Troup County School System
CCGPS Math Curriculum Map
Fourth Grade – Second Quarter
Click on the standard for assessment examples.
CCGPS / Example/Vocabulary / System ResourcesContinue teaching NBT.5 and NBT.6 through your number talks……
MCC4.OA.4 Find all factor pairs for a whole number in the range 1–100. Recognize that a whole number is a multiple of each of its factors. Determine whether a given whole number in the range 1–100 is a multiple of a given one‐digit number. Determine whether a given whole number in the range 1–100 is prime or composite.
This is new learning.
Essential Questions:
How are factors and multiples defined?
How do I find the factors of a given number?
How do I determine if a number is prime or composite? / MCC4.OA.4
Prime vs. Composite:
A prime number is a number greater than 1 that has only 2 factors, 1 and itself. Composite numbers have more than 2 factors. Students investigate whether numbers are prime or composite by:
• building rectangles (arrays) with the given area and finding which numbers have more than two rectangles (e.g. 7 can be made into only 2 rectangles, 1 x 7 and 7 x 1, therefore it is a prime number)
• finding factors of the number
Students should understand the process of finding factor pairs so they can do this for any number 1 -100.
To determine if a number between1-100 is a multiple of a given one-digit number, some helpful hints include the following:
• all even numbers are multiples of 2
• all even numbers that can be halved twice (with a whole number result) are multiples of 4
• all numbers ending in 0 or 5 are multiples of 5
Use tools such as the 100’s chart, multiplication chart, etc
Vocabulary
factor pairs, factor, multiplies, prime/composite / Vocabulary Cards and Word Wall
MCC4.OA.4
WMPWMV: directions for yearly spiral review
Whole Group
Eureka (NY Module) 3
Lesson 22: Complete the following
sections ONLY:
Concept Development
Problem Set
LearnZillion
Common Multiple
Least Common Multiple
Factor Findings (pg. 35)
Investigating Prime/Composite (pg. 23)
Number Riddles
Differentiation Activities
Hands On Standards:
· Finding Factor Pairs (Lesson 2)
· Identifying Multiples (Lesson 4)
Differentiation for Multiples
Differentiation for Factors
Differentiation for Prime/Composite
CCGPS / Example/Vocabulary / System Resources
MCC4.NF.1Explain why two or more fractions are equivalent a/b = n x a/n x b ex: ¼ = 3 x 1 / 3 x 4 by using visual fraction models. Focus attention on how the number and size of parts differ even though the fractions themselves are the same size. Use this principle to recognize and generate equivalent fractions.
In third grade, students had to generate and recognize general equivalent fractions using models.
Misconception Document – NF.1-2
Essential Questions:
How can I use visual models to find equivalent fractions?
What happens to the value of a fraction when the numerator and denominator are multiplied or divided by the same number? / MCC4.NF.1
This standard refers to visual fraction models. This includes area models, number lines, or it could be a collection/set model. Students will examine the idea that equivalent fractions can be created by multiplying both the numerator and denominator by the same number or by dividing a shaded region into various parts. INCLUDE SIMPLIFYING!!!!
Vocabulary
Fraction Simplify
Equivalent
Numerator
Denominator
/ MCC4.NF.1
Must watch video that explains how to teach this standard
WMPWMV: directions for yearly spiral review
Whole Group
Eureka (NY Module) 5
Lesson 7: Complete the following
sections ONLY:
Application Problem
Concept Development
Problem Set
Brain Pop: Fractions
Fraction Video
Fractions Flipchart
Math5Live Equivalent Fractions
LearnZillion
Fraction Number Lines (see activity on next page in middle column)
Fraction Number Lines Print
Fraction Circles Print
Differentiation Activities
Brain Pop, Jr.: More Fractions and Equivalent Fractions
Fraction Equivalent Activities (great activities for extending and re-teaching)
Race to 1 Game (pg. 12)
Comparing Cookies
Constructed Response:
· Lugging Water
Assessment
NF 1-2 Formative Assessment Task
CCGPS / Example/Vocabulary / System Resources
MCC4.NF.2 Compare two fractions with different numerators and different denominators, e.g., by using visual fraction models, by creating common denominators or numerators, or by comparing to a benchmark fraction such as 1/2. Recognize that comparisons are valid only when the two fractions refer to the same whole. Record the results of comparisons with symbols >, =, or <, and justify the conclusions, e.g., by using a visual fraction model.
In third grade, students had to compare two fractions with the same denominator or same numerator.
Misconception Document – NF.1-2
Essential Questions
What are some strategies I can use when comparing fractions?
How do I use benchmark fractions?
