Download Grade 4 Unit 6: Decimal Fractions ( 4 Weeks)

Grade 4 Unit 6: Decimal Fractions ( 4 Weeks)
Stage 1 – Desired Results
Established Goals
Unit Description
The Mathematical Practices should be evident throughout instruction and connected to the content addressed in this
unit. Students should engage in mathematical tasks that provide an opportunity to connect content and practices.
Common Core Learning Standards
Understand decimal notations for fractions, and compare decimal fractions.
4.NF.5: Express a fraction with denominator 10 as an equivalent fraction with denominator 100, and use this technique
to add two fractions with respective denominators 10 and 100. For example, express 3/10 as 30/100, and add 3/10 +
4/100 = 34/100.
4.NF.6: Use decimal notation for fractions with denominators 10 or 100. For example, rewrite 0.62 as 62/100; describe a
length as 0.62 meters; locate 0.62 on a number line diagram.
4.NF.7: Compare two decimals to hundredths by reasoning about their size. Recognize that comparisons are valid only
when the two decimals refer to the same whole. Record the results of comparisons with the symbols >, =, or <, and
justify the conclusions, e.g., by using a visual model.
Common Core Standards of Mathematical Practice
1. Make sense of problems and persevere in solving them.
2. Reason abstractly and quantitatively.
3. Construct viable arguments and critique the reasoning of others.
4. Model with mathematics.
5. Use appropriate tools strategically.
6. Attend to precision.
7. Look for and make use of structure.
8. Look for and express regularity in repeated reasoning.
ESL Language Standards
Standard 1: Students will listen, speak, read, and write in English for information and understanding.
1.1. Identify and use reading and listening strategies to make text comprehensible and meaningful.
1.3 Select information appropriate to the purpose of the investigation, relate ideas from one written or spoken source to
another, and exclude nonessential information.
1.5 Formulate, ask, and respond to various question forms to obtain, clarify, and extend information and meaning.
1.7 Present information clearly in a variety of oral and written forms for different audiences and purposes related to all
academic content areas.
1.9 Convey and organize information, using facts, details, illustrative examples, and a variety of patterns and structures.
1.16 Apply learning strategies to acquire information and make texts comprehensible and meaningful.
Big Ideas
1. Rational numbers can be named in an infinite number
of different but equivalent forms.
Essential Questions
1. How are decimals and fractions related?
2. The effects of addition with fractions and decimals are
the same as those with whole numbers.
2. When you compare two decimals, how can you
determine which one has the greater value?
Content (Students will know….)
A. Understand that 100 is 10 times larger than 10
(e.g., 4 x 1 = 4; 4 x 10 = 40; 4 x 100 = 400). (4.NF.5)
Skills (Students will be able to…)
A1. Rewrite fractions with denominators of 10 as
equivalent with denominators of 100.
A2. Add rewritten fractions with denominators of 100
A3. Model addition of fractions with base-ten
denominators (10, 100) using base ten models
A4. Represent decimal numbers on different models such
as tenths and hundredths grids, number lines and tenths
and hundredths circles.
B. Decimals are special types of fractions that can be
written with a denominator that is equal to 10 or
100 (4.NF.6)
B1. Read and write decimals to the hundredths place
B2. Rewrite fractions with a denominator of 10 or 100 and
vice versa (for example: .62 = 62/100)
B3. Locate decimal numbers on a number line diagram
C. Decimal values can only be compared when they
refer to the same whole. (4.NF.7)
C1. Compare two decimal values (to hundredths) with the
symbols >, =, or <.
C2. Record the comparison of two decimal values by using a
visual model, e.g., grid drawing, base ten blocks, pictures,
tile
C3. Justify the result of a comparison of two decimal values
by using a visual model.
D. Two decimal values can be written differently but
still be equivalent (0.1 = 0.10). (4.NF.7)
D1. Decompose decimal numbers (.62=.60+.02)
D2. Rewrite and recognize equivalent decimals.
Terms/ Vocabulary
base-ten fractions, common denominator, equivalent fraction, tenths, hundredths, expanded form, decimal, equivalent
fraction, decompose, equivalent, <,>, =
Stage 2 – Assessment Evidence
Other Evidence
Teacher observation, conferencing, teacher designed
assessment pieces, student work, exit slips, journal entries
Initial Task: Playground Plans
Final Performance Task: Hallway Duty
Stage 3 – Learning Plan
Everyday Mathematics/Impact Mathematics Lessons –
The following lessons may support some of the CCLS & essential questions outlined in this unit map:
4.NF.5 7.8, 7.9, 9.2, 9.6, 10.1
4.NF.6 4.2, 4.7, 7.8, 8.1, 9.1, 9.2, 9.3, 9.5, 10.6, 12.1
4.NF.7 4.3, 4.4, 4.7, 4.9
Additional Resources:
https://www.georgiastandards.org/CommonCore/Common%20Core%20Frameworks/CCGPS_Math_4_Unit5FrameworkS
E.pdf
http://commoncore.greenwich.wikispaces.net/Math+Resources
http://www.uen.org/commoncore/
Name: ______________________
Date: _____________
Grade 4 Unit 6
Initial Performance Task: Playground Plans
Below are two floor plans of a new playground they are planning to build at PS 129.
