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**Exploring Common Core Math Standards for First Grade**

Robin Ventura, NCDPI Instructional Coach Access Materials for Today’s Session at:

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**Goals for Today’s Session**

To explore and apply the Eight Mathematical Practices To identify the major works of 1st grade math To explore major works standards To analyze the difference between procedural and conceptual mathematics To explore and apply strategies for teaching the standards

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**Agenda Introductions Discussing the Four Major Works of 1st Grade**

Exploring the Eight Mathematical Practices Analyzing the difference between procedural and conceptual math Exploring the importance of subitizing Exploring math standards

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**Agreements Ask questions. Engage fully. Integrate new information.**

Open your mind to diverse views. Utilize what you learn. Share norms with group. Ask if any of the norms need to be edited or if additional norms need to be added. As adults, we’ll follow the norms and remind our peers of them if necessary.

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**Four Major Works of First Grade Math**

Not all of the content in first grade is emphasized equally in the standards. Some standards require greater emphasis than others based on the depth of the ideas, the time it takes to master, and/or their importance to future mathematics. Some things have greater emphasis is not to say that anything in the standards can safely be neglected in instruction. Tell participants we are going to explore the four major works of 1st grade as a means to provide an overview of what we’ll do throughout today. Ask participants to read slide.

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**Four Major Works of First Grade Math**

Developing understanding of addition, subtraction within 20 Developing understanding of whole number relationships and place value, including grouping in tens and ones Developing understanding of linear measurement and measuring lengths in units Reasoning about attributes of, and composing and decomposing geometric shapes Ask participants to turn to page in packet on the Four Major Works of 1st Grade Math. Ask them to read and annotate the text by highlighting and making notes. AsK participants to pair with a partner and discuss what they learned by reading about the major works. Tell participants our session today will focus on each of the four major works. Tell participants they will learn about and explore activities that can be used in whole group settings but are most effective in small groups to increase focus and participation. Will also allow you to know how to best formulate next lessons to meet the needs of the learner.

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**Benefits of Small Group Instruction**

Helps students to focus better because of increased student-teacher interaction. Provides teacher with an immediate picture of where students are and how to help them. Allows teacher to differentiate instruction to meet all needs. Allows students to gain foundational concepts they may have not been ready for in kindergarten.

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**Importance of Writing About Math**

Reflection allows students to review what they have just been taught. One method of recording student reflection is using math journals. According to Bay-Williams, Karp, and Van De Walle, "[j]ournals are a way to make written communication a regular part of doing mathematics" (85). By including journal-writing as closure to each lesson, teachers help students to better remember what they have learned. . As well, students should be expected to give reasons for their answers to problems. They could either write or draw pictures to explain their thinking or, show their work to explain their thinking. If they can do so, they will remember mathematics concepts for life. Ask participants to think about their own experiences in writing about math at students. Ask them to share experiences with writing and how it helped or hindered their learning. Ask for volunteers to share. Then, show the information about reflective writing. Ask them to read. Then, ask each participant to get journal and tell them they will be writing about learning experiences today in mathematics. Tell them we will discuss their experiences and how they can encourage the same for their students.

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**Building Math Vocabulary**

Mathematically proficient students communicate precisely by engaging in discussions about their reasoning using appropriate mathematical language. Mathematical vocabulary however should not be taught in isolation where it is meaningless and just becomes memorization. We know from research that meaningless memorization is not retained nor will it help build the deep understanding of the mathematical content. The students must be provided adequate opportunities to develop vocabulary in meaningful ways such as mathematical explorations and experiences. Please see your packets for a list of First Grade Math Vocabulary (2nd page) Ask participants to read slide. Ask them to find the list of math vocabulary and put a check mark beside the terms that are familiar and those that are not familiar. Ask participants to think about how they could help students build a strong math vocabulary in their classrooms.

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**Exploring the Eight Mathematical Practices**

Advanced Organizer Count off to make eight groups Each group will: read and discuss one of the Eight Mathematical Practices (see two page handout in packet). Use the materials in the large plastic bag to construct a model/representation of the assigned practice (15 minutes) Share their model and explain the practice to the larger group. Tell participants that with CC standards, eight mathematical practices have been incorporated throughout the standards to ensure students have experiences with collaborative problem-solving and mathematical exploration. Tell participants we will explore the eight mathematical practices and their importance in learning. Begin activity. Pass out one bag to each table. After 15 minutes, start with group 1 and show mathematical practices slides (11-20) as they go.

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**Exploring the Eight Mathematical Practices Activity**

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Mystery Number I am a three digit number. My second digit is four times more than my third digit. My first digit is seven less than my second digit. What number am I? 182

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Inside Out How does the measure of the interior angles of a trapezoid compare to a hexagon? Use your math journal to justify your answer.