How do I find common denominators? / MCC4.NF.2
This standard calls for students to compare fractions by creating visual fraction models, using benchmark fractions, or finding common denominators or numerators.
Fractions may be compared using ½ as a benchmark.
Possible student thinking by using benchmarks:
1/8 is smaller than ½ because when 1 whole is cut into 8 pieces, the pieces are much smaller than when 1 whole is cut into 2 pieces.
Possible student thinking by creating common denominators:
Fractions with common denominators may be compared using the numerators as a guide.
Fractions with common numerators may be compared and ordered using the denominators as a guide.
Example: There are two cakes on the counter that are the same size. The first cake has ½ of it left. The second cake has 5/12 left. Which cake has more left?
Vocabulary
Benchmark fractions, common numerator, common denominator, compare, visual fraction models / MCC4.NF.2
WMPWMV: directions for yearly spiral review
Whole Group
Eureka (NY Module) 5
Lesson 12: Complete the following
sections ONLY:
Fluency Practice
Application Problem
Concept Development
Lesson 13: Complete the following
sections ONLY:
Fluency Practice
Concept Development
Exit Ticket
Lesson 14: Complete the following
sections ONLY:
Fluency Practice
Concept Development
Comparing Fractions NCTM Lesson
LearnZillion
Using Benchmarks to Compare
Constructed Responses:
· Birthday Fractions
· Who Ate More?
· Which is Larger?
Marilyn Burns: Introducing Fractions
· Introducing ½ as a benchmark
· More or Less than ½
· Put in Order
· Nicholas Game
Marilyn Burns: Extending Fractions
· In Size Order
· The Comparing Game
More or Less (pg. 24)
Compare Fractions with Cross Multiplication
Compare Fractions with Common Denominators
Differentiation Activities
Spin It To Win It Game
Spin It To Win It Cards
Fractions Buckets Game (pg. 21)
Fraction Chain (pg. 28)
Comparing and Ordering Fractions
Differentiated Activities
Fraction Wall Sheet
Assessment
NF 1-2 Formative Assessment Task
CCGPS / Example/Vocabulary / System Resources
MCC4.NF.3 Understand a fraction a/b with a numerator > 1 as a sum of unit fractions 1/b.
Grade 4 expectations in this domain are limited to fractions with denominators of 2, 3, 4, 5, 6, 8, 10, 12, and 100.
This is new learning.
Misconception Document – NF.3-4
Teach these elements together….
a. Understand addition and subtraction of fractions as joining and separating parts referring to the same whole.
b. Decompose a fraction into a sum of fractions with the same denominator in more than one way, recording each decomposition by an equation. Justify decompositions, e.g., by using a visual fraction model. Examples: 3/8 = 1/8 + 1/8 + 1/8 ; 3/8 = 1/8 + 2/8 ; 2 1/8 = 1 + 1 + 1/8 =8/8 + 8/8 + 1/8.
c. Add and subtract mixed numbers with like denominators, e.g., by replacing each mixed number with an equivalent fraction, and/or by using properties of operations and the relationship between addition and subtraction.
d. Solve word problems involving addition and subtraction of fractions referring to the same whole and having like denominators, e.g., by using visual fraction models and equations to represent the problem.
Essential Questions
Which operation would I use if I wanted to join parts of a whole?
Which operation would I use if I wanted to separate parts of a whole?
How do I compose and decompose fractions as sums and differences of fractions with the same denominator in more than one way?
What is the relationship between a mixed number and an improper fraction?
What strategies can I use to add and subtract mixed numbers with like denominators?
How can I use addition and subtraction of fractions to solve real world problems? / MCC4.NF.3.a,b,c,d
A fraction with a numerator of one is called a unit fraction. When students investigate fractions other than unit fractions, such as 2/3, they should be able to decompose the non-unit fraction into a combination of several unit fractions.
Example: 2/3 = 1/3 + 1/3
Being able to visualize this decomposition into unit fractions helps students when adding or subtracting fractions. Students need multiple opportunities to work with mixed numbers and be able to decompose them in more than one way. Students may use visual models to help develop this understanding.
Example:
1 ¼ - ¾ =
4/4 + ¼ = 5/4
5/4 – ¾ = 2/4 or ½
Example of a word problem:
Mary and Lacey decide to share pizza. Mary ate 3/6 and Lacey ate 2/6 of the pizza. How much of the pizza did the girls eat together?
Solution: The amount of pizza Mary ate can be thought of a 1/6 and1/6 and 1/6. The amount of pizza Lacey ate can be thought of a 1/6 and 1/6. The total amount of pizza they ate is 1/6 + 1/6 + 1/6 + 1/6 + 1/6 or 5/6 of the whole pizza.
