ACES Regional Curriculum Consortium Math Unit Organizer

Grade/Subject 2nd Grade Math

Unit Title Unit 1- Fact Strategies: Addition and Subtraction Up to 20

Overview of Unit This is a short unit focusing on fact fluency and application of facts while setting up a community of math learners that will help them persevere. A variety of addition and subtraction strategies will be developed to promote an in depth understanding so students will have multiple approaches to help them persevere with complex problems. This unit will also be setting up “accountable talk” and standards for mathematical practices. Pacing 15 days= 10 days for instruction plus 5 for reteaching/enrichment

Background Information For The Teacher

Back ground Information:

In grade one, students learned to solve addition and subtraction facts fluently within 10 through the use of variety of strategies. In this unit students will review these strategies (such as counting on, make a ten, fact families, think addition, doubles, doubles plus one, etc.) in order to fluently add and subtract within 20.

Fluency is not only rote recall of memorized facts but includes reasoning that enables a student to arrive at an answer using mental math with their own strategy providing an answer within 1-3 seconds. As Van de Walle states “mastery of basic fact means that a child can give a quick response (in about 3 seconds) without resorting to non-efficient means, such as counting.” (Teaching Student-Centered Mathematics Grades K-3, Van de Walle Professional Mathematics Series, 2006)

A vocabulary word that will be used in this unit is decompose. Decompose means to break apart numbers. Students in previous grades have been introduced to this word. We apply decomposing within the “make a ten strategy” to add and subtract.

For example:

Make a Ten to add: 7 + 5= _____

 Step 1: Start with the smaller addend. Break apart the smaller addend to make a ten. *Be sure to choose two numbers that will allow you to make a ten with the greater addend.

7 + 5 ^ (3+2) 1 | M a t h U n i t O r g a n i z e r ACES Regional Curriculum Consortium Math Unit Organizer

 Step 2: You need to add 3 to 7 to make a ten so break apart 5 as 3 + 2. 7 + 5 ^ ^ (7) + (3+ 2) (7 + 3= 10) (2)  Step 3: Add on the rest to the 10. 10 + 2 = 12  Step 4: Write the sum. 7 + 5= 12 Make a ten to subtract: 14 - 5 = ______ Step 1: Start with the greater number. In this number, identify the digit in the ones column. (14) In this case, 4 is the digit in the ones column.  Step 2: Decompose the other number, 5, in a way so it is broken apart and includes a 4 (the digit from the ones column from the first number, 14) 5 ^ (4 + 1)  Step 3: 14 - 4= 10 (1)  Step 4: Now subtract the rest (what is left over from breaking apart the 5) from the 10. 1 is left over. 10 – 1= 9.  Step 5: Write the difference from the original number sentence. 14 - 5 = 9 Strategies:  Counting On- have students start with the greater number and add on the rest.  Fact Families- a group of numbers that are related to each other in that those numbers can be combined to create a number of equations. Example: 4 + 5= 9, 5 + 4= 9, 9 – 5= 4, 9 - 4= 5  Doubles- doubles fact is a number sentence where two of the same addends are added together.  Doubles plus 1- are the facts in which one addend is larger than the other by one. Examples 3+4=7, 6+7=13, 5+6=11, 3+2=5. Learning your doubles plus one should involve knowing the doubles and mentally adding the additional one.

 Make a ten: is used when the two addends in the number sentence can make exactly ten or more.

o Extensive practice with visualizing numbers on ten frames or double ten frames and other pictorial representation is especially helpful with this strategy, so that students can apply their understanding of decomposing numbers and the counting up strategy.

 Think- addition- relates subtraction to addition. So when a child sees 9-4, he or she thinks 4 and what makes 9. The student is using known addition facts to find the unknown addition part (applying their understanding of the relationship between addition and subtraction).

Further exploration of strategies and fluency will be ongoing and revisited in future units. Helping students to fill their mental toolboxes with multiple strategies will enable them to try multiple approaches when confronted with a complex

2 | M a t h U n i t O r g a n i z e r ACES Regional Curriculum Consortium Math Unit Organizer problem (persevere).

