4th Grade
3rd Nine Weeks Math
Domain:Number and Operations: Fractions
Cluster:
Build fractions from unit fractions by applying and extending previous understandings of operations on whole numbers.
Common Core Standards:
4.NF.4 Apply and extend previous understandings of multiplication to multiply a fraction by a whole number.
a. Understand a fraction a/b as a multiple of 1/b. For example, use a visual fraction model to represent 5/4 as the product 5 x (1/4), recording the conclusion by the equation 5/4 =5 x (1/4).
b. Understand a multiple of a/b as a multiple of 1/b, and use this understanding to multiply a fraction by a whole number. For example, use a visual fraction model to express 3 x (2/5) as 6 x (1/5), recognizing this product as 6/5. (In general, n x (a/b) = (n x a)/b.)
c. Solve word problems involving multiplication of a fraction by a whole number, e.g., by using visual fraction models and equations to represent the problem. For example, if each person at a party will eat 3/8 of a pound of roast beef, and there will be 5 people at the party, how many pounds of roast beef will be needed? Between what two whole numbers does your answer lie?
Key Vocabulary
Unit fraction
Multiple of a Fraction
Multiplication (Multiply)
Fraction Model / Justify
Reasonable
Simplest Form / Improper Fraction
Mixed Number
Product / Numerator
Denominator
Fraction
Habits of Mind
· Thinking Flexibly
· Applying Past Knowledge to New Situations
· Remaining Open to Continuous Learning / · Questioning and Posing Problems
· Persistence
· Thinking/Communicating with Clarity & Precision
Domain: Number and Operations: Fractions
Cluster: Build fractions from unit fractions by applying and extending previous understandings of operations on whole numbers.
Common Core Standard:
4.NF.4 Apply and extend previous understandings of multiplication to multiply a fraction by a whole number.
a. Understand a fraction a/b as a multiple of 1/b. For example, use a visual fraction model to represent 5/4 as the product 5 x (1/4), recording the conclusion by the equation 5/4 =5 x (1/4).
b. Understand a multiple of a/b as a multiple of 1/b, and use this understanding to multiply a fraction by a whole number. For example, use a visual fraction model to express 3 x (2/5) as 6 x (1/5), recognizing this product as 6/5. (In general, n x (a/b) = (n x a)/b.)
c. Solve word problems involving multiplication of a fraction by a whole number, e.g., by using visual fraction models and equations to represent the problem. For example, if each person at a party will eat 3/8 of a pound of roast beef, and there will be 5 people at the party, how many pounds of roast beef will be needed? Between what two whole numbers does your answer lie?
What does this mean? This standard builds on students’ work of adding fractions and extending that work into multiplication. This standard extended the idea of multiplication as repeated addition. When introducing this standard make sure student use visual fraction models to solve word problems related to multiplying a whole number by a fraction.
Math Practices:
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.
Essential Question:
· How can repeated addition help me multiply a whole number and a fraction?
· How can visual models assist me as I move from adding fractions to multiplying fractions?
· How can using visual models help in solving word problems?
· Why express quantities, measurements, and number relationships in different ways?
Learning Targets (KUD)
K: basic multiplication facts; vocabulary associated with fractions, multiplication, and problem solving; visual fraction models; multiplication is repeated addition; how to write a fraction in simplest form
U: how to decompose a fraction; fractions are part of a whole; use visual fraction models to solve problems; when a form of an answer needs to be changed to match the context of a problem or situation
D: construct visual fraction models to solve multiplication problems of whole numbers and a unit fraction; construct visual fraction models to represent multiples of a fraction; explain a fraction a/b as a multiple of 1/b; justify and explain why an answer to a word problem was changed to match the context of the word problem
I can:
· explain why a/b = a x 1/b by using visual models to show how to decompose fractions into unit fractions (e.g., ¾ = ¼ + ¼ + ¼ = 3 x ¼).
