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Mathematics

Math Avenues
Lessons, Enduring Understandings, Alignments to PEs

Lesson

Title

Enduring Understandings

Aligned PEs

1

What Does Area Mean?

  • Demonstrate understanding of the concept of area.
  • Estimate areas of irregular figures using manipulatives or pictures.

Teacher Materials:
Student Materials:
4.3.B, 4.3.E, 4.5.E
Assessment

2

Area & Perimeter

  • Demonstrate understanding of the concept of area and perimeter.

Teacher Materials:
Student Materials: 4.3.E
Assessment:
Q. 1-10 — 4.3.E

3

Experiences with Area

  • Demonstrate understanding of the concept of area and perimeter.
  • Demonstrate understanding of the differences between length units and area units using the US or metric system.
  • Use systemic procedures to measure, describe, and compare the area of rectangles. Identify area as the attribute to be measured, select and use appropriate units of measurement for area, select and use tools that match the unit chosen, count to determine the number of units.

Teacher Materials:
Student Materials:
3.4.D, 4.3.B
Assessment:
Q. 1, 4, 6, 7, 9 — 4.5
Q. 2 — 3.4.D
Q. 3, 5 — 4.3.B
Q. 8, 10 — 4.3.F

4

Don't Fence Me In

  • Demonstrate understanding of the concept of area and perimeter.
  • Demonstrate understanding of the differences between length units and area units using the US or metric system.

Teacher Materials:
Student Materials:
4.3.E
4.5.B, 4.5.E, 4.5.H
Assessment:
Q. 1, 3-10 — 4.3.F
Q. 2 — 3.4.D

5

Family Fun Festival

  • Demonstrate understanding of area and perimeter and have a thorough understanding of the comparison of area and perimeter.
  • Demonstrate understanding of the concepts of area and perimeter.
  • Use systematic procedures to measure, describe, and compare the area of rectangles.
  • Identify area as the attribute to be measure, select and use appropriate units of measurement for area, select and use tools that match the unit chosen, count to determine the number of units; use formulas to find the perimeter and area of rectangles.

Teacher Materials:
Student Materials:
4.3.E, 4.3.F
Assessment:
Q. 1-6, 8, 10 — 4.3.F
Q. 7 — 4.3.E
Q. 9 — 4.3.C

6

Creating Dog Mansions: Area, Perimeter, Surface Area, and Change

  • Demonstrate understanding of the concept of area.
  • Demonstrate understanding of the differences between length units and area (square) units using the US or metric system.
  • Use systematic procedures to measure, describe, and compare the area of rectangles.
  • Identify area as the attribute to be measure, select and use appropriate units of measurement for area, select and use tools that match the unit chosen, count to determine the number of units; use formulas to find the perimeter and area of rectangles.

Teacher Materials:
Student Materials:
4.3.E, 4.3.F
6.4.E
Assessment:
Q. 5-6 — 6.4.E
Q. 8-9 — 4.3.E, 4.3.F
Q. 10 — 6.4.B, 6.4.C, 6.4.D, 6.4.E

7

Boxed In!

  • Develop a better understanding of the concepts of volume and surface area of rectangular prisms.

Teacher Materials:
Student Materials:
4.3.C, 6.4.E
Assessment:
Q. 1, 11 — 6.4.E
Assessment:
Q. 8, 10, 12-13 — 6.6.B, 6.6.C, 6.6.D, 6.6.E
Q. 9 — 6.6.E
Q. 10 — 6.6.B, 6.6.C, 6.6.D, 6.6.E
Q. 11 — 6.4.E

8

Tiling and Filling “The Pool”

  • Demonstrate understanding of the concepts of volume and surface area of rectangular prisms.
  • Demonstrate understanding of the difference between square and cubic units.

Teacher Materials:
Student Materials:
4.5.B, 4.5.E, 4.5.H
6.6.B, 6.6.C, 6.6.D, 6.6.E
7.3.D
Assessment:
Q. 1- 5, 8, 10 — 6.4.E
Q. 6 — 4.3.F
Q. 9 —7.3.D

9

Landscaping: Changing Dimensions to Create Different Areas

  • Demonstrate understanding of how a change in one linear dimension affects other linear and area measurements of rectangles, triangles, and circles.
  • Demonstrate understanding of the concepts of volume and surface area of rectangular prisms.

