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Unit Design ForAddition, Subtraction, and Data

First Grade

Developed by:Katy Thomson

Cesar Chavez Academy 2011- 2012

UBD Unit Design Worksheet / Saginaw Valley State University 1

Understanding by DesignUnit Design Worksheet

Unit Title: Addition, Subtraction, and Data Subject/Course: Math

Topic: Addition, Subtraction, and Data Grade: First Staff Name: Katy Thomson

Stage 1 - Desired Results

Established Goals 1. OA.1 Use addition and subtraction within 20 to solve word problems involving situations of adding to,

taking from, putting together, taking apart, and comparing, with unknowns in all positions, e.g., by using objects, drawings, and equations with a symbol for the unknown number to represent the problem.

2. OA.2 Solve word problems that call for addition of three whole numbers whose sum is less than or equal to 20, e.g., by using objects, drawings, and equations with a symbol for the unknown number to represent the problem.

3. OA.3 Apply properties of operations as strategies to add and subtract. Examples: If 8 + 3 = 11 is known, then 3 + 8 = 11 is also known. (Commutative property of addition.) To add 2 + 6 + 4, the second two numbers can be added to make a ten, so 2 + 6 + 4 = 2 + 10 = 12. (Associative property of addition.)

4. OA.4 Understand subtraction as an unknown-addend problem. For example, subtract 10 – 8 by finding the number that make 10 when added to 8.

5. OA.5 Relate counting to addition and subtraction (e.g., by counting on 2 to add 2).

6. OA.6 Add and subtract within 20, demonstrating fluency for addition and subtraction within 10. Use strategies such as counting on; making ten (e.g., 8 + 6 = 8 + 2 + 4 = 10 + 4 = 14); decomposing a number leading to a ten (e.g., 13 – 4 = 13 – 3 – 1 = 10 – 1 = 9); using the relationship between addition and subtraction (e.g., knowing that 8 + 4 = 12, one knows 12 – 8 = 4); and creating equivalent but easier or known sums (e.g., adding 6 + 7 by creating the known equivalent 6 + 6 + 1 = 12 + 1 = 13).

7. OA.8 Determine the unknown whole number in an addition or subtraction equation relating three whole numbers. For example, determine the unknown number that makes the equation true in each of the equations 8 +? = 11, 5 = ＿ – 3, 6 + 6 = ＿.

8. MD.4 Organize, represent, and interpret data with up to three categories; ask and answer questions about the total number of data points, how many in each category, and how many more or less are in one category than in another.

9. NBT.4 Add within 100, including adding a two-digit number and a one-digit number, and adding a two-digit number and a multiple of 10, using concrete models or drawings and strategies based on place value, properties of operations, and/or the relationship between addition and subtraction; relate the strategy to a written method and explain the reasoning used. Understand that in adding two-digit numbers, one adds tens and tens, ones and ones; and sometimes it is necessary to compose a ten.

10. NBT.6 Subtract multiples of 10 in the range 10-90 from multiples of 10 in the range 10-90 (positive or zero differences), using concrete models or drawings and strategies based on place value, properties of operations, and/or the relationship between addition and subtraction; relate the strategy to a written method and explain the reasoning used.


Understandings:Students will understand…

1. that addition and subtraction is used in everyday situations.

2. that addition is used in everyday situations and sometimes has more than two numbers.

3. that numbers can be added in any order. 3. that in order to subtract, you must start with the

biggest number.4. that addition and subtraction are related and can be

solved by using the opposite operation (and changing the numbers around).

5. that when skip counting is adding the same number over and over again.

6. that when given a total number you can group that amount in any way and still have the total amount.

6. that when given a total amount you can take away different amounts in how ever many groups you would like and still get to 0.

7. that when missing a number in the middle of the number sentence, you can skip count to find a missing number by counting from the first number to the last number.

7. that when missing the number at the end, you can skip count by starting at the beginning number and adding the other number to it.

8. that a graph tells data.8. how to read a graph and compare the categories

together.9. that place values need to be lined up when adding

a two digit number and one digit number.9. that when adding a two digit number, you must

add the ones places together and the tens places together.