· decompose a fraction (a/b) into a multiple of unit fractions (a x 1/b) in order to show why multiplying a whole number by a fraction (n x (a/b)) results in (n x a)/b (e.g., 5 x 3/8 = 5 x (3 x 1/8) = (5 x 3) x 1/8 = 15 x 1/8 = 15/8)
· solve word problems that involve multiplying a whole number and fraction with visual models and equations. / Criteria for Success for Mastery
Students should be able to:
• Construct visual fraction models to solve multiplication problems of a whole number and a unit fraction.
• Construct visual fraction models to represent multiples of a fraction and record the conclusion as an equation (5/4 = 5 x (1/4)).
• Construct visual fraction models and equations to solve a word problem involving multiplication of a fraction by a whole number.
• Justify and explain why an answer to a word problem was changed to match the context of the word problem or situation.
Examples
a.
Number Line
3/6 = 1/6 + 1/6 + 1/6 = 3 x (1/6)
0 1/6 2/6 3/6 4/6 5/6 6/6 7/6 8/6
Area Model
1/6 / 2/6 / 3/6 / 4/6 / 5/6 / 6/6
b.
3 x (2/5) = 2/5 + 2/5 + 2/5 = 6/5 = 6 x (1/5). Students are expected to use and create visual fraction models to multiply a whole number by a fraction.
1/5 / 2/5 / 3/5 / 4/5 / 5/5 / 1/5 / 2/5 / 3/5 / 4/5 / 5/5
The same thinking, based on the analogy between fractions and whole numbers, allows students to give meaning to the product of whole number and a fraction.
3 x 2/5 = 2/5 + 2/5 + 2/5 = (3 x 2)/6 = 6/5
c.
c.
In a relay race, each runner runs ½ of a lap. If there are 4 team members how long is the race?
Student 1:
Draws a number line that shows 4 jumps of ½.
0 ½ 1 1 ½ 2 2 ½ 3
Student 2
Draws an area model showing 4 pieces of ½ joined together to equal 2.
½ / ½ / ½ / ½
Student 3
Draws an area model representing 4 x ½ on a grid, dividing one row into ½ to represent the multiplier
Textbook Resources
Math Expressions: 924-925, 966-970
Supplemental Resources
STAMS
Math Madness
Buckle Down
Houghton Mifflin Math Chapter Challenges
North Carolina Mathematics Coach
Math Intensive Intervention (Houghton Mifflin)
Houghton Mifflin Harcourt Strategic Intervention
Houghton Mifflin Harcourt Assessment Guide
Houghton Mifflin Harcourt Problem Solving Practice Book
Houghton Mifflin Harcourt Resource Book
Media Resources
Apple Fractions by Jerry Pallotta
Decimals and Fractions by Rebecca Wingard-Nelson
The Hershey’s Milk Chocolate Bar Fractions Book by Jerry Pallotta
Fractions by Michele Koomen
Fractions by Penny Dowdy
Full House by Dayle Ann Dodds
Go, Fractions! by Judith Stamper
Eating Fractions by Bruce McMillan
If You Were a Fraction by Trisha Shaskan
Inchworm and a Half by Elinor Pinczes
Manga Math Mysteries: A mystery with Fractions by Melinda Thielbar
Web Resources1. http://www.mail.clevelandcountyschools.org~ccselem/07BB59E1-00870B98?plugin=loft
2. Fractions Unit from DPI
3. http://www.brainpop.com
4. http://www.gamequarium.com/fractions.htm
5. http://www.illuminations.nctm.org/Activities.aspx?grade=2
6. http://www.smartexchange.com
7. http://www.jc-schools.net/tutorials/interact-math.htm
8. http://www.glencoe.com/sites/common_assets/mathematices/ebook_assets/vmf/VMFinterface.html
9. www.studyjams.com
Domain:
Number and Operations: Fractions
* Grade 4 expectations in this domain are limited to fractions with denominators 2, 3, 4, 5, 6, 8, 10, 12, 100*
Cluster:
Understand decimal notation for fractions and compare decimal fractions.
