'; font-size: 13.3333px;">units within a given measurement system. <span style="font-family: 'Arial','sans-serif'; font-size: 13.3333px;">A table <span style="font-family: 'Arial','sans-serif'; font-size: 13.3333px;">of equivalencies will be provided. <span style="font-family: 'Arial','sans-serif'; font-size: 13.3333px;">Example: <span style="font-family: 'Arial','sans-serif'; font-size: 13.3333px;">Convert 5 cm to meters.
 * **Measurement & Data**

<span style="font-family: 'Arial','sans-serif'; font-size: 13.3333px;">M05.D-M.2.1.2 <span style="font-family: 'Arial','sans-serif'; font-size: 13.3333px;">Display and interpret data shown in tallies, tables, <span style="font-family: 'Arial','sans-serif'; font-size: 13.3333px;">charts, pictographs, bar graphs, and line graphs, <span style="font-family: 'Arial','sans-serif'; font-size: 13.3333px;">and use a title, appropriate scale, and labels. A <span style="font-family: 'Arial','sans-serif'; font-size: 13.3333px;">grid will be provided to display data on bar graphs <span style="font-family: 'Arial','sans-serif'; font-size: 13.3333px;">or line graphs.

<span style="font-family: 'Arial','sans-serif'; font-size: 13.3333px;">M05.D-M.3.1.1 <span style="font-family: 'Arial','sans-serif'; font-size: 13.3333px;">Apply the formulas <span style="font-family: 'Arial','sans-serif'; font-size: 13.3333px;">V = l × w × h and V = B × h for <span style="font-family: 'Arial','sans-serif'; font-size: 13.3333px;">rectangular prisms to find volumes of right <span style="font-family: 'Arial','sans-serif'; font-size: 13.3333px;">rectangular prisms with whole-number edge <span style="font-family: 'Arial','sans-serif'; font-size: 13.3333px;">lengths in the context of solving real-world and <span style="font-family: 'Arial','sans-serif'; font-size: 13.3333px;">mathematical problems. <span style="font-family: 'Arial','sans-serif'; font-size: 13.3333px;">Formulas will be <span style="font-family: 'Arial','sans-serif'; font-size: 13.3333px;">provided.

<span style="font-family: 'Arial','sans-serif'; font-size: 13.3333px;">M05.D-M.3.1.2 <span style="font-family: 'Arial','sans-serif'; font-size: 13.3333px;">Find volumes of solid figures composed of two <span style="font-family: 'Arial','sans-serif'; font-size: 13.3333px;">non-overlapping right rectangular prisms. ||  || <span style="font-family: 'Arial','sans-serif'; font-size: 13.3333px;">M05.D-M.2.1.1 <span style="font-family: 'Arial','sans-serif'; font-size: 13.3333px;">Solve problems involving computation of fractions <span style="font-family: 'Arial','sans-serif'; font-size: 13.3333px;">by using information presented in line plots. ||