10. how to subtract or add in groups.

Essential Questions:

1. How can you solve a number story?2. What are some different ways to add three whole

numbers together?3. When given a number family, how can you show

me two ways to add/subtract?3. When given three one-digit numbers to add

together, how do you simplify it to be adding two numbers instead?

4. When a number is missing in the middle of a subtraction number sentence, how do you figure out what it is?

5. How might you be able to add numbers more quickly?

6. How can you group numbers together to make it easier to add or subtract?

7. When a number is missing in an addition or subtraction number sentence, how do you figure out what it is?

8. How would you create a graph based on given data?

8. How would you interpret this data?9. What are different strategies to add two two-digit

numbers?10. How would you show me in a number sentence

when we are subtracting ten from any number?

Students will know...

1. how to add and subtract numbers between 0 and 20.

1. how to pull numbers out of a number story to solve a problem.

2. how to add and subtract three numbers.3. how to add two numbers together and be able to

switch the numbers around (turn around).

Students will be able to...

1. apply previous learned ways to solve addition and subtraction problems.

1. read a story problem and decipher the important information from it.

2. distinguish which method to use to solve a three addend problem.

3. implement the turn-around facts to solve an


3. how to add numbers in any order to get the same answer.

4. how to skip count by ones.4. how to find a missing number in an equation.5. how to count up and back by 1s, 2s, 5s, and 10s.6. how to group numbers/ items to make adding

easier.6. how to add and subtract numbers up to 20.7. how to add and subtract numbers.7. how to find an unknown number whether in the

beginning, middle, or end of the equation.8. how to read and understand a graph.8. how to compare data from a graph.9. how to add two digit numbers to one digit

numbers.9. how to add two digit numbers to two digit

numbers.9. what place value is (ten’s and one’s place).10. how to count up and back by 10’s.10. how to subtract and add by 10’s.10. how to use place value to help add and subtract

by 10’s.

addition problem.3. recognize when an addition equation can be

turned around to make solving easier.4. count backward and forward by ones.4. solve an equation which contains a missing

number.5. count by ones, twos, fives, and tens.6. find numbers that can be easily added together

(decompose an equation).6. solve addition and subtraction problems within

10 by using and applying various strategies learned.

7. solve addition and subtract by implementing various strategies learned.

7. calculate a missing number within an addition or subtraction equation.

8. read and interpret a graph.8. compare the data on a graph.9. add a two digit number by adding the ones place

to one’s place and the ten’s place to the ten’s place.

10. count forward and backward by tens.10. incorporate various strategies to add and subtract

by tens.10. draw or use base ten blocks or other

manipulatives to add and subtract by tens.

Unit Enduring Understanding:

Students will understand that there are rules to mathematical procedures and how to apply them.

Unit Question:

What are different ways to represent mathematical concepts?

Stage 2 - Assessment EvidencePerformance Tasks:

Goal: Students will solve different scenarios to show their understanding of addition, subtraction, and graphing.

Role: Students will play the role of a ticket booth attendant.

Audience: Carnival Consumers (students)

Situation: Ticket booth attendants will be given different scenarios as they play out the role. Each scenario will either have them add, subtract, or find to find missing number within the equation.


First Scenario (adding one digit to one digit number): Consumers will choose two rides to go on. Ticket attendant will have to add those two numbers up to tell consumer how much he/she owes. Student must write down the equation they just created on paper. (Must be done correctly 5 times in a row to master.) Students may only choose from list one.

Second Scenario (adding one digit to a two digit number): Consumers will choose two rides to go on. Ticket attendant will have to add those two numbers up to tell consumer how much he/she owes. Student must write down the equation they just created on paper. Student must write down the equation they just created on paper. (Must be done correctly 5 times in a row to master.) Students must first pick one ride from list one AND THEN one ride from list two.

Third Scenario (adding two digit to a one digit number): Consumers will choose two rides to go on. Ticket attendant will have to add those two numbers up to tell consumer how much he/she owes. Student must write down the equation they just created on paper. (Must be done correctly 5 times in a row to master.) Students must first pick one ride from list two AND THEN one ride from list one.

