Troup County School System

CCGPS Math Curriculum Map

Third – First Quarter

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CCGPS / Example/Vocabulary / System Resources
MCC3.NBT.1 Use place value understanding to round whole numbers to the nearest 10 or 100.
In second grade, students used place value understanding to understand the ones, tens, and hundreds place. They used base ten numerals, number names, and expanded form. Students compared two three digit numbers.
Misconception Document: NBT.1-3
Essential Questions:
How do I round numbers to the nearest 10 and 100?
Why do I need to know how to round numbers?
How can I use a hundreds chart or number line to round numbers? / MCC3.NBT.1
Students should have numerous experiences using a number line and a hundreds chart as tools to support their work with rounding.
Vocabulary
Place value
Round / MCC3.NBT.1
The Hands On Standards lessons can also be used in whole group as introductory lessons.
Whole Group
BBY: What’s My Place, What’s My Value
BBY: Dots
Rounder Rabbit Powerpoint
Rounder Rabbit Sheet
Rounding Journal Prompt
Island Hop pg. 22
10’s Number Lines
100’s Blank Number Lines
Differentiation Activities
Hands On Standards:
·  Estimating the Sum or Difference (lesson 1)
The Great Round Up pg. 35
Rounding Tricky Triangles (extends to 1,000)
Shake Rattle and Roll pg. 29
Writing to Win Prompts
Differentiated Activities
Click here for other lessons and assessments
CCGPS / Example/Vocabulary / System Resources
MCC3.NBT.2 Fluently add and subtract within 1000 using strategies and algorithms based on place value, properties of operations, and/or the relationship between addition and subtraction.
Add and Subtract within 1,000 – The sum of two numbers should not exceed 1,000. The minuend of subtraction problems should not exceed 1,000.
Misconception Document: NBT.1-3
In second grade, students had to fluently add and subtract within 100 using strategies based on place value, properties of operations, and/or the relationship between addition and subtraction. Students also had to add and subtract within 1,000, using concrete models or drawings and strategies based on place value, properties or operations, and/or the relationship between addition and subtraction. Students learned to mentally add 10 or 100 to a given number and mentally subtract 10 or 100 from a given number.
Algorithm - a set of predefined steps applicable to a class of problems that gives the correct result in every case when the steps are carried out correctly.
Strategy – purposeful manipulations that may be chosen for specific problems, may not have a fixed order, and may be aimed at converting one problem into another.
A range of computational algorithms and computational strategies will be used.
The standard algorithm does not have to be explicitly taught and mastered until 4th grade.
Continued from page 2
Essential Questions:
Which strategies help me add and subtract numbers? / MCC3.NBT.2
Problems should include both vertical and horizontal forms, including opportunities for students to apply the commutative and associative properties. Adding and subtracting fluently refers to knowledge of procedures, knowledge of when and how to use them appropriately, and skill in performing them flexibly, accurately, and efficiently. Students explain their thinking and how they work by using strategies and algorithms. Students verify that their answer is reasonable.
Example:
65 + 25
Breaking Each Number Into It’s Place Value:
(60 + 5) + (20 + 5) = 80 + 10 = 90
Making Landmark or Friendly Numbers:
I broke apart 65 into 50 + 15 because it is easy to work with 50. Then I added 50 + 25 which was 75. That left 75 + 15 = 90.
Adding Up in Chunks:
I started at 65 and counted up 25 by tens and ones and I landed at 90.
Continued from page 2
Compensation Strategy:
65 + 25
65 + 5 = 70 25 -5 = 20
70 + 20 = 90
The difference between compensation and friendly numbers is that compensation revokes a specific amount from one addend and gives that exact amount to the other addend.