Anchor Chart
Example of word problem:
Susan and Maria need 8 3/8 feet of ribbon to package gift baskets. Susan has 3 1/8 feet of ribbon and Maria has 5 3/8 feet of ribbon. How much ribbon do they have altogether? Will it be enough to complete the project? Explain why or why not.
Example of word problem:
Trevor has 4 1/8 pizzas left over from his soccer party. After giving some pizza to his friend, he has 2 4/8 of a pizza left. How much pizza did Trevor give to his friend?
Possible solution:
Trevor had 4 1/8 pizzas to start. This is 33/8 of a pizza. The x’s show the pizza he has left which is 2 4/8 pizzas or 20/8 pizzas. The shaded rectangles without the x’s are the pizza he gave to his friend which is 13/8 or 1 5/8 pizzas.
Example of word problem:
Elana, Matthew, and Kevin painted a wall. Elana painted 5/9 of the wall and Matthew painted 3/9 of the wall. Kevin painted the rest of the wall. Use the box below to represent the wall. Show the fraction of the wall Kevin painted.
Vocabulary
Joining
Separating
Unit fraction
Whole
Decompose
Mixed number / MCC4.NF.3 a
WMPWMV: directions for yearly spiral review
Whole Group
Brain Pop: Adding and Subtracting Fractions
Fraction Rap
LearnZillion
Sweet Fraction Bars (pg. 31)
Constructed Response:
· Write About Fractions (pg. 17)
Differentiation Activities
Adding Fractions with Like Denominators
Hands on Standards:
· Add and Subtract Fractions (Lesson 4)
Sense or Nonsense
Watch this video that explains the standard
MCC4.NF.3 b
BBY: WMPWMV Q2
Whole Group
Constructed Responses:
· Decomposing Fractions
· Different Ways
· Pizza Share
Fraction Relay Race (pg. 72)
Differentiation Activities
Hands On Standards:
· Breaking Apart Fractions (Lesson 5)
MCC4.NF.3 c
WMPWMV: directions for yearly spiral review
Whole Group
Eureka (NY Module) 5
Lesson 19: Complete the following
sections ONLY:
Problem Set
Equivalent Fractions w/Mixed Numbers Unit - Bridges (pgs. A6.5-6)
Fraction Field Event (pgs. 66-67)
Brain Pop: Mixed Numbers
Constructed Responses:
· Adding Mixed Numbers
· Subtracting Mixed Numbers
· Peaches Task
· Mixed Numbers Task
· Plastic Building Blocks
Differentiation Activities
Brain Pop, Jr.: Mixed Numbers
Hands On Standards:
· Add and Subtract
Fractions (Lesson 4, EIP Group)
Mixed Numbers Bingo
Assessment
NF 3-4 Formative Assessment Task
MCC4.NF.3 d
BBY: WMPWMV Q2
Whole Group
Mixed Number Word Problems
Fraction Word Problems
Differentiation Activities
Addition Word Problems with Fractions
Subtraction Word Problems with Fractions
Cookie Orders (pg. 41)
CCGPS / Example/Vocabulary / System Resources
MCC4.NF.4 Apply and extend previous understandings of multiplication to multiply a fraction by a whole number.
This is new learning
Misconception Document – NF.3-4
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 × (1/4), recording the conclusion by the equation 5/4 = 5 ×(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 × (2/5) as 6 × (1/5), recognizing this product as 6/5. (In general, n × (a/b) = (n × 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?
Essential Questions
How can I represent a fraction as a multiple of 1/b?
How can I use a visual fraction model to express a/b as a multiple of 1/b?
How can I use visual fraction models and equations to multiply a fraction by a whole number?
How can I use visual fraction models and equations to solve word problems involving multiplication of a fraction by a whole number? / MCC4.NF.4
MCC4.NF.4.a
Students will connect the relationship between whole number multiplication and repeated addition with fraction multiplication and repeated addition. Students understand that 4 + 4 + 4 means 3x 4, so they can see that 1/5 + 1/5 + 1/5 means 3 x 1/5. By making this connection, students are able to write fractions as the product of a whole number and a unit fraction. The fractions 7/8 can be written as 7 x 1/8.
Example: 3/6 = 1/6 + 1/6 + 1/6 = 3 x (1/6)
Number line:
Area Model:
MCC4.NF.4.b – Students will make the connection between multiples of whole numbers and multiples of unit fractions. A multiple is the product of a number and a counting number. Multiples of 4 are the products of 1 x 4, 2 x 4, and 3 x 4, or 4,8, and 12. Multiples of 1/6 are the products of 1 x 1/6, 2 x 1/6, 3 x 1/6 or 1/6, 2/6 and 3/6. Students use models and number lines to help make the connection.