Fourth Scenario (adding two digit to a two digit number): Consumers will choose two rides to go on. Ticket attendant will have to add those two numbers up to tell consumer how much he/she owes. Student must write down the equation they just created on paper. (Must be done correctly 5 times in a row to master.) Students must pick two rides from list two.

Fifth Scenario (finding the missing addend): Consumers will buy tickets, but not know how many they need. They will tell the ticket attendant how many they have and what ride they want to go on. The ticket attendant will need to figure out how many tickets to give the consumers. Student must write down the equation they just created on paper. (Must be done correctly 5 times in a row to master.).

Sixth Scenario (subtraction) :Consumer will tell ticket attendant how many tickets they have. They will tell them what ride they want to go on (from list one). Ticket attendant will have to figure out how many tickets they will have left after they pay it. Student must write down the equation they just created on paper. (Must be done correctly 5 times in a row to master.).

Seventh Scenario (graphing): All students will be given a graph to interpret. They will have to tell which ride was the most liked the least liked, compare two rides together and state how many more people liked it. Last they will have to add their own favorite and then compare that ride to another.

Product: You will choose a method to solve each scenario.

Standards for Success: Students will be observed within each scenario. Scenario papers will be collected after each scenario to ensure students’ understanding. A rubric will be used to grade the students’ performance (how long it took them to solve the problem) and mathematical usage (equations they wrote down).


Key Criteria:

Rubric for Carnival Ticket Attendant

Other Evidence: Lesson pretests, observations, student work samples, posttests

BEFOREPrior knowledgeTeacher will ask questions to see what students already know about each topic.

Pictures and manipulativesStudents will be able to use manipulatives to solve problems

DURING

Using manipulatives and drawing picturesStudents will use pictures and manipulatives to help solve problems they are given.

Conference

AFTER

PosttestA posttest will be given after each standard is taught.

ConferenceTeacher will walk about the classroom and conference with


MMastered

Able to solve scenario with little

problem.

PProgressing

Able to solve scenario with some

problems.

UUnderdevelopedUnable to solve

scenario independently

Scenario 1: Adding a one digit to one digit numberScenario 2:Adding a one digit to two digit number

Scenario 3:Adding a two digit to one digit number

Scenario 4:Adding a two digit to two digit number

Scenario 5: Finding the missing number within an equation

Scenario 6: Subtracting a one digit number form a two digit numberScenario 7: Interpret a Graph

given.

PretestA pretest will be given before each standard is taught.

BrainstormStudents will brainstorm ideas of how to solve a problem before they have learned any strategies in the classroom.

QuestionsStudents will ask questions on what they may not understand about the topic.

DiscussionStudents will question and answer questions about each topic.

Count up and back by 1’s, 2’s, 5’s, and 10’sStudents will orally practice counting out loud.

KWLStudents will state what they already know about the topic, what they want to know about the topic (and later) what they learned about the topic.

Teacher will walk about the classroom and conference with students as they work on independent work.

Small group/ whole group workStudents will work together to reinforce learning.

Class discussionStudents will question and answer questions about each topic.

Counting objects in groupsStudents will orally practice counting out loud.

Create a graphStudents will read and interpret a graph after the topic is taught.

students as they work on independent work.

Add to brainstorming listStudents will add information they have learned for the day to the brainstorming list to reference to later.

Daily assignmentStudents will complete assignment based on each standard taught to gain experience with the topic.

Class discussionStudents will question and answer questions about each topic.

Mental Math Test adding 1’s, 2’s, 5’s, and 10’sStudents will orally practice counting out loud.

Create and interpret graphsStudents will read and interpret a graph after the topic is taught.

Describe the assessment/s and state the prompt if applicable. x F x S

What type of scoring tools will be used for evaluation?

□ Analytic rubric □ Checklist□ Holistic rubric □ Answer Keyx Criterion rubric □ Other


Student Self-Assessment and Reflection:

Students will write down what property they have used and compare it to the correct answer given to them. They will reassess how they solved the problem and attempt to figure out where they may have made a mistake. Students may use pictures, manipulatives, or equations to solve the problems each time.