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Playing with Numbers How can you add eight 8's to get the number 1,000? Use your math journal to record your thinking. Note: You can only use eight number eights and only use addition) = 1,000

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**Applying the 8 Mathematical Practices: The Taxicab Problem**

Materials: chart paper, markers, The Taxicab Problem, calculators With your table group read the Taxicab Problem in your handouts. Use chart paper to present your case for Taxicab A or B. You may represent your case using charts, diagrams, graphs or whatever you deem best. You have 15 minutes to analyze and present your case. Choose someone from your group to present! Materials: chart paper with t-chart, slide 22, TimeTimer, chart paper (one page for each table group), markers, Tell participants will now have a chance to apply most of the 8 mathematical practices in a group problem-solving activity. Pass out chart paper and tell participants to find the calculator and markers in their table containers. Also ask them to turn to problem in their packets. Tell they they will work together to solve the problem and then represent their answer(s) by using a chart, diagram, graph or whatever the group would like to use. Ask them to appoint a representative to present the case. Ask if any questions. Start clock at 15 minutes. Once finished, ask each group to post their problem and then do a gallery walk. Ask representative to stand beside the poster and become an exhibit guide to answer any questions. Once finished, share the 8 mathematical practices poster and ask the participants to share how they used the practices. Tell them that for many classrooms, this is a major shift in instuction. Formerly, teachers taught a lesson, showed students how to arrive at an answer using one specific method and then, students were provided an opportunity to practice the skill. Ask participants to discuss the pros and cons of using a problem-solving approach as compared to traditional approach. Chart their answers using a t-chart. Ask participants to lay down ‘tracks of thinking’ in their journal.

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**Procedural vs. Conceptual Math**

Procedural math involves working out a problem using a process that is usually memorized. However, students may not understand the reasoning behind a procedure. Conceptual knowledge is understanding the concepts in order to solve problems (so students may use any procedure). A great example is with long division. Many students can do okay with long division on a test because they memorize a procedure only to forget two weeks later. Thus, the students have not mastered the conceptual understanding. Procedural math is knowing what to do; conceptual math is knowing why you’re doing it. Tell participants that learning math facts, practice drills, one method of approaching a problem are all largely procedural approaches to math. However, research and our own experiences tell us these approaches don’t work for many of our students. What will work is more of a focus on learning concepts first and then applying procedures. For example, tell about 5th grade class and working on equivalent fractions.

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**A Problem to Help with Understanding Procedural vs. Conceptual Math**

With the members of your group solve the following problem (no calculators please!): 1/4 x 2/3= Can you show how you found your answer in a different way? Tell participants we will explore the difference between procedural and conceptual math. Ask each table to work on the problem ¼ x 2/3 and provide an answer. Then, ask them if they can show how they can find their answer in a different way. Take all suggestions. Take through a paper folding activity. Then, ask what the difference was between the original way of finding the answer and the 2nd way. Explain that many of us were taught math procedurally. We could memorize the procedure but usually no real world application. All math is applicable and if we understand it conceptually, we can understand any apply.

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**Where to Start with 1st Grade?? The Importance of Subitizing**

Subitizing is the ability to immediately recognize the quantity of a small number of objects without counting. Research has shown subitizing to be foundational to basic math skills. Many children who struggle with basic math also have trouble subitizing. Subitizing can be improved through games and practice Tell participants current research shows that the ability for children to subitize is a very important foundational skill. Reach the screen. Ask participants to turn to page in packet on subitizing and ask them to read. Tell them we will have an opportunity to practice subitizing next.

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**Subitizing Simulation**

Directions: In your math journal, write the title “Subitizing” at the top of the page. Number the page from As each card is shown, write the number of dots you see on the card. We will check answers once you are finished. Subitizing- Get Ready!

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**Make Your Own Subitizing Cards**

Materials: index cards (20 per person), colored adhesive dots, hole punchers, metal rings Directions: Make cards for the numbers 1-9 in a linear fashion (i.e. straight horizontal or vertical lines, four square, t-squares, etc.). Then, use the rest of the cards to makes the numbers 1-9 but in a non-linear fashion. Once finished, punch a hole in the top of each card and place on metal ring. Ask a partner to practice subitizing. Materials: Subitizing cards, note cards, dots, hole punchers, ring Show subitizing cards. Tell participants will now make their own

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Exploring Standards 1.NBT.2: Understand that the two digits of a two digit number represent amounts of tens and ones. Understand the following as special cases: A. 10 can be thought of as a bundle of ten ones- called a “ten.” b. The numbers from 11 to 19 are composed of a ten and one, two, three, four, five, six, seven, eight, or nine ones. c. The numbers 10, 20, 30, 40, 50, 60, 70, 80, 90 refer to one, two, three, four, five, six, seven, eight, or nine tens (and 0 ones).