Teacher Materials:
Student Materials:
4.5.B, 4.3.C, 4.3.E, 4.3.F
5.3.F
6.4.A
Assessment:
Q. 1-4, 7-8, 10 — 4.3.F
Q. 5 — 6.4.C
Q. 9 — 5.3.I

10

Pizza! Pizza!

  • Demonstrate understanding of how a change in one linear dimension affects other linear and area measurements of rectangles and circles, or volume of rectangular prisms and cylinders.
  • Use formulas to determine missing measurements of circles, squares, rectangular prisms, and cylinders.

Teacher Materials:
Student Materials:
Assessment:
Q.1, 7— 7.3.A
Q. 2 — 6.4.E
Q. 3-4 — 6.4.A
Q. 5-6 — 6.4.C
Q. 8 — 6.6.B, 6.6.C, 6.6.D, 6.6.E

11

Exploring Patterns in Perimeter and Area for Deep Understanding

  • Demonstrate an understanding of how a change in one linear dimension affects other linear and area measurements of rectangles, triangles, and circles.
  • Demonstrate an understanding of how a change in one linear dimension affects perimeter and area, and how changes in two linear dimensions affect perimeter and area of rectangles.

Teacher Materials:
Student Materials:
Assessment:
Q. 1—4.3.C
Q. 2 —3.4.D
Q. 3, 5 —3.4.E
Q. 4, 6-7—9, 4.3.F
Q. 8, 4.3.F—4.1.B, 4.5.F
Q. 10—4.5.B, 4.5. E, 4.5.H

12

Designing Boxes at the Acme Box Company

  • Students will analyze data and use formulas to understand how the change in one linear measurement affects area and volume of rectangular prisms.

Teacher Materials:
Student Materials:
Assessment:
Q. 5.3.F
Q. 2—5.3.I
Q. 3— 4.3.F
Q. 4-5 —7.3.A
Q. 6-9—7.3.D
Q. 10—8.2.G

13

Cylinder Savvy

  • Demonstrate how change in one linear dimension affects area measurements of circles and volume and surface area of cylinders.
  • Use formulas to determine missing measurements of circles and cylinders.
  • Identify situations in which estimated measurements are sufficient; estimate the volume and surface area of cylinders.

Teacher Materials:
Student Materials:
SM-1 6.4.A,6.4.C, 6.4.E
SM-2 to 5 7.3.A
SM-6 to 9 7.6.B, 7.6.C, 7.6.D, 7.6.E
SM-10 7.3.D
Assessment:
Q. 1-7, 10 —7.3.D
Q. 8 — 7.6.B, 7.6.C, 7.6.D, 7.6.E
Q. 9—7.3.A

14

Solar Energy Harvesting

  • Demonstrate understanding of how a change in one linear dimension affects surface area and volume or how changes in two linear dimensions affect perimeter, area, and volume.

Teacher Materials:
Student Materials:
Assessment:
Q. 1— 6.4.E
Q. 2-3, 6-7, 9 — 7.3.C
Q. 4 —7.3.D
Q. 5 —7.6.B-E
Q. 8-10 —7.3.D

15

Supermarket Boxes

  • Develop an understanding of how changes in one or two linear dimensions affect surface area and volume.
  • Demonstrate understanding of rate and other derived units of measurement.
  • Demonstrate understanding of how to convert within the US or metric system to achieve an appropriate level of precision.
  • Explain why different situations require different levels of precision.

Teacher Materials:
Student Materials:
Assessment:
Q. 1, 7-12—7.3.D
Q. 3 —7.3.C

16

Designing an Energy Drink Can

  • Demonstrate understanding of how a change in one linear dimension affects surface area and volume or how changes in two linear dimensions affect perimeter, area, and volume.
  • Use formulas to determine measurements related to right prisms, cylinders, cones, or pyramids.

Teacher MaterialsA:
Teacher MaterialsB:
Student Materials:
7.3.D, 8.1
Assessment:
Q. 1-4, 7-10 — 7.3.D
Q. 5-6— 7.3.C

17

Extreme Make-Over

  • Demonstrate understanding of the differences between length units and area (square) units.
  • Use systematic procedures to measure, describe, and compare the area of rectangles; identify area as the attribute to be measured; select and use appropriate units of measurement and tools that match the unit chosen.
  • Identify situations in which estimated measurements are sufficient; estimate areas of rectangles.

