Unit 3 Assessment Kehoegreen 1 Unit: Goal: Students will master multiplying fractions by whole number and fractions, and dividing fractions by whole numbers and fractions. Standards Alignment: CCSS: Lesson 1: CCSSM 5.NF.4 Apply and extend previous understandings of multiplication to multiply a fraction or whole number by a fraction. a. Interpret the product (a/b) × q as a parts of a partition of q into b equal parts; equivalently, as the result of a sequence of operations a × q ÷ b. For example, use a visual fraction model to show (2/3) × 4 = 8/3, and create a story context for this equation. Do the same with (2/3) × (4/5) = 8/15. (In general, (a/b) × (c/d) = ac/bd.) b. Find the area of a rectangle with fractional side lengths by tiling it with unit squares of the appropriate unit fraction side lengths, and show that the area is the same as would be found by multiplying the side lengths. Multiply fractional side lengths to find areas of rectangles, and represent fraction products as rectangular areas. Lesson 2: CCSSM 5.NF.7 Apply and extend previous understandings of division to divide unit fractions by whole numbers and whole numbers by unit fractions. a. Interpret division of a unit fraction by a non-zero whole number, and compute such quotients. For example, create a story context for (1/3) ÷ 4, and use a visual fraction model to show the quotient. Use the relationship between multiplication and division to explain that (1/3) ÷ 4 = 1/12 because (1/12) × 4 = 1/3. b. Interpret division of a whole number by a unit fraction, and compute such quotients. For example, create a story context for 4 ÷ (1/5), and use a visual fraction model to show the quotient. Use the relationship between multiplication and division to explain that 4 ÷ (1/5) = 20 because 20 × (1/5) = 4. CCSSM.6.NS. Apply and extend previous understandings of multiplication and division to divide fractions by fractions. 1. Interpret and compute quotients of fractions, and solve word problems involving division of fractions by fractions, e.g., by using visual fraction models and equations to represent the problem. For example, create a story context for (2/3) ÷ (3/4) and use a visual fraction model to show the quotient; use the relationship between multiplication and division to explain that (2/3) ÷ (3/4) = 8/9 because 3/4 of 8/9 is 2/3. (In general, (a/b) ÷ (c/d) = ad/bc.) How much chocolate will each person get if 3 people share 1/2 lb of chocolate equally? How many 3/4-cup servings are in 2/3 of a cup of yogurt? How wide is a rectangular strip of land with length 3/4 mi and area 1/2 square mi? Lesson 3: CCSSM 5.NF.6 Solve real world problems involving multiplication of fractions and mixed numbers, e.g., by using visual fraction models or equations to represent the problem. CCSSM 5.NF.7 Apply and extend previous understandings of division to divide unit fractions by whole numbers and whole numbers by unit fractions.
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Unit 3 Assessment Kehoegreen 1
Unit:
Goal:
Students will master multiplying fractions by whole number and fractions, and dividing fractions
by whole numbers and fractions.
Standards Alignment:
CCSS:
Lesson 1:
CCSSM 5.NF.4 Apply and extend previous understandings of multiplication to multiply a
fraction or whole number by a fraction.
a. Interpret the product (a/b) × q as a parts of a partition of q into b equal parts;
equivalently, as the result of a sequence of operations a × q ÷ b. For example, use a
visual fraction model to show (2/3) × 4 = 8/3, and create a story context for this
equation. Do the same with (2/3) × (4/5) = 8/15. (In general, (a/b) × (c/d) = ac/bd.)
b. Find the area of a rectangle with fractional side lengths by tiling it with unit squares of
the appropriate unit fraction side lengths, and show that the area is the same as would be
found by multiplying the side lengths. Multiply fractional side lengths to find areas of
rectangles, and represent fraction products as rectangular areas.
Lesson 2:
CCSSM 5.NF.7 Apply and extend previous understandings of division to divide unit fractions
by whole numbers and whole numbers by unit fractions.
a. Interpret division of a unit fraction by a non-zero whole number, and compute such
quotients. For example, create a story context for (1/3) ÷ 4, and use a visual fraction
model to show the quotient. Use the relationship between multiplication and division to
explain that (1/3) ÷ 4 = 1/12 because (1/12) × 4 = 1/3.
b. Interpret division of a whole number by a unit fraction, and compute such quotients.
For example, create a story context for 4 ÷ (1/5), and use a visual fraction model to show
the quotient. Use the relationship between multiplication and division to explain that 4 ÷
(1/5) = 20 because 20 × (1/5) = 4.
CCSSM.6.NS. Apply and extend previous understandings of multiplication and division to
divide fractions by fractions.
1. Interpret and compute quotients of fractions, and solve word problems involving division
of fractions by fractions, e.g., by using visual fraction models and equations to represent the
problem. For example, create a story context for (2/3) ÷ (3/4) and use a visual fraction
model to show the quotient; use the relationship between multiplication and division to
explain that (2/3) ÷ (3/4) = 8/9 because 3/4 of 8/9 is 2/3. (In general, (a/b) ÷ (c/d) = ad/bc.)
How much chocolate will each person get if 3 people share 1/2 lb of chocolate equally?
How many 3/4-cup servings are in 2/3 of a cup of yogurt? How wide is a rectangular strip
of land with length 3/4 mi and area 1/2 square mi?
Lesson 3:
CCSSM 5.NF.6 Solve real world problems involving multiplication of fractions and mixed
numbers, e.g., by using visual fraction models or equations to represent the problem.