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**Importance of Five and Ten Frames**

Five frames and ten frames are one of the most important tools we can use to help students understand our system of mathematics (Base 10). Five frames are a 1x5 array and ten frames are a 2x10 array in which counters or dots can be placed to illustrate groups of numbers, addition and subtraction For students in kindergarten and 1st grade who have not yet explored a ten frame, it’s best to begin with a five frame as an anchor. Show five and ten frames and ask participants to locate in their packet. Ask them to take out 12 counters from plastic bin. Ask them to put on the hat of a first grader and tell them they will build numbers with five and ten frames. Go to next slide.

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**Five Frame http://illuminations.nctm.org/ActivityDetail.aspx?ID=74**

Start with five frame and build numbers 5 and less. Then, build numbers such as 6, 8, 9. Tell them they want to help students build onto the idea of a set of five. Anything over five can be thought of as 5 and some more. Show illuminations activities.

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**Ten Frame http://illuminations.nctm.org/ActivityDetail.aspx?ID=75**

Show ten frame. Tell participants that our whole framework of mathematics in the U.S. is built upon the base ten system. Orient to the 10 frame and ask how they might think about the ten frame. (2 sets of fives). Also, ask them about one to one correspondence experiences with children. Tell them one of the most beneficial ways to help students with one-to-one correspondence, addition, subtraction, grouping is via the use of a ten frame. Explain that you want to teach the students to start in the top left corner and build across. Show a number like 8 and explain that it’s important to build the idea that 8 is 5 and some more and 8 is close to ten and only lacks 2 to make 10. Students need lots of practice using 10 frames. Show addition problem. Ask participants to build the number four. Then, ask them to add 3 more and provide the answer. Tell them that many students lack the idea of grouping which is essential to the operations. For example, if a student adds four and counts to four and then after adding 3 more has to start back at one, then the child needs help with counting on. This is a good assessment and students that lack the ability need small group instruction to learn the skill. Show illuminations activities.

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**Dot Card and Ten Frame Activities**

For more activities with dot cards and ten frames, visit: Or Ask participants to go to site and look at some of the activities that can be used to teach numbers and operations with dots, 5 and 10 frames. Ask participants to spend a few minutes to journal about what they’ve learned.

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**Using Ten Frames and Hundreds Boards to Build Larger Numbers**

To help students understand numbers beyond 10, use of multiple ten frames is helpful. Large and small group instruction with hundreds boards is also helpful. Ask students to use markers and hundreds boards to explore concepts such as one more, one less, two more, two less, 10 more, 10 less. Use hundreds boards to build concepts of one more, one less, two more, two less, 10 more, 10 less. Addition- 5 plus 6= etc. Play

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Fill the Stairs Materials Needed for Pairs: spinner card with numbers 0-9, golf tee, paper clip, “Fill the Stairs” gameboards. Directions: read at the top of the gameboard Tell participants to join a partner. Find the activity, “Fill the Stairs”, spinner card, golf tee, and paper clip. Ask them to read directions on the game sheet. Tell them they will use spinner rather than 0-9 cards. Show them how to use the golf tee and a paper clip to spin. Tell them this activity is useful after students have a thorough understanding of the hundreds board.

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Exploring Standards 1.OA6 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 =12+1=13) How Many Under the Shell?

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**Building Strategies for Addition and Subtraction**

Avoid Premature Drill Practice Strategy Selection or Strategy Retrieval- process of deciding what strategy is appropriate for a particular fact. If you don’t think to use a strategy, you probably won’t. Discuss use of strategies before students attack problems Avoid Premature Drill: It is critical you don’t introduce drill too soon. Suppose that a child doesn’t know the 9+5 fact and has no other way to deal with it other than to count fingers or use counters. Premature drill introduces no new information and encourages no new connections. It’s a waste of time and is a frustration to the students.

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**Strategies for Addition Facts**

Near Doubles facts for addition (i.e. 7+7 to find 8+7) There are only 10 doubles facts from to this is a great place to start with facts to help students with near doubles. Double Dice Plus One: Roll a single dice with numerals or dot sets and say the complete double plus-one fact. That is, for 7, students should say, 7 +8 =15 One More Than and Two More Than (i.e. 2 +8; 2 more than 8 is 10) One-/Two-More-Than Dice: Make a die labeled +1, +2, +1, +2, “one more,” and “two more.” Use with another die labeled 4, 5, 6, 7, 8, 9. After each roll of the dice, children should say the complete fact: “Four and two is six.”