Teacher Materials:
Student Materials:
3.4.D
4.3.B, 4.3C, 4.3.F
Assessment:
Q. 1-4, 6-9— 4.3.F
Q. 5 —2.3.B, 2.5.F
Q. 10 —4.3F, 4.5.B, 4.5.E, 4.5.H

18

String, Tiles, and Cubes

  • Understand the differences between area (square) units and volume (cubic) units.
  • Use systemic procedures to measure, describe, and compare the area of rectangles and the volume of rectangular prisms – identify area or volume as the attribute to be measured; select and use appropriate units for area or volume; select and use a tool that matches the unit chosen; count to determine the number of units.

Teacher Materials:
Student Materials:
Pre 6.4.E
Assessment:
Q. 1-8 — pre 6.4.E
Q. 9 — 4.3.C, 4.5.H
Q. 10 — 6.4.E, 6.6.GQ

19

Be Precise

  • Students will demonstrate precision in measuring objects. The students will explain how the selection of a unit affects the precision of a measurement in a given situation.

Teacher Materials:
Student Materials:
Precursor to 3.4.D, 3.3.A
4.3.C, 4.4.B
Assessment:
Precision in length measurement and 4.4.B

20

How Good is Estimation?

  • Demonstrate understanding of rate and other derived units of measurement.
  • Demonstrate understanding of how to convert within the US or metric system to achieve an appropriate level of precision.
  • Explain why different situations require different levels of precision.
  • Identify situations in which estimated measurements are sufficient; use estimation to obtain reasonable measurements at an appropriate level of precision.

Teacher Materials:
Student Materials:
Pre-Assessment:
3.4.E
4.3.B, 4.3.F
4.5.B, 4.5.E, 4.5.H, 4.5.I
6.4.A
7.3.C
7.6.B, 7.6C, 7.6.D, 7.6.E
Assessment:
4.4.B, 5.3.I

21

Perimeter, Area, and Volume

  • Use systematic procedures to measure, describe, and compare the perimeter and area of rectangles and the volume of rectangular prisms.
  • Identify perimeter, area, or volume as the attribute to be measured.
  • Select and use appropriate units for perimeter, area, or volume and use tools that match the unit chosen.
  • Accurately count to determine the number of units.
  • Use formulas to find the perimeter and area of rectangles and the volume of rectangular prisms.

Teacher Materials:
Student Materials:
3.4.D, 3.4.E
4.3.B, 4.3.C, 4.3.F
6.4.E
7.3.D
Assessment:
Q. 1 —3.4.D
Q. 2, 6 —6.4.E
Q. 7—3.4.E
Q. 8, 10—4.3.F
Q. 9 —7.3.D

22

Painting Sidewalks

  • Use systemic procedures to measure, describe, and compare the area of rectangles, figures composed of rectangles, and right triangles.
  • Identify area as the attribute to be measured, select and use appropriate units of measurement for area, select and use tools that match the unit chosen, count to determine the number of units.
  • Use formulas to find the area of rectangles and right triangles.

Teacher Materials:
Student Materials:
4.3.B, 4.3.C, 4.3.F
5.3.D, 5.3.E, 5.3.F
Assessment:
Q. 1, 6 — 5.3.F
Q. 2, 7 — 4.3.F
Q. 3 — 6.4.B
Q. 4, 10 — 5.3.I
Q. 8 — 4.3.F, 4.4.B
Q. 9 — 6.4.E

23

Sort It Out

  • Develop a deeper conceptual understanding of the differences between area and perimeter and the vocabulary linked with these concepts.

Teacher Materials:
Student Materials:
4.3.F, 4.5.F
Assessment:
Q. 2 — 4.3.C
Q. 3 — 3.4.E, 4.3.C
Q. 4, 6-7, 9 — 4.3.F
Q. 5 — 3.4.E
Q. 8 — 4.3.F, 5.3.I, 6.1.F
Q. 10 — 4.3.F, 4.5.F

24

Sally's Bedroom

  • Use systematic procedures to measure, describe, and compare the area of rectangles, figures composed of rectangles, and right triangles.
  • Identify area as the attribute to be measured, select and use appropriate units of measurement for area, select and use tools that match the unit chosen, count to determine the number of units.
  • Use formulas to find the perimeter and area of rectangles and right triangles.