Stage 3 - Learning Plan

Differentiated Instruction:

VOCABULARYObjective: Students will be able to show understanding of vocabulary taught for each lesson.Layer C: (Chose one of the following two choices)

1. Students will read and use hand gestures to define each vocabulary word.2. Students will use manipulatives and pictures to demonstrate the vocabulary word (if possible).

Layer B: (Chose one of the following two choices)1. Students will match the vocabulary word with the definition on paper.2. Students will verbally define the vocabulary word.

Layer A: (Chose one of the following two choices)1. Students will write a definition for the vocabulary words given.2. Students will verbally teach another child what each vocabulary word means.

ADD/ SUBTRACT WHOLE NUMBERSObjective: Students will be able to add and subtract whole numbers. They will have both (+ and -) situations to show their understanding of both addition and subtraction.Layer C: (Chose one of the following two choices)

1. Students will use dominoes to count the number and then add each side to find the sum. They will record the domino and the sum of each domino on a recording sheet. Repeat with subtraction.

2. Students will orally count out loud forwards by 2’s, 5’s, and 10’s and forwards and backwards by 1’s.

Layer B: (Chose one of the following two choices)1. Students will solve one digit to one digit addition and subtraction problems within a timed limit.2. Students will create their own addition and subtraction equation using a one digit and two digit addition

or subtraction and have a friend solve it, as well as solve one for a friend.

Layer A: (Chose one of the following two choices)1. Students will solve a missing addend worksheet. (2 + ___ = 5)2. Students will solve scenario problems in the unit assessment carnival game.

FACT FAMILIESObjective: Students will be able to recognize that the three numbers within an addition or subtraction problem are related.Layer C: (Chose one of the following two choices)

1. Students will use an interactive whiteboard to physically move numbers from the family to create the UBD Unit Design Worksheet / Saginaw Valley State University 9

related addition and subtraction facts.2. Students will use fact family flashcards to verbally say the addition and subtraction facts.

Layer B: (Chose one of the following two choices)1. Given a fact family, students will write out the addition and subtraction facts that relate to them.2. Students will use fact family flashcards to physically write the addition and subtraction facts.

Layer A: (Chose one of the following two choices)1. Students will fill in missing numbers on the fact family triangle then solve for the addition and

subtraction facts.2. Students will create their own fact family to have a friend solve for them.

WORD PROBLEMSObjective: Students will be able to solve real world problems using addition and subtraction strategies.Layer C: (Chose one of the following two choices)

1. Students will act out word problems and physically use their bodies to solve the problem. (There are 26 students in the class 3 go home sick, how many are left. Three students leave the group to show 26 – 3).

2. Students will play computer game which incorporates pictures and movements in a word problem. (Also, word problem is read to them by the computer.)

Layer B: (Chose one of the following two choices)1. Students will work in a small group (3 – 4 students) to solve problems. They will draw pictures to

represent the word problem.2. Students will work as a group to use manipulatives to solve word problems given to them as they

compete against other groups.

Layer A: (Chose one of the following two choices)1. Students will create a real world problem for their peers to solve.2. Students will solve scenario problems in the unit assessment carnival game.

GRAPHSObjective: Students will be able to read and interpret a graph.Layer C: (Chose one of the following two choices)

1. Students will read a graph within a group of peers and compare elements on it.2. Students will work as a group to transfer the tallied information (example favorite ice cream:

strawberry= They would then graph five for strawberry, etc. onto a graph and then count how many each element has.)

Layer B: (Chose one of the following two choices)1. Students will read and interpret a given graph.2. Students will fill in a labeled graph based on given information (through labels and tallies, example

favorite ice cream: strawberry= They would then graph five for strawberry, etc.)

Layer A: (Chose one of the following two choices)1. Students will label and fill in their own graph by keeping tallies on student voting and then creating a

graph based on that information.2. Students will compare and record a graph (already created). Then they will add their own opinion onto

it and compare again.


Learning Activities:

W: In this unit of study, first grade students will discover the world of numbers. They will understand when adding two numbers, the sum will be larger and when subtracting two numbers, the first number will get smaller. Additionally, they will read and interpret graphs based on relatable information.

