1. Name:_______________________________ 6 th Grade Math- Unit 7 Measurement: Two-Dimensional This unit bundles student expectations that address length and area in order to investigate measurement relationships. Prior to this unit, in Grade 5 Unit 06, students connected the area model used to represent multiplication with the concept of area as a measure. During this unit, students explore measurement relationships within formulas for length, including perimeter, circumference, and area. In addition, students investigate pi to describe the relationships between the diameter, radius, and circumference of a circle. After this unit, in Grade 6 Unit 08, students will continue to explore measurement concepts to include standard measurement conversions, capacity, weight, time, temperature, and volume. In Grade 7 Unit 08, students will estimate measurements and solve application problems involving the length and area of polygons and other shapes as well as the volume of prisms and cylinders. --------------------------------------------------------------------------------------------------------------------------- 6.4B: The student uses letters as variables in mathematical expressions to describe how one quantity changes when a related quantity changes. The student is expected to: Use tables of data to generate formulas representing relationships involving perimeter and area. ------------------------------------------------------------------------------------------------------------------------------------------------------ 6.6C: The student uses geometric vocabulary to describe angles, polygons, and circles. The student is expected to: Describe the relationship between radius, diameter, and circumference of a circle. ------------------------------------------------------------------------------------------------------------------------------------------------------ 6.8A: The student solves application problems involving estimation and measurement of length, and area. The student is expected to: Estimate measurements (including circumference) and evaluate reasonableness of results. ------------------------------------------------------------------------------------------------------------------------------------------------------ 6.8B: The student solves application problems involving estimation and measurement of length, and area. The student is expected to: Select and use appropriate units, tools, or formulas to measure and to solve problems involving length (including perimeter), and area.

2. Perimeter Definition for Perimeter: the distance around a two-dimensional shape. Memory Aid for Perimeter: Formulas for Perimeter: Square: P = 4sP  Perimeter s  side length Rectangle: P = 2 l + 2wP  Perimeter l  length w  width *You can also find the perimeter by adding all of the side lengths together.*

3. Perimeter Practice 14 ft 86 in. 16 in. 48 yd 39 mi 24.2 km 32 km 154 cm

4. Area Definition for Area: the amount of space inside the boundary of a flat (2-dimensional) object Memory Aid for Area: Different Ways to Find the Area: 1) Counting the Square Units: A=______________ B=______________ C=______________ 12345 678910 1112131415 1617181920 21 22 23 2425 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 24.5 25 units 2 36 units 2 24.5 units 2

5. h b h b1b1 b2b2 h b

6. Area Examples Square :A = s 2 A = (4) 2 A = 4 x 4 4 cmA = 16 cm 2 ------------------------------------------------------------------------------------------------------------------------------------------------------ Rectangle : A = lwORA = bh 8 ydA = (17)(8)A = (17)(8) A = 136 yd 2 17 yd ------------------------------------------------------------------------------------------------------------------------------------------------------ Parallelogram : 6m 5 mA = bh A = (9)(5) 9 m A = 45 m 2 ------------------------------------------------------------------------------------------------------------------------------------------------------ Trapezoid : 8 in. A = (b 1 + b 2 )h 2 7 in. 7 in.A = (8 + 10)6 2 A = (18)6 10 in. 2 A = 108 2 A = 54 in. 2 ------------------------------------------------------------------------------------------------------------------------------------------------------ Triangle : A = bh 2 5 km 5 kmA = (6)(4) 2 A = 24 2 6 kmA = 12 km 2 6 in. 4 km

7. Area Practice 36 cm 2 99 yd 2 71.5 ft 2 14 m 2 22.5 m 2 21 m 2 72 yd 2 105 m 2 110 ft 2

8. Parts of a Circle Definition for Radius: a straight line that is the distance from the center to the edge of a circle Memory Aid for Radius: Definition for Diameter : a straight line going through the center of a circle connecting 2 points on the cirlcle Memory Aid for Diameter: Relationship between the Radius and the Diameter: The radius x 2 = the diameter The diameter ÷ 2 = the raidus Definition for Chord: a straight line connecting 2 points on the circle Memory Aid for Chord:

9. Parts of a Circle Practice diameter center radius center chord radius chord diameter center

10. Circles

11. Circumference and Area Practice 1)AB = 13 cm XY = 11 cm Circumference=___________________Area=____________________ ----------------------------------------------------------------------------------------------------------------------------------- 2)ZX = 10 in. WK = 4 in. YW = 6 in. Circumference=___________________Area=____________________ ----------------------------------------------------------------------------------------------------------------------------------- 3)XM = 2 m YX = 8 m NL = 5 m Circumference=___________________Area=____________________ ----------------------------------------------------------------------------------------------------------------------------------- 4)WY = 16 ft RX = 14 ft Circumference=___________________Area=____________________ ----------------------------------------------------------------------------------------------------------------------------------- 5)BA = 21 mi XC = 18 mi Circumference=___________________Area=____________________ 66 cm 363 cm 2 30 in. 75 in. 2 30 m 75 m 2 48 ft 192 ft 2 108 mi 972 mi 2

12. Table Practice

14. Volume Definition for Volume: The amount of 3- dimensional space an object occupies. Formulas for Volume: Cube: V = s 3 Volume = side x side x side s s s Rectangular Prism: V = l wh Volume = length x width x height h l w

15. Volume Practice 24 mi 3 512 cm 3 360 km 3 44,268 ft 3 64 cm 3 1,386 in. 3

16. Perimeter  units 1 Area  units 2 Volume  units 3