K.MD.2

**Longer or Shorter?**

Directly compare two objects with a measurable attribute in common, to see which object has "more of"/"less of" the attribute, and describe the difference.

K.MD.2

**Heavy or Light?**

Directly compare two objects with a measurable attribute in common, to see which object has "more of"/"less of" the attribute, and describe the difference.

K.MD.3

**How Many in Each Group?**

Classify objects into given categories; count the numbers of objects in each category and sort the categories by count.

K.MD.3

**Sort Objects**

Classify objects into given categories; count the numbers of objects in each category and sort the categories by count.

1.MD.1

**Order Three Objects by Length**

Order three objects by length; compare the lengths of two objects indirectly by using a third object.

1.MD.2

**Measure Without a Ruler**

Express the length of an object as a whole number of length units, by laying multiple copies of a shorter object (the length unit) end to end; understand that the length measurement of an object is the number of same-size length units that span it with no gaps or overlaps.

1.MD.3

Tell and write time in hours and half-hours using analog and digital clocks.

1.MD.3

**Tell Time to the Hour**

Tell and write time in hours and half-hours using analog and digital clocks.

1.MD.4

**Sort and Count Objects**

Organize, represent, and interpret data with up to three categories; ask and answer questions about the total number of data points, how many in each category, and how many more or less are in one category than in another.

2.MD.1

**Measure Length**

Measure the length of an object by selecting and using appropriate tools such as rulers, yardsticks, meter sticks, and measuring tapes.

2.MD.7

**Tell and Write Time**

Tell and write time from analog and digital clocks to the nearest five minutes, using a.m. and p.m.

2.MD.8

Solve word problems involving dollar bills, quarters, dimes, nickels, and pennies, using $ and ¢ symbols appropriately.

2.MD.8

**Coin Values**

Solve word problems involving dollar bills, quarters, dimes, nickels, and pennies, using $ and ¢ symbols appropriately.

2.MD.10

Draw a picture graph and a bar graph (with single-unit scale) to represent a data set with up to four categories. Solve simple put-together, take-apart, and compare problems using information presented in a bar graph.

3.MD.1

**Tell and Write Time in Minutes**

Tell and write time to the nearest minute and measure time intervals in minutes. Solve word problems involving addition and subtraction of time intervals in minutes, e.g., by representing the problem on a number line diagram.

3.MD.3

**Represent and Interpret Data**

Draw a scaled picture graph and a scaled bar graph to represent a data set with several categories. Solve one- and two-step "how many more" and "how many less" problems using information presented in scaled bar graphs.

3.MD.6

**Area of Rectangles**

Measure areas by counting unit squares (square cm, square m, square in, square ft, and improvised units).

3.MD.7.a

**Area of Rectangles**

Find the area of a rectangle with whole-number side lengths by tiling it, and show that the area is the same as would be found by multiplying the side lengths.

3.MD.7.b

**Area of Rectangles**

Multiply side lengths to find areas of rectangles with whole-number side lengths in the context of solving real world and mathematical problems, and represent whole-number products as rectangular areas in mathematical reasoning.

3.MD.7.c

**Area of Rectangles**

Use tiling to show in a concrete case that the area of a rectangle with whole-number side lengths a and b + c is the sum of a × b and a × c. Use area models to represent the distributive property in mathematical reasoning.

3.MD.8

**Perimeter of Polygons**

Solve real world and mathematical problems involving perimeters of polygons, including finding the perimeter given the side lengths, finding an unknown side length, and exhibiting rectangles with the same perimeter and different areas or with the same area and different perimeters.

4.MD.1

**Customary and Metric Measurement**

Know relative sizes of measurement units within one system of units including km, m, cm; kg, g; lb, oz.; l, ml; hr, min, sec. Within a single system of measurement, express measurements in a larger unit in terms of a smaller unit. Record measurement equivalents in a two-column table.

4.MD.2

**Measurement Word Problems**

Use the four operations to solve word problems involving distances, intervals of time, liquid volumes, masses of objects, and money, including problems involving simple fractions or decimals, and problems that require expressing measurements given in a larger unit in terms of a smaller unit. Represent measurement quantities using diagrams such as number line diagrams that feature a measurement scale.

4.MD.3

Apply the area and perimeter formulas for rectangles in real world and mathematical problems.

4.MD.4

**Fractional Line Plots**

Make a line plot to display a data set of measurements in fractions of a unit (1/2, 1/4, 1/8). Solve problems involving addition and subtraction of fractions by using information presented in line plots.

4.MD.5.a

**Measuring Angles**

An angle is measured with reference to a circle with its center at the common endpoint of the rays, by considering the fraction of the circular arc between the points where the two rays intersect the circle. An angle that turns through 1/360 of a circle is called a “one-degree angle,” and can be used to measure angles.

4.MD.5.b

**Measuring Angles**

An angle that turns through n one-degree angles is said to have an angle measure of n degrees.

4.MD.6

**Measuring Angles**

Measure angles in whole-number degrees using a protractor. Sketch angles of specified measure.

4.MD.7

**Additive Angles**

Recognize angle measure as additive. When an angle is decomposed into non-overlapping parts, the angle measure of the whole is the sum of the angle measures of the parts. Solve addition and subtraction problems to find unknown angles on a diagram in real world and mathematical problems, e.g., by using an equation with a symbol for the unknown angle measure.

5.MD.1

**Converting Measurements**

Convert among different-sized standard measurement units within a given measurement system (e.g., convert 5 cm to 0.05 m), and use these conversions in solving multi-step, real world problems.

5.MD.3.a

**Concepts of Volume**

A cube with side length 1 unit, called a "unit cube," is said to have "one cubic unit" of volume, and can be used to measure volume.

5.MD.3.b

**Concepts of Volume**

A solid figure which can be packed without gaps or overlaps using n unit cubes is said to have a volume of n cubic units.

5.MD.4

**Counting Units to Find Volume**

Measure volumes by counting unit cubes, using cubic cm, cubic in, cubic ft, and improvised units.

5.MD.5.a

**Volume of Rectangular Prisms**

Find the volume of a right rectangular prism with whole-number side lengths by packing it with unit cubes, and show that the volume is the same as would be found by multiplying the edge lengths, equivalently by multiplying the height by the area of the base. Represent threefold whole-number products as volumes, e.g., to represent the associative property of multiplication.

5.MD.5.b

**Volume of Rectangular Prisms**

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.

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