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**Strategies for Addition Facts**

Make-Ten Facts: These facts all have at least one added or 8 or 9. Build onto the 8 or 9 up to 10 and then add on the rest. For 6 + 8, start with 8, then 2 more makes 10, and that leaves 4 for 14. Say the Ten Fact: Hold up a ten-frame card and have children say the “ten fact.” (i.e. 7 card and children would say, 7 +3=10) Make 10 on the Ten-Frame: Give students a mat with two 10 frames. Flash cards are placed next to the ten frames (or fact can be given orally). The students should model each number on the two frames and then decide on the easiest way to show the total. Do- Say the Ten Fact and Make 10 on the Ten-Frame. Participants will need the double ten frame from packet and I will use flash cards. Ask them about the different ways they did the totals.

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**Strategies for Subtraction Facts**

Think Addition: View Subtraction as “Think-Addition” (count-count-count approach is largely ineffective) Ex. 9 – 4 should be thought of as 4 + ? =9 “Think-Addition Strategy depends on mastery of addition facts first Build Up Through the Ten-Frame: Use a 10 frame with 9 dots. Discuss how you can build numbers between 11 and 18, starting with 9 in the 10 frame. Stress the idea of one more to get to 10 and then the rest of the number. Call out numbers between 11 to 18 and have students explain how they can figure out the difference between the number and the one on the 10 frame. Do the same with 8 in the 10 frame. Ask participants to get counters and demonstrate.

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**Strategies for Subtraction Facts**

-Back Down Through the Ten-Frame: Start with two 10 frames, one filled completely and the other partially filled. For 13, for example, discuss what is the easiest way to think about taking off 4 counters. Repeat with other numbers between 11 and 18. Have students write or say the corresponding fact. Ask participants to do this activity with their double ten frames and counters. Make fact cards to use.

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**Using Literature to Build Mathematical Thinking and Writing: The Grapes of Math by Greg Tang**

Ask participants to use their math journals to record strategies they’ll use as I read the book. Ask them to think about strategies they could use to help their students do the same?

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Exploring Standards CCSS.Math.Content.1.MD.A.2 Express the length of an object as a whole number of length units, by laying multiple copies of a shorter object (the length unit) end to end; understand that the length measurement of an object is the number of same-size length units that span it with no gaps or overlaps.

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**Measuring with Connecting Cubes**

Materials: connecting cubes and math journals Directions: Use connecting cubes to measure the length of three different objects in the classroom In your journal, use pictures, numbers and words to show what you measured and how many connecting cubes you used. What was the shortest object you measured? What was the longest object you measured? What was the difference in length between the shortest and longest objects you measured?

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Exploring Standards 1.G2 Compose two-dimensional shapes (rectangles, squares, trapezoids, triangles, half-circles, and quarter-circles) or three-dimensional shapes (cubes, right rectangular prisms, right circular cones, and right circular cylinders) to create a composite shape and compose new shapes from the composite shape. Ropes activity: Read Mouse Shapes by Ellen Stoll Walsh: Tell participants will explore shapes using a couple of different methods. Divide participants into groups of four and give each group a length of rope. Tell participants they have what is called a line segment. Ask them to tie the ends of the rope together. Then, ask them to formulate the following shapes: triangle, square, rectangle, hexagon, octogon. Then, ask groups to work together to make a cube, rectangular prism, triangular prism,.

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Mouse Shapes Mouse Shapes Materials: Copy of ‘Mouse Shapes’, pattern blocks Listen to the story, ‘Mouse Shapes’ by Ellen Stoll Walsh. Use shapes to make your own big, scary creature to frighten the cat away. Record and write about the shapes you used. Tell participants it is very important to teach students about shapes by looking at our environment (go on a Scavenger Hunt to find shapes in the school building or as a homework activity). Read the story of Mouse Shapes . Give participants pipe cleaners

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**Fold a Square Materials: paper squares, scissors Directions:**

Fold a square in half in two different ways. Cut your square along the fold lines so that you have four pieces. How many different ways can you put the pieces back together? (Rule: Sides that touch must be the same length) Draw the shapes in your math journal and describe using math vocabulary words.

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**Skeletal Models of 3D Shapes**

Materials: toothpicks, playdough balls Directions: Choose one of the three-dimensional shapes below Make a skeletal model of the shape using the toothpicks and playdough balls In your math journal, sketch the shape you made Describe the shape you made using math vocabulary

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**Work Time Make and Take Options:**

Create additional subitizing cards to add to your stack Make a set of ten-frame cards Explore websites and bookmark activities you want to share with others Make some of the activities you used in small group/center time. Explore additional small group/center activities you were not able to previously Use chart paper to create number riddles- see The Grapes of Math by Greg Tang Make math activities by using Teaching Student-Centered Mathematics by Van de Walle and his blackline masters-wps.ablongman.com/ab_vandewalle_math_6/0%2C12312%2C %2C00.html

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