Grade 3 Unit 1: Rounding, Addition and Subtraction Algorithms of

Numbers to 100 (4 Weeks)

Stage 1 – Desired Results

Unit Description Students build on their work they did in grade 2 in order to fluently add and subtract within 1000 using strategies and algorithms based on place value, properties of operation, and/or the relationship between addition and subtraction. 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. Established Goals Common Core Learning Standards 3.NBT.1. Use place value understanding to round whole numbers to the nearest 10 or 100. 3.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. 3.OA.9 Identify arithmetic patterns (including patterns in the addition table) and explain them using properties of operations. For example, an odd number plus and odd number will always be an even number. Common Core Standards of Mathematical Practice

Make sense of problems and persevere in solving them.

Reason abstractly and quantitatively.

Construct viable arguments and critique the reasoning of others.

Model with mathematics.

Use appropriate tools strategically.

Attend to precision.

Look for and make use of structure.

Look for and express regularity in repeated reasoning. ESL Language Standards

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 information, using a variety of organizational patterns or structures.

3.4 Evaluate students’ own and others’ work, individually and collaboratively, on the basis of a variety of criteria.

3.9 apply learning strategies to examine, interpret, and evaluate a variety of materials. Bridge Guidance Grade 2 Standards

2.OA.1 Use addition & subtraction strategies within 100 to solve one & two3

step word problems involving situations of

adding to, taking from, putting together, taking apart, & comparing, with unknowns in all positions,4

e.g., by using drawings & equations with a symbol for the unknown number to represent the problem. 2.NBT.3 Read & write numbers to 1000 using base-ten numerals, number names, & expanded form. 2.NBT.7 Add & subtract within 1000, using concrete models or drawings & strategies based on place value, properties of operations, &/or the relationship between addition & subtraction: relate the strategy to a written method. Understand that in adding or subtracting three-digit numbers, one adds or subtracts hundreds & hundreds, tens & tens, ones & ones; & sometimes it is necessary to compose or decompose tens or hundreds.

Before teaching this unit – students should know: Numbers – the set of real numbers is infinite, and each real number can be associated with a unique point on the number line.

Big Ideas 1. The base ten numeration system is a scheme for

recording numbers using digits 0-9, groups of ten, and place value.

2. Any number, measure, numerical expression, algebraic

expression or equation can be represented in an infinite number of ways that have the same value.

3. The same number sentence can be associated with different concrete or real world situations, AND different number sentences can be associated with the same concrete or real world situations.

4. Numerical calculations can be approximated by replacing numbers with other numbers that are close and easy to compute with mentally.

Essential Questions 1. How does where we place a digit change its value? 1. Why is our number system called the Base-10 system? 2. How can decomposing numbers help us become mental math masters? Is there a limit to the number of ways we can represent numbers? 2. How can we use place value to rename numbers in a variety of ways? (2 hundreds + 4 tens = 24 tens) 3. Addition and subtraction have an inverse relationship. What does that mean? 3. How can the inverse relationships between addition and subtraction help us to compute and problem solve? 4. Why and when do we need to round numbers?

Content (Students will know….) A. Our number system is built around groups of 10

(powers of 10)

B. Digits have different values depending on which place they are in

C. Multiple strategies and algorithms for addition and

subtraction

D. Arithmetic patterns exist in the addition and multiplication table that can be explained using properties of operations* (see Learning Plan resources for more guidance on this standard)

Skills (Students will be able to…) A1. Round numbers to the nearest 10 or 100

B1. Round numbers using a number line or 100s chart

C1. Fluently add and subtract numbers up to 1,000 using their choice of strategies and algorithms such as:

Decomposing numbers

Making tens or hundreds

Skip Counting

Distributive property (partial sums)

Commutative property (a + b = b + a)

Associative Property (a+ b) + c = a + (b + c)

Vertical algorithms

Horizontal algorithms

Use the relationship between addition and subtraction (if a + b = c, then c – a = b and c – b = a)

D1. Identify arithmetic patterns in both addition and multiplication (patterns that change by the same rate such as 2, 4, 6, 8….)