H: Through hands on experiences with manipulatives and pictures, students will be exposed to addition and subtraction in a variety of ways. They will take a classroom vote on favorite things to create a classroom graph and then read and interpret it. Furthermore, related learning centers will occur throughout the unit.

E: Students will be equipped for expected performance through whole group teaching and modeling, small group practice, independent practice, and hands on experiences. The application of the each core standard will be evident through their homework, group work, independent work, “extra time,” or bell work.

R: To help students rethink and revise during this unit of teaching, students will have many opportunities to discuss and share strategies for each day. The teacher will take time to conference with students during independent practices to ensure that he/she understands and does not have any questions. Student will also have time to interact with other students during small group practice as well as learning centers.

E: Students will be able to self-evaluate and reflect on their learning during whole group discussion, as well as small group practice, independent work, and learning centers, in which they can share their strategies and questions.

T: Learning will be tailored for students by teaching many strategies for each standard. Students will not be expected to solve a mathematic problem only one way. They will be free to choose how they want to solve a problem whether they are working in a group, independently, or completing an assessment. Also, students will not move on to the next level until they have shown progression or understanding or have mastered the concept. (see Layered Curriculum)

O: The unit will be taught starting with the most basic (adding and subtracting one digit numbers) and progressively move into more complex concepts. Each concept will be applied to the next level as they are taught. Students will not move on until the previous level is progressing or mastered. The unit will be completed with an interactive activity that will test on all core standards stated. However, students will be assessed on each core standard as they are taught. (see Calendar)

Essential Vocabulary

Add: to find the sum of

Addition: the act or process of adding or uniting

Adding to: to unite or join so as to increase the number, quantity, size, or importance

Associative Property: adding or multiplying regardless of how the numbers are grouped within the parenthesis

Comparing: to examine (two or more objects, ideas, people, etc.) in order to note similarities and differences

Commutative property: having the property that one term operating on a second is equal to the second operating on the first

Concrete Models: using an object or pictures to represent one’s thinking


http://dictionary.reference.com/browse/add

Counting: to list or name numerals in order

Data: individual facts, statistics, or items of information

Data points: a single fact or piece of information from a graph

Equal: like or alike in quantity

Equations: equally balanced state

Equivalent: equal in value, measure

Fluent: spoken or written with ease

Less: to a smaller extent, amount, or degree

Multiples of 10: any number ending in zero

More: in greater quantity, amount, measure, degree, or number

Objects/ manipulative: objects or pictures to help solve problems

One digit: a number containing only one place value

Operations: the action of applying a mathematical process to a quantity or quantities

Place value: the value of the place, or position, of a digit in a number or series

Properties of Operations: identifying which operation to use (associative or commutative)

Putting together: adding

Strategies: a plan, method, or series of maneuvers

Subtract: to withdraw or take away, as a part from a whole

Subtraction: to withdraw or take away, as a part from a whole

Symbols: a letter, figure, or other character or mark or a combination of letters or the like used to designate something

Sum: a series of numbers or quantities to be added up

Taking apart: subtract

Taking from: the act of subtracting a number from another number

Two digit: a number containing two place values

Unknown Addend: a number which is part of an addition

Whole numbers: one of the positive integers or zero; any of the numbers (0, 1, 2)

Word Problems: mathematical problems expressed in narrative form


http://dictionary.reference.com/browse/integers

Sequencing the Learning

MONDAYLesson 1/ Day 1

Pretest for lesson 1- Addition/ Subtraction of Whole Numbers

Introduce vocabulary

Vocabulary layer C activity

Introduce addition subtraction whole numbers. Have students brainstorm different ways to add or subtract.

Do layer C activities for this lesson. Students will use manipulatives to add and subtract.

Teacher led activities and minimum independent work.

Homework daily assignment

TUESDAYLesson 1/ Day 2

Review vocabulary

Vocab layer C activity

Review addition and subtraction of whole numbers

Teacher will ask and answer questions about addition and subtraction.