CCSSM 5.NF.7 Apply and extend previous understandings of division to divide unit fractions
by whole numbers and whole numbers by unit fractions.
Unit 3 Assessment Kehoegreen 2
c. Solve real world problems involving division of unit fractions by non-zero whole
numbers and division of whole numbers by unit fractions, e.g., by using visual fraction
models and equations to represent the problem. For example, how much chocolate will
each person get if 3 people share 1/2 lb of chocolate equally? How many 1/3-cup
servings are in 2 cups of raisins?
Technology Standards:
NETSS 1. Students demonstrates creative thinking, construct knowledge, and develop
innovative products and processes using technology.
c. Students use models and simulations to explore complex systems and issues.
NETSS.3.c: Students evaluate and select information sources and digital tools based on the
appropriateness to specific tasks.
NETST.2.a: Design or adapt relevant learning experiences that incorporate digital tools and
resources to promote student learning and creativity.
NETST.2.c: Customize and personalize learning activities to address students diverse learning
styles working strategies and abilities using digital tools and resources.
Unit Outcomes:
Students will solve multiplication and division of fractions by whole numbers and by fractions
on a post-assessment with 90% accuracy.
Specific Lesson Outcomes:
Lesson 1: The student will be able to solve multiplication fractions by whole numbers and by
fractions through the completion of pages 55 and 58 with 90% accuracy.
Lesson 2: The student will be able to solve division of fractions by whole numbers and by
other fractions through the completion of pages 61 and 64 with 90% accuracy.
Lesson 3a: The student will be able to apply knowledge of multiplying and dividing fractions
to problem solving with fractions through the completion of page 67 with 90% accuracy.
Lesson 3b: The student will be able to compare and contrast multiplying and dividing
fractions by producing a Venn diagram containing at least 4 similarities and differences.
Technology Outcomes:
1. Students will use technology to help them solve, mathematical problems and to assist them in
mastering the content.
Timeline:
Pre-Assessment: Topic Introduction – Page 11 in Appendix A – Tuesday October 16, 2012
Lesson 1:
Day 1: Multiplying fractions by whole numbers - Thursday October 18, 2012
Day 2: Multiplying fractions by fractions - Tuesday October 23, 2012
Lesson 2:
Day 1: Dividing Fractions by whole numbers - Thursday October 25, 2012
Day 2: Dividing fractions by fractions - Thursday November 1, 2012
Lesson 3:
Day 1: Problem Solving with Fractions – Thursday November 8, 2012
Unit 3 Assessment Kehoegreen 3
Post-Assessment: Topic Summary and Mixed Review (Problems 2 & 7) - Page 27 and 28
Appendix A -Tuesday November 13, 2012
Prior Knowledge:
The student just finished working with adding and subtracting fractions and has a strong mastery
of multiplication and division.
Analysis of Student:
As I am currently working only with students one on one, I choose one student to base this unit
around. Kasey (name changed) is an 8th
grade female, who was recommended to receive SRBI
support in math based on her STAR Math Winter and Spring 2012 benchmarks, as well as her
CMT scores (in 2011, 209 and in 2012, 215) . Her NWEA benchmark fell into the 24th
percentile
which is actually above the Tier III SRBI cut-off, but due to failing grades on quizzes and
assignments in math class and her CMT score is being kept in SRBI intervention until the end of
the quarter. Kasey’s strengths lie in that she is very hard-working and focused. A weakness is
that she tends to complete her assignments without always checking her work or thinking
through conceptually what she is doing. Kasey would benefit from a unit which shows her the
concepts behind the numbers and which has her verbalize or write the steps in the processes she
completes to have as a reference.
Unit 3 Assessment Kehoegreen 4
Lesson 1:
Goal:
Students will master multiplying fractions by whole number and fractions, and dividing fractions
by whole numbers and fractions.
Standards Alignment:
CCSSM 5.NF.4 Apply and extend previous understandings of multiplication to multiply a
fraction or whole number by a fraction.
a. Interpret the product (a/b) × q as a parts of a partition of q into b equal parts;
equivalently, as the result of a sequence of operations a × q ÷ b. For example, use a
visual fraction model to show (2/3) × 4 = 8/3, and create a story context for this
equation. Do the same with (2/3) × (4/5) = 8/15. (In general, (a/b) × (c/d) = ac/bd.)
b. Find the area of a rectangle with fractional side lengths by tiling it with unit squares of
the appropriate unit fraction side lengths, and show that the area is the same as would be
found by multiplying the side lengths. Multiply fractional side lengths to find areas of
rectangles, and represent fraction products as rectangular areas.
NETSS 1. Students demonstrates creative thinking, construct knowledge, and develop
innovative products and processes using technology.
c. Students use models and simulations to explore complex systems and issues.
NETST.2.c: Customize and personalize learning activities to address students diverse learning
styles working strategies and abilities using digital tools and resources.
Lesson Objective:
The student will be able to solve multiplication fractions by whole numbers and by fractions
through the completion of pages 15-1C and 15-2C with 90% accuracy.
Materials:
Bedley, Tim. (2012). Cross-Simplify Fractions. Retrieved from
http://www.youtube.com/watch?v=0HfZcO3VPLg.
from http://nlvm.usu.edu/en/nav/frames_asid_194_g_3_t_1.html?from=search.html
Grade Math Help. Fraction Strips. Retrieved from http://www.gradeamathhelp.com/free-
fraction-strips.html (Adapted - Adding Elevenths Strip on Word, See Appendix A,