D2. Identify patterns related to properties of operations (even numbers are divisible by 2, multiples of even numbers are always even, the products in a multiplication

table increase by the same amount, etc)

D3. Explain why patterns observed in addition and multiplication tables make sense mathematically (use the commutative property to explain that 6 x 8 = 8 x 6 and show that in a multiplication table, etc)

Terms/ Vocabulary add addend addition sum commutative property associative property distributive property difference expanded notation decompose groups (equal and not equal)

Interval Inverse operation Place value Tens, hundreds, ones, thousands Round Base ten Number Digit Number line Horizontal Vertical

Standard form Efficient Compute Strategies Subtract Subtrahend Subtraction Operation Represent Algorithm

Stage 2 – Assessment Evidence

Performance Task Initial Performance Task Final Performance Task: Sweet Tooth

Other Evidence Teacher observations, conferencing, teacher designed formative assessment pieces, student work, exit slips, journals, reflections, etc.

Stage 3 – Learning Plan

Everyday Mathematics CCLS aligned lessons – the following lessons will support some of the CCLS and essential questions found in this unit map.

3.NBT.1: 1-11, 2-7, 2-8, 5.2, 5.5 (7.7 if students are ready)

3.NBT.2: 1-4, 1-8, 1-9, 1-11, 1-13, 2-1, 2-3, 2-4, 2-5, 2-6, 2-7, 2-8, 2-9

3.OA.9 : 1-9, 2-2, 4-8 Throughout the course of this unit students should be given opportunities to engage in the following:

Know when/how to apply the correct operation in problem solving situations

Write their own addition and subtraction number stories in a variety of formats (see table 1 below)

Represent their solutions in a variety of ways and modalities

Share computational strategies and build upon the mathematical thinking of peers

Judge and prove/disprove the efficiency of problem solving/computation strategies

Apply estimation to solve problems, and determine when it is necessary and appropriate to apply estimation strategies

Teaching resources *For guidance on any standard, especially 3.OA.9:

http://www.dpi.state.nc.us/docs/acre/standards/common-core-tools/unpacking/math/3rd.pdf http://www.rda.aps.edu/mathtaskbank/pdfs/tasks/3-5/t35build.pdf Introductory task “Build 1000” - this link provides a hands on place value task to get students excited about building and representing large numbers. It is very teacher friendly and easy to follow. http://www.explorelearning.com/index.cfm?method=cResource.dspDetail&ResourceID=1024 Here's a link to an interactive number line that teaches students how to round. The website includes student investigation sheets. A free trial is available https://www.georgiastandards.org/Common-

Acknowledgements: This unit and tasks were developed by Elyse Mattiaccio (PS 396X) and Martina Henry (PS 85X) in conjunction with Caitlin Boyle (CFN 109), Yehonela Ortiz (CFN 109), and Melissa Torres (CFN 109) and edited by Minnie Shu Iannuzzi (CFN 109)

Core/Common%20Core%20Frameworks/CCGPS_Math_3_Unit1FrameworkSE.pdf This site provides a unit on number sense and numeration – some of the lessons and tasks provided cover the standards and essential questions addressed in this unit. The resources are readily accessible and teacher friendly. http://www.k-5mathteachingresources.com/3rd-grade-number-activities.html This site shares a variety of games and activities organized by CCLS. Includes read-alouds, sample problems, center activities and task cards that will support the teaching of this unit. http://nlvm.usu.edu/en/nav/category_g_2_t_1.html National library of Virtual Manipulatives: Base Blocks, Base Blocks Addition, and Base Blocks Subtraction are especially helpful during this unit.

Name __________________________________

Grade 3 Unit 1

Initial Performance Task

1. Jose used base ten blocks to make the number 263. Show two or more possible

combinations for the number 263 using pictures, words or symbols in the space below

2. Round 263 to the nearest 10 ________

3. Round 263 to the nearest 100________

4. Using what you know about place value, explain why your answers to #2 and #3 are

correct.

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5. Jose’s school just ordered 294 chapter books and 407 picture books.

a) How many total books did the school order? Show your work

b) How many more picture books did they order than chapter books? Show your work.

c) Write an addition equation that will help you check your work to 5b.

6. Look at the addition table below:

Write down at least one pattern in the numbers from the table.

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Explain why you think this pattern formed.