Common Core Standards:
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.
Key Vocabulary
Fraction
Fraction Pair
Denominator / Numerator
Equivalent Fractions
Tenths / Hundredths
Decimal
Tenths Grid / Hundredths Grid
Equivalent
Rational Numbers
Habits of Mind
· Thinking Flexibly
· Remaining Open to Continuous Learning
· Striving for Accuracy
· Thinking Interdependently / · Questioning and Posing Problems
· Persistence
· Thinking/Communicating with Clarity & Precision
Domain: Number and Operations: Fractions
Cluster: Build fractions from unit fractions by applying and extending previous understandings of operations on whole numbers.
Common Core Standard:
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.
What does this mean? This standard continues the work of equivalent fractions by having students change fractions with a 10 in the denominator into equivalent fractions that have a 100 in the denominator.
Math Practices:
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.
Essential Question:
· Why express quantities, measurements, and number relationships in different ways?
· How is a place value chart used to make connections between fractions with denominations of 10 and 100?
· How can base-ten blocks be used to show the relationship between fractions with a denominator of 10 and denominator of 100?
Learning Targets (KUD)
K: vocabulary associated with fractions
U: the place value system
D: rewrite equivalent fractions with denominators of 10 and 100; add fractions with denominators of 10 and 100
I can:
· rewrite a fraction with a denominator 10 as an equivalent fraction with denominator 100.
· add two fractions with denominators 10 and 100. / Criteria for Success for Mastery
Students should be able to:
· List equivalent fraction pairs using 10 and 100 as denominators.
· Use base ten blocks to model relationships between given fractions with denominators of 10 and 100.
· Express a fraction with denominator 10 as an equivalent fraction with denominator 100.
· 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.)
Examples
a.
Show 3/10 is equal to 30/100
/
b.
Express 3/10 as 30/100, and add 3/10 + 4/100 = 34/100.
Textbook Resources
Use Teacher Created Resources
Supplemental Resources
STAMS
Math Madness
Buckle Down
Houghton Mifflin Math Chapter Challenges
North Carolina Mathematics Coach
Math Intensive Intervention (Houghton Mifflin)
Houghton Mifflin Harcourt Strategic Intervention
Houghton Mifflin Harcourt Assessment Guide
Houghton Mifflin Harcourt Problem Solving Practice Book
Houghton Mifflin Harcourt Resource Book
Media Resources
Apple Fractions by Jerry Pallotta
Decimals and Fractions by Rebecca Wingard-Nelson
The Hershey’s Milk Chocolate Bar Fractions Book by Jerry Pallotta
Fractions by Michele Koomen
Fractions by Penny Dowdy
Full House by Dayle Ann Dodds
Go, Fractions! by Judith Stamper
Eating Fractions by Bruce McMillan
If You Were a Fraction by Trisha Shaskan
Inchworm and a Half by Elinor Pinczes
Manga Math Mysteries: A mystery with Fractions by Melinda Thielbar
Web Resources1. http://www.studyladder.com/learn/mathematics/topic/fractions-and-decimals-444
2. http://illuminations.nctm.org/Activities.aspx?grade=2
3. Fractions Unit from DPI
4. http://www.brainpop.com
5. http://www.gamequarium.com/fractions.htm
6. http://www.jc-schools.net/tutorials/interact-math.htm
7. http://www.studyjams.com
1. http://harcourtschool.com/hspmath
Domain: Number and Operations: Fractions
Cluster: Build fractions from unit fractions by applying and extending previous understandings of operations on whole numbers.
Common Core Standard:
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.
What does this mean? Decimals are introduced for the first time. Students should have ample opportunities to explore and reason about the idea that a number can be represented as both a fraction and a decimal. Students make connections between fractions with denominators of 10 and 100 and the place value chart.
Math Practices:
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.