5Th Grade Everyday Mathunit 1 Area and Volume

5th Grade Everyday MathUnit 1 – Area and Volume

5th Grade

Everyday Math

Unit 1

“Area and Volume”

Name: ______

Day 1: Unit Launch

Think – Ink – Share: What math do you think is behind filling a Scholastic Book Box with books? What skills, tools, or habits might you need?

______

Unit Pretest Score: ______/ ______points

Lesson 1 - 1 – Introduction to the Student Reference Book

LQ: How can I write and solve numerical expressions?
Mental Math & Fluency
Write an expression for each item. You do not need to calculate answers.
5 plus 4 The quotient of 25 and 5 Double 40
Math Message: Read and transact with SMJ (p. 1). Then look through the rest of the booklet. In your RJ (Math section), tell how it is different than the one that you had in fourth grade.
Vocabulary:

MB –

RJ –

MM –

MM&F

HL –

SMJ –

SRB –

SYW –

Unit Family Letter –

SMJ Pages: 1 – 4
Main Concept
Uses of the SRB:

Example Problems

Explanations

Tables & Charts

Vocabulary
Grouping symbols

expression

Interactive SRB

Summary: Turn and Talk: With your partner discuss how the icon and the SRB will be helpful to you as a mathematical tool.
Think-Ink-Pair-Share, then in your RJ, write a $2.00 summary on when/why the SRB will be used.
ACI: MB 1-1: 2 & 3 How did you do? [ ] + [ ] √ [ ] -
Assignment(s):

MB 1-1
HL 1-1 (Family Letter)

Lesson 1 – 2 – Area of a Rectangle, Part 1

LEQ: How can I write and solve numerical expressions?
Mental Math & Fluency
Solve:
+ + + + + +
Math Message: Read page 221 in the SRB. Then complete SMJ page 5.
Vocabulary:

area – the surface inside closed boundaries

unit squares –

square units – units used to measure area

row –

column -

SMJ Pages: 5-7
Main Concept
Area of Rectangles:
Counting Square:
Thinking about a Row or Column:
Area Formula:
Summary: Read SRB, page 225 silently to yourself and be ready to share out information from the page that you feel needs to be added to our Area poster.
ACI: SMJ p. 6 How did you do? [ ] + [ ] √ [ ] -
Assignment(s) – DUE TOMORROW:

MB 1-2: 1,2,3,4 (1st and 3rd rows), 5,6 (a,c,e)
HL 1-2: odds

Lesson 1-3 – Quilt Area: Day One

LEQ: How can I write and solve numerical expressions?
Mental Math & Fluency
Convert between feet and inches.
12 inches equals how many feet?
5 feet equals how many inches?
1 feet equals how many inches?
3 inches equals how many feet?
Math Message: Complete SMJ p. 8.
Open Response Problem:
*Don’t forget to:
- explain how Justin and Allyson arrived at their answers, even if you don’t agree with them.
- work together but each person should record their own solution.
- use sentences like this one: “I agree/disagree with ______’s answer because ______.”
SMJ Pages: 8
Summary: Read SRB p. 10-11 with a partner. Be ready to answer, “Why is it important to make sense of others’ mathematical thinking?”

Lesson 1-3 – Quilt Area: Day Two

LQ: How can I write and solve numerical expressions?
Guidelines for Discussion
During our class discussions, we can:
Make mistakes and learn from them
Share ideas and strategies respectfully
Change our minds about how to solve a problem
Ask questions of our teacher and classmates
Example:Using one of the sentence starters below, how could you appropriately respond if you saw a problem like this in a classmates’ work or your own?
10 x 20 = 20

I noticed ______.
Could you explain ______?
I agree because ______.
I don’t understand ______.
I disagree because ______.
I’d like to add ______.

Revising Work/Summarizer:
After analyzing and critiquing other students’ work, what did you notice you need/wanted to change about your response in order to make it better?
Assignment(s)- DUE TOMORROW:

MB 1-3: 1,2 (a,c), 3(a,c), 4,5
HL 1-3: odds

Lesson 1-4 – Area of a Rectangle, Part 2

LQ: How can I use tiling with unit squares to calculate area?
Mental Math & Fluency
Solve.
4 + 4 3 + 4 3 + 2
Home Link Review – In your RJ, write a reflection on how you did with last night’s homework (minimum of one complete sentence).
Math Message: Complete Problem 1 on journal page 10.
Vocabulary:

Pattern –

SMJ Pages: 10-12
Main Concept
Strategy:

Cover the floor completely with tiles and ______the number of tiles.