3 | M a t h U n i t O r g a n i z e r Essential Questions (and Corresponding Big Ideas)  How can models and pictures help us solve mathematical problems? o ModelsACES and Regionalpictures are Curriculum concrete ways Consortium to help us make Math sense Unit of Organizer problems and persevere in solving them.  Why is it important to understand place value? o Place value is based on groups of ten.  How do different models for addition and subtraction help to efficiently find sums and differences? o We combine or break apart numbers in different ways in order to solve real world problems. o Quick recall of mental addition and subtraction strategies helps to compute larger and smaller numbers. Core Content and Practice Standards Explanations and Examples* 2.OA.1. Use addition and subtraction within 2.OA.1. Word problems that are connected to students’ lives 100 to solve one- and two-step word can be used to develop fluency with addition and subtraction. problems involving situations of adding to, The examples below describe the four different addition and taking from, putting together, taking apart, subtraction situations and their relationship to the position of and comparing, with unknowns in all the unknown. positions, e.g., by using drawings and equations with a symbol for the unknown Examples: number to represent the problem. • Take-from example: David had 63 stickers. He gave 37 to Susan. How many stickers does David have now? 63 – 37 = • Add to example: David had $37. His grandpa gave him some money for his birthday. Now he has $63. How much money did David’s grandpa give him? $37 + = $63 • Compare example: David has 63 stickers. Susan has 37 stickers. How many more stickers does David have than Susan? 63 – 37 = Even though the modeling of the two problems above is different, the equation, 63 - 37 = ?, can represent both situations (How many more do I need to make 63?) • Take-from (Start Unknown) David had some stickers. He gave 37 to Susan. Now he has 26 stickers. How many stickers did David have before? - 37 = 26

It is important to attend to the difficulty level of the problem situations in relation to the position of the unknown.

• Result Unknown problems are the least complex for students followed by Total Unknown and Difference Unknown. • The next level of difficulty includes Change Unknown, Addend Unknown, followed by Bigger Unknown. • The most difficult are Start Unknown, Both Addends Unknown, and Smaller Unknown.

Second grade students should work on ALL problem types regardless of the level of difficulty. Students can use interactive whiteboard or document camera to demonstrate and justify their thinking. 4 | M a t h U n i t O r g a n i z e r This standard focuses on developing an algebraic representation of a word problem through addition and subtraction --the intent is not to introduce traditional algorithms or rules. 2.OA.2. Fluently add and subtract within 20 ACES Regional Curriculum Consortium Math Unit Organizer

Academic Vocabulary

 addition  subtraction  fluent (fluently)  strategies  mental math  sum  difference  equal  addends  solve  composing/decomposing  part-part-whole  Strategies: Count on, think addition, decompose, doubles, doubles plus two Literature Connections

Children’s Literature: 12 Ways To Get To 11 by Eve Merriam 12 Ways To Get To 11 by Eve Mernam Just Enough Carrots by Stuart Murphy Double The Ducks by Stuart Murphy Mice Twice by Joseph Low Grapes of Math by Greg Tang Bunches and Bunches of Bunnies by Matthews Annie’s One to Ten by Annie Owen Two Ways to Count to Ten by Ruby Dee Math Potatoes by Greg Tang Counting Crocodiles by Judy Sierra One Watermelon Seed by Celia Barker The M&M's Brand Counting Book by Barbara McGrath Lottridge Annno’s Counting House by Mitsumasa Anno More Than One by Miriam Schlein The Doorbell Rang by Pat Hutchins What Comes In 2's, 3's, 4's? by Suzanne Aker Six Dinner Sid by Inga Moore One Hungry Cat by Joanne Rocklin Each Orange Had 8 Slices by Paul Giganti Monster Math by Grace Maccarone Domino Addition by Lynette Long, Ph.D. The Baseball Counting Book by Barbara McGrath My Little Sister Ate One Hare by Bill Grossman One Hundred Hungry Ants by Elinor Pinczes Ten for Dinner by Jo Ellen Bogart The King's Commissioners by Aileen Friedman A Chair for My Mother by Vera B. Williams The 100th Day of School by Angela Sheaf Medearis How Much Is A Million? by David Schwartz Emily’s First 100 Days of School by Rosemary Wells Mouse Count by Ellen Stoll Walsh

Interdisciplinary Connections

Literacy connections (see books above). a) Students can create own addition and subtraction problems based on the book. Classmates can try to solve each other’s problems. Real World application a) Pose addition and subtraction problems involving shopping, game pieces, classmates, etc. Science (during life science unit) a) Graph plant growth using centimeter cubes and tools for standard measurement. Find total

5 | M a t h U n i t O r g a n i z e r ACES Regional Curriculum Consortium Math Unit Organizer measurements over a period of time or differences in measurements in plant heights.