Example:
573 – 399
Students may use several approaches to solve the problem including the traditional algorithm. Examples of other methods students may use are listed below:
Removal or Counting Back Strategy:
573 – 3 = 570
570 – 100 = 470
470 – 70 = 400
400 – 1 = 399
So 3 + 100 + 70 + 1 = 174
Adding up strategy
399 + 1 = 400, 400 + 100 = 500, 500 + 73 = 573, therefore 1 + 100 + 73 = 174 (adding up strategy)
Friendly Numbers Strategy
399 is close to 400. So I will change the problem to 573 – 400 which gives me 173. Then I need to add that 1 back to my 173 to make it 174. / MCC3.NBT.2
Whole Group
BBY: Dots
Let’s Think About Add/Sub pg.68 (with word problems)
Addition Strategy Notebook
Subtraction Strategy Notebook
Introducing Addition and Subtraction with Sketching
Arrow Cards pg.20
I Can Fluently Add
I Can Fluently Subtract
Show What I Know Addition
Show What I Know Subtraction
Show What I Know Strategies
Continued from page 2
Differentiation Activities
Hands On Standards:
·  Adding and Subtracting (lesson 2)
Mental Mathematics pg. 41
Subtraction with Base Ten Blocks
Perfect 500 pg. 47
Take 1,000 pg. 53 (uses estimation)
Take Down pg. 77(subtract from 999 instead of 1,000)
Writing to Win Prompts
Win Win Math Games (“4 Strikes” and “101 and Out”)
Differentiation for Addition Strategies
Differentiation for Subtraction Strategies
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CCGPS / Example/Vocabulary / System Resources
MCC3.MD.3 Draw a scaled picture graph and a scaled bar graph to represent a data set with several categories. Solve one-and two-step “how many more” and “how many less” problems using information presented in scaled bar graphs. For example, draw a bar graph in which each square in the bar graph might represent 5 pets.
In second grade, students drew a picture graph and a bar graph (with a single scale unit) to represent a data set with up to four categories. They had to solve simple addition and subtraction problems using the information presented in the bar graph.
Essential Questions:
How can picture graphs and bar graphs be used to display data?
How do I create a scaled picture graph? How do I create a scaled bar graph?
How do I decide what increments to use for my scale?
How do I use a graph to answer one, two-step questions? / MCC3.MD.3
Students should have opportunities reading and solving problems using scaled graphs before being asked to draw one. The following graphs all use five as the scale interval, but students should experience different intervals to further develop their understanding of scale graphs and number facts.
·  Pictographs: Scaled pictographs include symbols that represent multiple units. Below is an example of a pictograph with symbols that represent multiple units. Graphs should include a title, categories, category label, key and data.
How many more books did Juan read than Nancy?
·  Single bar graphs: Students use both horizontal and vertical bar graphs. Bar graphs include a title, scale, scale label, categories, category label, and data.
Vocabulary
Scale
Scaled picture graph/bar graph
data / MCC3.MD.3
The Hands On Standards lessons can also be used in whole group as introductory lessons.
Whole Group
Animal Investigations
Our Favorite Candy
Creating Pictographs
What’s Your Favorite pg. 107 (Venn diagram section can be an extension to this lesson)
It’s a Data Party pg. 103
Differentiation Activities
Hands On Standards:
·  Pictographs (lesson 7)
·  Bar Graphs (lesson 8)
Differentiation for Pictographs
Differentiation for Bar Graphs
Differentiation for Problem Solving with Data
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CCGPS / Example/Vocabulary / System Resources
MCC3.OA.1 Interpret products of whole numbers, e.g., interpret 5 × 7 as the total number of objects in 5 groups of 7 objects each. For example, describe a context in which a total number of objects can be expressed as 5 × 7.
This is new learning. Second grade did explore with repeated addition.
Essential Questions:
How does multiplication relate to “groups of”? / MCC3.OA.1
Students recognize multiplication as a means to determine the total number of objects when there are a specific number of groups with the same number of objects in each group. Multiplication requires students to think in terms of groups of things rather than individual things. Students learn that the multiplication symbol ‘x’ means “groups of” and problems such as 5 x 7 refer to 5 groups of 7.