Determine how many tiles cover a ______.

______the total number of tiles by the number of tiles that cover a square foot.

Summary: Turn and Talk: What is your favorite method for find the area of a rectangle with fractional side length?
ACI: SMJ p. 11 How did you do? [ ] + [ ] √ [ ] -
Assignment(s):

MB 1-4: 1, 2, 3, 4 (a,c), 5, 6
HL 1-4: odds

Mid-unit Quiz –Area of Rectangles
These items are very similar to ones that we’ve done so far in this unit.
Answer them in the boxes below, but do not use your calculator unless directed to do so.
1. Find the area of this rectangle.
8u.

12 u.2

4 u.2

32 u.

32 u.2

/ 2. Find the area of this rectangle.
7u.

63 u.2

56 u.2

49 u.2

15 u.2

3. Find the area of this rectangle.

12 cm2

7 cm2
2 cm2
12 in.2

/ 4. Find the area of this rectangle.

5 in.2

7 in.2
6 cm2
6 in.2

5. What is the formula for finding the area of a rectangle?
______

Lesson 1-5 – Introduction to Volume

LQ: How can I calculate the space of a three-dimensional solid? How do formulas help me model math and solve problems efficiently? How can I write and solve numerical expressions?
Mental Math & Fluency
Write an expression for each item. You do not need to calculate answers.
9 less than 18
7 times the sum of 3 and 2
3 less than double the sum of 9 and 1
Math Message: Looking at the 3-dimensional objects listed below, which is the largest? Be prepared to explain your answer.
mailboxes bookshelf baskets
Vocabulary:

3 – dimensional – objects that have ______,______, and ______.

Volume – how much ______is taken up by an object

Conjecture – a mathematical ______.

SMJ Pages: 13-14
Main Concept
Draw an example of two objects that would have the same volume:
Draw an example of two objects that would have different volumes:
Summary: In your RJ, make a list of items that you can measure their volume. Try to write as many as you can.
ACI: SMJ p. 13 How did you do? [ ] + [ ] √ [ ] -
Assignment(s):

MB 1-5: 1 (a,c), 2, 3, 4, 5
HL 1-5: 1, 3, (for 1 only), 5

Lesson 1-6 –Exploring Nonstandard Volume Units

LQ: How can I calculate the space of a three-dimensional solid? How do formulas help me model math and solve problems efficiently? How can I write and solve numerical expressions?
Mental Math & Fluency
Record measurement equivalencies for these units of length.
2 meters equals how many centimeters?
900 centimeters equals how many meters?
850 centimeters equals how many meters?
¼ meter equals how many centimeters?
Math Message: In your RJ, draw a rectangle. Think about what you would do if someone asked you to find the volume of your rectangle. Record your ideas in your RJ and be ready to share.
Vocabulary:

Rectangular prism - ______- dimensional shape with rectangular bases and rectangular faces

Volume – the amount of space a figure takes up

SMJ Pages: 15 - 17
Main Concept
Record you findings for your rectangular prism here before determining the volume. Once you have all the dimensions, record the volume of your rectangular prism on SMJ p. 15.
Square:
Triangle:
Hexagon:
Summary: In your RJ: What 3-dimensional shape do you think would be easiest to pack tightly into a rectangular prism without gaps or overlaps? Why do you think so?
ACI: SMJ p. 15, #1 and 2 How did you do? [ ] + [ ] √ [ ] -
Assignment(s):