Tools/Manipulatives

 dice  number lines  dominoes  connecting cubes  flashcards (addition and subtraction)  decks of playing cards  “make ten” frame  double ten frame  colored chips  fact family house template

Supplemental Materials and Resources

On Core Mathematics: Grade 2 Houghton Mifflin Harcourt by Houghton Mifflin Harcourt Publishing Company. 2012 http://www.k-5mathteachingresources.com/2nd-grade-number-activities.html http://www.apples4theteacher.com/math/addition/games/addup.html http://softschools.com/grades/2nd_grade/math/ Electronic Abacus http://illuminations.nctm.org/ActivityDetail.aspx?ID=8 Ten Frame http://illuminations.nctm.org/ActivityDetail.aspx?ID=75 Comparing Connecting Cubes http://illuminations.nctm.org/LessonDetail.aspx?id=U41 In On the Ground Floor http://www.creativille.org/groundfloor/index.htm A counting lesson for two digit numbers http://www.sasked.gov.sk.ca/docs/elemath/gr2lessp.html http://illuminations.nctm.org Websites for classroom use: http://sheppardsoftware.com http://www.figurethis.org/index.html http://www.funbrain.com http://www.aplusmath.com http://www.kidsnumbers.com http://www.aaamath.com http://mathplayground.com http://www.coolmath4kids.com Apps for classroom use on iPad:

Addition Coach Ladybug Addition

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Dinosaur Kids Math Math Toppers: Find Sums Key Learning Activities/Possible Lesson Focuses

Suggested lesson sequence *After students have shown proficiency with independent practice, and while the teacher is meeting with small groups, centers have been provided that reinforce concepts from this unit. Please see below: Math Centers for Unit 1 Math Center: Apples in a Basket Math Center: Building Fact Fluency- Speedy Addition & Subtraction Math Center: Problem Solvers Math Center: Nine Plus Day 1  Administer pre-assessment such as mad minute, AIMSweb, etc. in order to demonstrate fluency with addition and subtraction facts. Use this pre-assessment to determine focus for explicit instruction (whole group and small group) throughout unit.  Students will share and discuss what addition and subtraction means as teacher charts responses in order to determine which strategies students know. Days 2-14 *Teacher will choose lessons according to needs of students:  Counting On: Teacher will model the “counting on” strategy by using 5+1, 5+2, 5+3 trains using 2 different color cubes. Think aloud to show “counting on” strategy. o Students will use manipulatives of their choice (cubes, chips, dominoes, number line, ten frame, illustrations, etc.) to show proficiency when using the counting-on strategy for addition. Additional practice: In small groups or pairs  Think Addition: Teacher will model the “think addition” strategy as a mental strategy to model subtraction. Teacher will use the example 11-4 and ask: What are some subtraction strategies we could use to solve this? Acknowledge the counting back strategy, however, point out that counting back more than 1, 2, or 3 can be somewhat time-consuming and inaccurate. Model other subtraction strategies to use when subtracting 4 or more. Teacher will say: What is the related addition fact? (Discuss & explain their thinking). Teacher will describe this strategy as the “think addition” strategy. Continue modeling using trains using 2 different color cubes (emphasizing the relationship of addition to subtraction). o Students will use manipulatives of their choice (cubes, chips, dominoes, number line, ten frame, illustrations, etc.) to show proficiency when using the “think addition” strategy for subtraction. *Decompose: There are many ways to decompose a number to help students add and/or subtract. These are some lessons to teach decomposing, however, students may generate other ways to decompose. These other strategies should be charted and referred to throughout the year.