Do layer C activities for this lesson in which students use pictures and manipulatives to help them add.

Whole group activities and moderate independent work.


WEDNESDAYLesson 1/ Day 3

Review vocabulary

Vocab layer B activity


Students will practice counting forward and backward to review an addition and subtraction strategy.

Do layer B activities for this lesson which will include students solving addition and subtraction problems.

Teacher will walk around and conference with students to check for understanding.

Whole group activities and moderate independent work

THURSDAYLesson 1/ Day 4

Review vocabulary



Students will take a mental math test to test their understanding.

Do layer B activities for this lesson which will include students solving addition and subtraction problems.

Teacher will walk around and conference with students to check for understanding.

Small group activities and independent work


FRIDAYLesson 1/ Day 5

Review vocabulary

Vocab layer A activity


Do layer A activities for this lesson. Here students will solve missing problems with addends.

Posttest for lesson 1- addition and subtraction



Pretest for lesson 2- Fact Families

Introduce


Review vocabulary

Vocab layer B


Review vocabulary

Vocab layer B


Review vocabulary

Vocab layer A


Pretest for lesson 3- Word Problems

Introduce


vocabulary

Vocab layer C

Introduce fact family triangles

Access prior knowledge through discussion on addition and subtraction.

Have students discuss what they know about addition and subtractions. Fill out KWL chart.

Do layer C activities for this lesson.

Teacher led whole group activities


Review fact family

Do layer B activities for this lesson. Here the students will work in a small group to find the addition and subtraction facts.

Teacher will conference with groups.



Review fact family through discussion

Students will add to KWL brainstorming list to show what they have learned about fact families.

Do layer B activities for this lesson. Students will have more practice in small groups to solve for addition and subtraction facts.



Review fact families

Do layer A activities for this lesson. Students will fill in missing number in a triangle then find the addition and subtraction facts.

Posttest for lesson 2- fact families


vocabulary

Vocab layer C

Introduce word problems

Do layer C activities for this lesson. Here teacher will have students act out word problems.

Teacher led whole group activities.



Review vocabulary

Vocab layer C

Review word problems

Do layer C activities for this lesson. Students will take turns on computers to play games which include word problem solving skills. (centers


Review vocabulary

Vocab layer B


Do layer B activities for this lesson. Given manipulatives, students will solve word problems in a small group.

Small group


Review vocabulary

Vocab layer A


Do layer A activities for this lesson. Students will create a word problem by themselves and have a friend solve it. If time allotted, students will create


Pretest for lesson 4- graphs

Introduce vocabulary

Vocab layer C

Introduce graphs

Do layer C activities for this lesson. As whole group, have students decide what kind of ice


Review vocabulary

Vocab layer C activity

Review graphs

Do layer C activities for this lesson. Create another graph as a group. Read and interpret asking questions including more than, less than, how many


based)

Whole group activities, small group activities, and moderate independent work.


activities and independent work


more.

Teacher will conference with students during independent work.

Posttest for lesson 2- word problems


cream they like, add a tally to a list for each flavor. Create a graph based on this and have students read and interpret it.

Teacher led whole group activities


more, etc.

Whole group activities and moderate independent work



Review vocabulary


Review graphs

Do layer B activities for this lesson. As small groups, pass out a graph to each group and have students read the graph and answer the questions given.




Review vocabulary


Review graphs

Do layer B activities for this lesson. Have students use information given and create (fill in) a graph with the information. (6 kids like dogs… students fill in 6 squares by dog).




Review vocabulary

Vocab layer A activity

Review graphs

Do layer A activities for this lesson. Students will keep track by taking tallies (on a certain topic) and create their own graph based off of it. They will then interpret and answer questions based on it.

Posttest for lesson 4- graphs


THURSDAYUnit Review

Review ALL vocabulary

Do layer A activities in a center like environment. Include addition of one digit and two digit numbers, three one digit numbers, subtraction, missing addends, addition and subtraction facts, word problems, and graphs.

(Each activity is done by a group for about 10 minutes, then they switch to another activity)


FRIDAYUnit Test

Students will complete assessment by solving scenario problems.


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