MB 1-6: 1, 2, 3, 4 (a,c), 5 (1st one), 6
HL 1-6: 1, 2, 3, 5

Lesson 1-7 – Measuring Volume by Counting Cubes

LQ: How can I calculate the space of a three-dimensional solid? How do formulas help me model math and solve problems efficiently? How can I write and solve numerical expressions?
Mental Math & Fluency
Evaluate:
2 x (2 + 3)
(24 ÷ 4) + 8
(42 ÷ 6) x (27 ÷ 9)
Math Message: SMJ p. 18 and Activity Sheet 1
Cut out and assemble Rectangular Prisms A, B, and C. Take 25 cubes. Estimate how many cubes will fit in each prism. Record your estimates in the second column of the table on journal page 18.
Vocabulary:

Unit cube – a cube with a length, width, and height of 1 unit

Cubic unit –any cube used to measure volume

SMJ Pages: 18 - 20
Main Concept
Record at least two strategies for finding the number of cubes needed to fill each rectangular prism:
Strategy 1:
Strategy 2:
Summary: In your RJ, record which cube-stacking problem was the easiest to solve and which was the most difficult. Explain why.
ACI: SMJ p. 19 How did you do? [ ] + [ ] √ [ ] -
Assignment(s):

MB 1-7: 1(a,c), 2, 3, 4(a), 5
HL 1-7: odds

Lesson 1 – 8 – Measuring Volume by Iterating Layers

LQ: How can I calculate the space of a three-dimensional solid? How do formulas help me model math and solve problems efficiently? How can I write and solve numerical expressions?
Mental Math & Fluency
Answer yes or no for each:
Is the value of the expression greater than 4 x 5?
(4 x 5) – 2
Is the value of the expression twice as large as 8 + 17?
(8 + 17) x 2
Is the value of the expression less than 12 x 4?
(12 x 4) x (4 ÷ 2)
Math Message: SMJ Activity Sheet 2
Cut out and assemble Rectangular Prisms D, E, and F. Take 25 cubes. Estimate how many cubes will fit in each prism. Record your estimates in your RJ.
Vocabulary:
Draw a picture

/ Write a Definition
Describe a Non- Example / Describe an Example
SMJ Pages: 13-14
Main Concept
Explain how you can use layers to calculate volume:
Summary: Choose one problem from today’s SMJ pages and explain how you solved it.
ACI: SMJ p. 22-23 How did you do? [ ] + [ ] √ [ ] -
Assignment(s):

MB 1-8: 1(a,c), 2(a,c), 3, 4(a), 5(1st, 3rd), 6(1st, 3rd)
HL 1-8: odds

Lesson 1 – 9 – Two Formulas for Volume

LQ: How can I calculate the space of a three-dimensional solid? How do formulas help me model math and solve problems efficiently? How can I write and solve numerical expressions?
Mental Math & Fluency
Evaluate: Write your answers on your whiteboards.
4 x (6-2)
10 x (4 x 2)
(6 x 5 x 2) / 5
Math Message: Find the volume of Prism E (from lesson 1-8); record your process and results in your RJ.
Vocabulary:
SMJ Pages: 25
Main Concept
List any formulas to find volume from today’s lesson:
Summary: Compare and contrast the two formulas for finding the volume of a rectangular prism.
ACI: SMJ p. 25 How did you do? [ ] + [ ] √ [ ] -
Assignment(s):

MB 1-9: 1, 2, 3, 4(a), 5
HL 1-9: odds

Lesson 1 – 10 – Visualizing Volume Units

LQ: How can I calculate the space of a three-dimensional solid? How do formulas help me model math and solve problems efficiently? How can I write and solve numerical expressions?
Mental Math & Fluency
Give measurement equivalencies for length.
How many inches are in…
2 ½ feet?
How many feet are in…
1 ½ yard?
How many meters are in…
½ kilometer?
How many centimeters are in…
1 decimeter?
Math Message: In your RJ, compare and contrast centimeters, square centimeters, and cubic centimeters.
Vocabulary:
SMJ Pages: 28-31
Main Concept
Summary: Tell at least two things that you have learned about cubic units and measuring with them.
ACI: SMJ p. 28-29 How did you do? [ ] + [ ] √ [ ] -
Assignment(s):

MB 1-10: 1, 2, 3, 4(a,c), 5(a,c), 6
HL 1-10: 1, 3, 5, 6, 8, 9

Lesson 1 – 11 – Volume Explorations

(27 x 10) – 50

Is the value of the expression less than 498 + 672?