7 | M a t h U n i t O r g a n i z e r ACES Regional Curriculum Consortium Math Unit Organizer  Introductory Lesson: *See attached Math02_Unit01_LP01.doc for detailed lesson to introduce decomposing. This lesson will review: “What does it mean to decompose?” and will show students ways to think breaking apart an addend in order to help them apply a mental strategy to add. Students will decompose numbers (using illustrations, number sentences, or manipulatives) to add or subtract fluently. *See attached explicit lesson for introductory lesson. This strategy is more conceptual and therefore may require multiple lessons and experiences to practice.  “Making a Ten” strategy for addition (adapted from Lesson 10: On Core Mathematics- Grade 2, Houghton Mifflin Harcourt Publishing Company, 2012)- The teacher will show children how to add 2 numbers by “Making a Ten.” First the teacher will explain that ten is an important value in our number system and children should know and be able to make different amounts that equal 10. For the “Making a Ten” strategy, the teacher will model with 8+5= ? The teacher will start with the greater addend 8 and connect 8 cubes to show 8. Then create a train of 5. Break apart the 5 as 2+3. Because 2+8=10, the teacher will connect the 2 and 8 to make 10 and then add the 3 (10+3=13). So, 8+5=13. o Students will practice with other number sentences, demonstrating their understanding of this strategy by circling the greater addend and then they make a ten with the greater addend. o See “Math02_Unit01WS04.doc”  “Making a Ten” strategy for subtraction (adapted from Lesson 14: On Core Mathematics- Grade 2, Houghton Mifflin Harcourt Publishing Company, 2012)- Teacher will ask: How does getting to 10 in subtraction help when finding differences? Students will “turn and talk” to discuss. Students will share responses so teacher can quickly assess students’ understanding. Then teacher will write on chart: 13- 7=? A picture of 13 unifix cubes in a “train” should be drawn underneath the subtraction sentence. The teacher will “Think Aloud” to show steps to get to ten to help find differences. (Teacher will model): Step 1- Start with the first number. In this number, identify the digit in the ones column. In this case, 3 is in the ones column. Step 2- Decompose the other number, the 7, in a way so it is broken apart and includes a 3 (the digit from the ones column from the first number, 13). Step 3- (Teacher will write 13-3= 10 on chart and cross off 3 cubes from the train. Step 4- Now subtract the rest from the 10 (cross off 4 cubes from the train). 10-4=6. I have 4 left. Step 5- Write the difference from the original number sentence: 13-7=6 o Students will practice (teacher will give a different example for students to practice) with a partner on a white board and show their thinking. Teacher will monitor students working. When pairs are done with example, teacher will guide students through process on the chart. The teacher may continue to model if needed (or pull small group if some students are struggling). Students will then practice independently with other examples, showing their thinking and application of decomposing to make a ten. o See “Math02_Unit01WS05.doc”  Doubles: Teacher will ask: What does double mean? Elicit responses & chart student responses that demonstrate understanding of doubles (give credit to student by adding name after charted response). Teacher will then ask: What are double facts? Elicit responses from students & chart examples (1+1, 2+2, 3+3, 4+4…) Ask: What do you notice about the addends? (Review the word addend. Emphasize 8 | M a t h U n i t O r g a n i z e r ACES Regional Curriculum Consortium Math Unit Organizer the addends are the same). Why do you think it is important for us to know our double facts? Students “turn and talk” and share responses. Teacher will model 6+6 by creating 2 towers of six cubes, side by side, so students can see the towers are the same. The teacher will explain that by knowing the double facts, it will help us to add more quickly. The teacher will pass out “Doubles Book” (this book is a way for students to practice the double facts by completing the picture, identifying the double fact, and then writing the double fact that matches the picture). o Students will create a “Doubles Book” (make copies Doubles Book) so that they can show understanding of doubles. Students will then cut apart pages and staple together to make their “Double Facts Book.” (1+1= “snake fact”, 2+2= “butterfly fact”, 3+3= “insect fact”, 4+4= “spider fact”, 5+5= “finger fact”, 6+6= “dozen fact”, 7+7= “2 week fact”, 8+8= “crayon box fact”, 9+9= “tractor trailer fact”). Students can then practice with a partner by saying, “Snake fact!” Partner responds: “1+1=2!” etc.  Doubles plus one: The teacher will use double facts as a strategy for finding sums for near double facts. Teacher will display connecting cube towers (trains) with 4 cubes in each. Have students name the doubles fact (4+4=8). Add a cube to one tower and have students name the addition (4+5=9). o Students will practice using double facts to find sums for other facts. After practice, students could test each other by creating a towers and having a partner name their double plus 1 fact.  