Vocabulary
Products
Groups of
Multiplication/multiply
Factor / MCC3.OA.1
The Hands On Standards lessons can also be used in whole group as introductory lessons.
Whole Group
BBY: Dots
BBY: WMPWMV
100 Hungry Ants pg. 19 (need book “100 Hungry Ants” for this activity)
Pictures and Models
Building Arrays
Egg Tower (use egg carton image as a discussion piece for understanding multiplication)pg. 102
Multiplication and Division Representations (just do multiplication part)
Great Video for an Activator
Playing Circles and Stars (pg.5) – Repeated Addition!
Seeing Arrays as Equal Groups pg.16
Differentiation Activities
Hands On Standards:
·  Multiplying with Arrays (lesson 1)
·  Multiplying by 5 (lesson 2)
What’s My Product pg. 39
Array Problems
Array Picture Cards (just multiplication section)
Writing to Win Prompts
Differentiation Activities
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CCGPS / Example/Vocabulary / System Resources
MCC3.OA.2 Interpret whole-number quotients of whole numbers, e.g., interpret 56 ÷ 8 as the number of objects in each share when 56 objects are partitioned equally into 8 shares (how many in each group), or as a number of shares when 56 objects are partitioned into equal shares of 8 objects each (how many groups can you make). For example, describe a context in which a number of shares or a number of groups can be expressed as 56 ÷ 8.
This is new learning.
Essential Questions:
What is the meaning of division?
How can I write a number sentence to represent the two types of division?
How can I tell if a division problem is asking “how many in each group” or “how many groups?” / MCC3.OA.2
Students will need to use repeated subtraction, equal sharing, and forming equal groups to divide large collections of objects and determine factors for multiplication.
This standard focuses on two distinct models of division: partition models and measurement (repeated subtraction) models.
Partition models focus on the questions “How many in each group”? A context for partition models would be: There are 12 cookies on the counter. If you are sharing the cookies equally among three bags, how many cookies will go in each bag?
Measurement (repeated subtraction) models focus on the question, “How many groups can you make”? A context for measurement models would be: There are 12 cookies on the counter. If you put 3 cookies in each bag, how many bags will you fill?
Vocabulary
Quotients/dividend/divisor
Partitioned equally
divide / MCC3.OA.2
The Hands On Standards lessons can also be used in whole group as introductory lessons.
Whole Group
BBY: WMPWMV
Divide and Ride
The Doorbell Rang pg. 43 (Your library should have the children’s book needed for this lesson)
Multiplication and Division Representations (just do division part)
Stuck on Division pg. 64(repeated subtraction)
Solving Division Problems pg.10
Fish Tanks Task
Markers in Boxes
Differentiation Activities
Hands On Standards:
·  Exploring Division (lesson 3)
·  Meaning of Division (lesson 4)
·  More Division (lesson 5)
Array Picture Cards
Writing to Win Prompts
Differentiation Activities
Click here for other lessons and assessments
CCGPS / Example/Vocabulary / System Resources
MCC3.OA.3 Use multiplication and division within 100 to solve word problems in situations involving equal groups, arrays, and measurement quantities, e.g., by using drawings and equations with a symbol for the unknown number to represent the problem.
Students will use drawings or pictures in this quarter for word problems.
In second grade, students learned how to partition a rectangle into rows and columns of same size squares and count to find the total number of them. They did not learn multiplication or division.
Multiplication and division within 100 - Multiplication and division of two whole numbers with whole number answers, and with product or dividend in the range 0 – 100. Example: 72 divided by 8 = 9
See Glossary, Table 2. for examples (click here)
Essential Questions:
In which situations can multiplication and division be used to solve real world problems?
How do I know if I have to multiply in a word problem?
How do I know if I have to divide in a word problem?
See page 7 / MCC3.OA.3
Word problems should be used anytime you are teaching the operations. Students may not know by memory their multiplication/division facts this quarter but they can use other strategies to find the answer. See the table at the end of this document for examples. Students will use drawings or pictures in this quarter for word problems.