(498 + 672) – (498 + 672)

Is the value of the expression half of 1,315 x 6?

(1,315 x 6) ÷ 2

Math Message: In your RJ, find the volume of a suitcase that is 14 inches long, 8 inches wide, and 20 inches tall. Then, tell how its volume would change if it were laid down on its side.
Vocabulary:
mathematical model –draw objects to represent the problem
SMJ Pages: 32-33
Main Concept
Summary: When solving real-world problems, why is it useful to use object models with rectangular prisms?
ACI: SMJ p. 32 How did you do? [ ] + [ ] √ [ ] -
Assignment(s):

MB 1-11: 1, 2, 3, 4(a, c), 5
HL 1-11: 1 & 2

Lesson 1 – 12 – Playing Prism Pile-Up

Prisms are 3-dimensional shapes.
Volume measures the surface of a 2-dimensional shape.
The amount of space enclosed by a 3-dimensional shape can be measured in cubic units.
If two containers have the same volume, they must have the same length, width, and height.
The volume of a prism is the number of cubes that fit in its base.
A rectangular prism completely packed with 24 unit cubes has a volume of 24 cubic units.

Math Message: Imagine you had this prism in front of you. In your RJ, write how you would tell a partner to find the volume of the prism. List as many strategies as you can. Use one of your strategies to find the volume of the prism.

Vocabulary:
Nested parentheses – When one set of parentheses is ______another set of parentheses. The operations inside the ______parenthesesis solve ______.
Brackets – When parentheses are nested, the ______parentheses are sometimes replaced with different symbols. Braces, brackets, and parentheses all mean the ______.
Braces - When parentheses are nested, the ______parentheses are sometimes replaced with different symbols. ______, ______, and parentheses all mean the ______.
SMJ Pages: 34
Main Concept

Summary: Explain to your partner how you found the volume of one of the figures on the game cards.
ACI: Prism Pile-Up How did you do? [ ] + [ ] √ [ ] -
Assignment(s):

MB 1-12: 1, 2, 3, 4(a, c), 5 (a, c), 6
HL 1-12: Rounds 1 & 2

Unit Posttest
Complete these problems, without using your calculator unless told to by a problem’s directions. When finished, keep your posttest at your seat until it is time to go over the answers as a class.
1. Find the area of this rectangle.
5u.

8 u.

15 u.

8 u.2

15 u.2

/ 2. Solve.
(7+ 5) / 3 – 1 =

3. Find the area of this rectangle.

7 u.2

b. 14 u.
c. 14 u.2
d. 7 u. / 4. Which one doesn’t have volume?

a bowling ball

a post-it note

Mrs. Sadvari

the image on a photograph

5. If you needed to measure the volume of a rectangular prism by filling it with many smaller, congruent 3-D shapes, which would probably work better – spheres or cubes?

spheres

cubes

/ 6. Find the volume of this prism.

13 cm3

113 cm3

123 cm3

120 cm3

7. Find the volume of this prism.

15 ft2

56 ft2

56ft3

15ft3

/ 8. Find the volume of this irregular prism.

165 cm

165 cm3

165 cm2

26 cm3

When your work is complete, begin working to complete the problems on your Unit 1 review sheet.
Along with completing the unit review packet, study by reviewing this unit’s MBs and HLs. Also, begin working on your MB and HL quiz; it will be due the morning after the unit test. Complete this by going back into your Unit 1 MBs and HLs and recording the correct answers you have down after going over answers in class.
Unit Assessment Reflection
If an item is a question, your answer should be a complete, thoughtful sentences, which includes part of the question in your answer.
If you need more space, use the back or attach lined paper.
I. Look through your test.

Check to ensure that your score was correctly totaled.

Write your grade, as a percentage.

Are you satisfied with your performance?

II. Analyze your errors! Notice the types of problems that you got wrong and the types of errors that you made. Then answer the questions below.

What types of problems gave you trouble?

Why did you get these problems incorrect?

After reviewing your test, do you now know how to do those problems or do you need more instruction?

III. How much have you grown as a mathematician from the beginning to the end of the unit? (Revisit your Unit Pretest and reflect on your performance at that time.
III. Look to the future! In the next unit, what could you do to be more successful?