Doubles plus one: The teacher will create a 2-color train (using cubes) showing a double-fact and write the doubles number sentence by decomposing the doubles plus one fact. For example: 4+5 “think” 4+ (4+1)…showing the decomposing of 5=4+1. Next the teacher will model by thinking aloud and demonstrating how to add one and write the new doubles plus one number sentence. o Students will play “Doubles Plus 1” game to demonstrate their understanding of doubles plus 1 addition strategy. ( http://www.k-5mathteachingresources.com/support-files/doubles-plus- one.pdf)  Relationship of Addition and Subtraction: Teacher will ask, “How are addition and subtraction related?” Elicit responses from whole group. Then teacher will model a cube train of 2 different colors to show the 2 addition turn-around facts and the related subtraction facts. o Students will practice with a partner (then independently) to create cube trains of 2 colors to write fact families and related subtraction sentences to show the relationship of addition to subtraction (“fact families”). Follow http://www.k-5mathteachingresources.com/support- files/factfamilyhouse.pdf for additional practices.  Missing Addends: Teacher will present a real-life math situation. For example: “Boys and girls, this morning, I put 13 pencils in the can. Now there are only 6 left! How many pencils were taken?” Write the equation to represent the problem: 13-  = 6 How can we solve this? Can we use cubes to help? Think about what you already know about subtraction…turn and talk with a partner (students could even show their thinking with partner on a white board) and discuss different ways you could solve this. Teacher will listen to partner discourse and discuss different strategies heard that could solve the problem. Teacher may want to point out that, if we relate subtraction to addition, we could set it up: 6 +  = 13. Have children share ways they solved the problem and the teacher will quickly illustrate 9 | M a t h U n i t O r g a n i z e r ACES Regional Curriculum Consortium Math Unit Organizer various strategies on the chart-- labeling, counting up, drawing pictures, and crossing off, etc. Pose another example to partners written on chart paper: There are 15 insects in a container. 8 are ladybugs. The rest are pill bugs. How many pill bugs are there? Have students discuss strategies with partners and solve problem together (in a variety of ways, if possible). Have children share ways they solved the problem and the teacher will quickly illustrate various strategies on the chart-- labeling, crossing off, etc. o Students will practice more problems with a partner, or, students may begin to practice independently with other real-world problems. At this point, the teacher may want to pull small group if some students are struggling and/or challenge those that are solving with ease.  Word Problems- Teacher will ask: How do you write a number sentence to represent a problem? Are there important words in the problem that act as clues? Turn and talk with a partner and discuss word clues, number sentences, etc. Teacher will then reveal a real-life addition situation. John and his friends went to the park. They saw 15 worms and 9 caterpillars. How many critters did they see in all? Have students read over the problem and develop strategies they could use to solve the problem. Work with a partner to solve on white boards and share out. Teacher will record strategies on chart. o Students will practice more problems with a partner, or, students may begin to practice independently with other real-world problems. At this point, the teacher may want to pull small group if some students are struggling and/or challenge those that are solving with ease. *Teacher should provide word problems that include addition, subtraction, and solving for the unknown (missing addends).  Day 15- Performance Task

Suggested Formative Assessment Practices/Processes

 Journal entries  Anecdotal notes, observations  Exit slips: o Create a fact family using 5, 6, 11. o Here is 8 + 4 = __ Explain how you use the strategy to solve this problem. o How are addition and subtraction related? Draw an example to show your thinking. o Peter wants to find the sum of 6 + 7 in his head. Explain how he could use a “double fact” to do this. Show some other word problems where you could use this strategy.  “Mad-minutes” (fact fluency assessments)  Quick assessment questions such as: What equations can you write that total a sum of 20?

10 | M a t h U n i t O r g a n i z e r ACES Regional Curriculum Consortium Math Unit Organizer Work Cited

Common Core State Standards Initiative. (2010). Common core state standards for English language arts & literacy in history/social studies, science, and technical subjects. Washington, DC: National Governors Association Center for Best Practices and the Council of Chief State School Officers.

(2012). On core mathematics. Grade 2 Houghon Mifflin Harcourt. Van de Walle, J. A., & Lovin, L. H. (2006). Teaching student-centered mathematics, grades k-3. (Vol. 1). New York: Allyn & Bacon.

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