1. The designers plan to cover 4/10 of the playground with square foam tiles for the
swing set area. Help the designers by shading 4/10 of the playground on both
Plan A and Plan B:
Plan A
Plan B
2. Rewrite 4/10 as a decimal number. Show how you arrived at your answer:
3. The designers also plan on covering 35/100 of the playground in square foam
tiles for the jungle gym. Which part of the playground is covered with more
square tiles: the swing set or the jungle gym? Prove your answer using numbers
and one of the models below.
Prove with numbers:
Prove with a model:
Playground
Jungle Gym
4. Write an expression comparing the area of the swing set to the area of the jungle
gym using <, >, or =
_______________________________________
5. What is the TOTAL area of the playground that is covered by the swing set and
the jungle gym? Show your math thinking using a model and numbers:
Grade 4 Unit 6
Initial Task Scoring Guide
Playground Plan Scoring Guide
1. (4.NF.5)
Student correctly shades in 4/10 of Plan A and 40/100 of Plan B.
Please note: there is a variety of ways to shade in that are correct.
2. (4.NF.6)
Student correctly expresses 4/10 as .4 or .40 and shows how they
arrived at answer. Such as 4/10 = 40/100 = .40 or references the
model and shows equal area in both the tenths and hundredths grids.
3. (4.NF.7)
Student uses numbers to prove that the area for the playground is
greater than the area for the jungle gym. For example: 4/10 =
40/100. 40/100 is greater than 35/100.
Student uses any of the three provided models to prove their answer.
4. (4.NF.7)
Student writes any of the acceptable expressions such as:
.40 > .35
4/10 > 3.5/10
40/100 > 35/100
.35 < .40
3.5/10 < 4/10
35/100 < 40/100
5. (4.NF.5)
Student correctly shows that the total area is .35 + .40 = .75 with
numbers
Student correctly shows that the total area is .75 using any model
Total Points
Novice
0 - 3 points
Points
Section
Points
1
1
2
2
2
2
4
2
1
1
1
3
2
12
Apprentice
Practitioner
Expert
4 - 7 points
8 - 11 points
12 points
12
Name: __________________________
Date: _____________
Grade 4 Unit 6
Final Performance Task: Hallway Duty
Ms. Collins, the principal at PS 226 has asked teachers to monitor certain sections of
the hallways during dismissal. Below is a floor plan of the hallways at PS 226.
1) Color in the section of the school that each teacher could have been asked to
take care of.
Teacher
Mrs. Darling
Mrs. Woodley
Mr. Hunter
Mr. Bailey
Ms. Baker
Section
Size
2/10
1/2
.15
.10
5/100
Color to
shade
Green
Red
Yellow
Orange
Blue
2) Who covered more of the hallway: Mrs. Darling or Mr. Hunter?
3) Use any model and/or numbers to prove which teacher covered more of the
hallway
4) Write an expression using <, >, or = comparing Mrs. Darling’s section to Mr.
Hunter’s section using decimal numbers
________________________________________
5) Mrs. Woodley says that the sections are not fair. She claims that her section is
bigger than everyone else’s sections combined! Is she right? Use any model
and numbers to illustrate your thinking.
Grade 4 Unit 6
Hallway Duty Scoring Guide
Hallway Scoring Guide
Points
Section
Points
1. (4.NF.5)
a. Student correctly shades 2/10 of the floor plan (or 20 squares)
b. Student correctly shades ½ of the floor plan (or 50 squares).
c. Student correctly shades .15 of the floor plan (or 15 squares).
d. Student correctly shades 1/10 of the floor plan (or 10 squares).
e. Student correctly shades 5/100 of the floor plan (or 5 squares)
1
1
1
1
1
5
2. (4.NF.7)
Student correctly states that Mrs. Darling covered more of the hallway
1
1
2
4
3. (4.NF.7)
Student correctly uses any model such as a number line, hundredths
circle or hundredths grid to prove that Mrs. Darling covers 20/100
while Mr. Hunter only covers 15/100
2
Student also uses numbers to prove that Mrs. Darling covers more
area by converting 2/10 to 20/100 and .15 to 15/100 or another such
viable method.
4. (4.NF.6, 4.NF.7)
Student writes a correct expression (with decimals) such as:
.15 < .20
.2 > .15
1
1
5. (4.NF.5, 4.NF.7)
Student correctly states that Mrs. Woodley’s one section is equal to all 1
of the other sections combined, not more than.
6
Student proves, using any model (can count the number of shaded
squares) that Mrs. Woodley’s section = all the other sections
combined
Student uses math to show the addition of the other 4 sections by
converting all section sizes into a common denominator such as 100.
Then, shows how it is equal to Mrs. Woodley’s section.
Total Points
2
3
17
17
Novice
Apprentice
Practitioner
Expert
0-4 points
5 - 9 points
10- 14 points
15-17 points