Teacher Materials:
Student Materials:
4.3.F, 5.3.I, 5.3.F, 5.6.B
5.6.E, 5.6.H
Assessment:
Q. 1 — 4.3.C
Q. 2, 5-6, 10 — 4.3.F
Q. 4, 9 — 4.3.E
Q. 7 — 4.3.F, 4.5.H
Q. 8 — 4.3.D
Q. 11 — 5.3.E

25

Ballpark Figure

  • Use systematic procedures to measure, describe, and compare the area of rectangles and right triangles.
  • Identify area as the attribute to be measured, select and use appropriate unit for area, select and use a tool that matches the unit chosen, count to determine the number of units, use formulas to find the perimeter and area of rectangles and right triangles.
  • Identify situations in which estimated measurements are sufficient; estimate area of rectangles and right triangles.

Teacher Materials:
Student Materials:
4.3.C, 4.3.F
4.5.B, 4.5.E, 4.5.H
5.3.E, 5.3.I
6.1.F
Assessment:
Q. 2 – 4, 6, 9 4.3.F
Q. 5 — 4.3.C

26

Queezmo’s Wall Hanging “Extreme Makeover”

  • Use systematic procedures to measure, describe, and compare the area of rectangles and right triangles.
  • Use the tool that matches the unit chose, count to determine the number of units, use formulas to find the perimeter and area of rectangles and right triangles.

Teacher Materials:
Student Materials:
4.3.F, 4.6.B, 4.6.E, 4.6.H
Assessment:
Q. 1 - 9 — 4.3.F

27

Wrecked Triangles

  • Analyze how a change in a linear dimension affects other linear measurements and perimeter measurements, and differentiate the attributes of area and perimeter of rectangles in solving problems.

Teacher Materials:
Student Materials:
5.3.I
6.4.E
6.6.B, 6.6.C, 6.6.D, 6.6.E
Assessment:
Q. 1-2, 4-5 — 4.3.E, 4.3.F
Q. 3 — 4.3.E
Q. 6, 8-15 — 4.3.F
Q. 7 — 4.1.B, 4.3.F

28

Purchasing Our New Park

  • Demonstrate understanding of the concept of volume of rectangular prisms in a real life situation.
  • Describe the systematic procedure to determine the volume of rectangular prisms.
  • Use formulas to find the perimeter and area of rectangles and right triangles.

Teacher Materials:
Student Materials:
4.3.F, 6.1.E, 6.3.D, 6.4.E, 7.3.D
Assessment:
Q. 1 — 3.4.E
Q. 2 — 5.3.I
Q. 3 — 4.3.F
Q. 4 — 5.3.E
Q. 5-6 — 6.4.E

29

Demystifying Surface Area and Volume

  • Develop an understanding of height in a three-dimensional shape versus height in a two-dimensional shape.
  • Use formulas, including the Pythagorean Theorem, to determine measurements in prisms and cylinders.

Teacher Materials:
Student Materials:
7.3.D
Assessment:
Q. 1, 7 — 7.3.A
Q. 3 – 6 —7.3.D
Q. 8 — 4.3.F, 4.5.B, 4.5.E, 4.5.H
Q. 9 — 7.3.A, 7.6.G
Q. 10 — 7.3.D, 7.6.B, 7.6.C, 7.6.D, 7.6.E

30

Around and On the San Juan Islands

  • Identify situations in which estimated measures are sufficient and use estimation to obtain reasonable measurements at an appropriate level of precision.

Teacher Materials:
Student Materials:
6.4.B,
G.6.E, G.6.F
G.7.C, G.7.F
Assessment:
Q. 1 — G.6.E
Q. 2 – 3 — 7.2.I, G.4.E
Q. 4 — 4.3.C
Q. 5 — 7.2.I
Q. 6 — 4.3.B
Q. 7 — 4.3.F
Q. 8 – 11— 6.4.B

31

Working Backward with Area and Volume

  • Use formulas, including the Pythagorean Theorem, to determine measurements of triangles, prisms, or cylinders.

Teacher Materials:
Student Materials:
6.4.A, 6.4.B, 6.4.D, 6.4.E, 6.4.F
7.3.A, 7.3.B, 7.3.D
8.2.F, 8.2.G
A1.2.E, A1.2.F, A1. 7.D
Assessment:
Q. 1- 4, 6 — 7.3.D
Q. 5 — 6.4.E
Q. 7, 11 — 8.2.F, 8.2.G
Q. 8 — 6.4.B
Q. 9 — 7.3.A
Q. 10 — 6.4.B, 6.4.E

 

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