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Grade 3 Unit 1 Initial Task Scoring Guide

Initial Task Rubric

Points Section Points

1. Using pictures, words, or symbols:

Student shows one equivalent representation of the number 263

Student shows another equivalent representation of the number 263

1

1

2

2. Student correctly rounds 263 to the nearest 10 (260) 1 1

3. Student correctly rounds 263 to the nearest 100 (300) 1 1

4. Student explanation shows a clear understanding of place value. For

example, “I know 263 is between 260 and 270. It is 3 whole numbers away

from 260, but 7 away from 270. It’s closer to 260. (1 point for clearly

explaining each rounded number)

2 2

a) Student adds and gives correct answer of 701 Student uses traditional algorithm or an efficient strategy such as counting up from 294 in 2 or 3 friendly jumps (+6, +107 or +6, +100, +7)

b) Student subtracts and gives a correct answer of 110 Student uses traditional algorithm or an efficient strategy

c) Student uses the inverse operation to check (113 + 297 = 407)

1

1

1

1

1

5

5. Student names at least one pattern Student explains the pattern. For example, “the diagonal 2, 4, 6, 8, 10, 12... are all even numbers because they are the sums of doubles facts. Both even+ even or odd+ odd will always give an even sum” or, “The numbers increase by 2s because each addend is increasing by 1 (and there are 2 addends)”

**There are many possible responses here. Award points if they use mathematically sound reasoning.**

1

1

2

Total Points

13

13

Novice Apprentice Practitioner Expert

0- 3 points 4 - 6 points 7 - 10 points 11 - 13 points

Name: ____________________________

Grade 3 Unit 1 Final Performance Task: Sweet Tooth

1) Leo went the candy shop and bought two (2) bags of Sour Patch Kids. Each bag has an EVEN number of candies. Is the sum of the bags odd or even? Prove your thinking with MORE THAN 1 example. 2) Kayla buys two (2) bags of Skittles. Each bag has an ODD number of candies.

a) Will the sum be odd or even? Show how you know.

b) Janna decides to buy another bag, for a total of three (3) bags. Will the sum be odd or even? Show how you know.

3) Jasmine loves candy. On Monday, she buys 4 Swedish Fish. On Tuesday, she buys 8 Swedish Fish. On Wednesday, she buys 12 Swedish Fish. a) If this pattern continues, how many Swedish fish will Jasmine buy on Sunday? b) How many Swedish Fish in all will she have bought during the week? Using pictures, words, symbols or charts, show all of your mathematical thinking below.

*Adapted from Exemplars, “Flying South”

4) Michonne’s teacher bought 2 mystery bags filled with m & m’s. She is trying to guess the amount in each bag by using these clues:

Clue #1: When you add 573 to the mystery amount in bag A, the sum is 800.

a) How many m & m’s does the teacher have in Bag A? Show your work. Clue #2: If you take 389 m & m’s out of bag B, you’ll be left with 247.

b) How many m & m’s does the teacher have in Bag B? Show your work.

5) Another teacher has 428 m & m’s. One student says that’s about 400. Another

student says that’s about 430. Use what you know about place value and rounding to explain why they are both correct.

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_____________________________________________________________________ _____________________________________________________________________

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BAG B ??? BAG A ???

Grade 3 Unit 1 Final Performance Task Scoring Guide

Points Section

Points

1. Student gives correct answer (even) Student gives numerical (2+4=6) or pictorial examples to show their thinking

1

1

2

2. a) Student gives correct answer (even)

Student shows with at least one example (pictures, words or number sentence)

b) Student gives correct answer (odd) Student shows answer with at least one example (pictures, words, or number sentence)

1

1

1

1

4

3. a) Student gives correct answer (28 Swedish Fish) and

shows their mathematical thinking. For example: Shows the arithmetic pattern of +4, shows a t- chart, multiplies by 4, etc

b) Student gives correct answer (112 Swedish Fish) and shows their mathematical thinking. For example, using a t- chart with a running total, adding on or adding all numbers from 7 days together using a traditional algorithm

2

2

4

4. a) Student gives correct answer (227)

Student shows a correct procedure or method

b) Student gives correct answer (636) Student shows a correct procedure or method

1

1

1

1

4

5. Student gives correct answer: They’re both correct, because we can round to different places. If we choose to round to the nearest 100, then 400 is correct because 428 is closer to 400, than 500. If we choose to round to the nearest ten, then 430 is correct because 428 is only 2 whole numbers away from 430, but it’s 8 away from 420.

2 2

Total Points 16 16

Novice Apprentice Practitioner Expert

0 - 4 5- 8 9 - 13 14 - 16