Exploring Common Core Math Standards for First Grade

Robin Ventura, NCDPIInstructional Coach

Access Materials for Today’s Session at: http://bit.ly/13MTjAL

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

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

Agreements

Ask questions.Engage fully. Integrate new information. Open your mind to diverse views.Utilize what you learn.

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.

Four Major Works of First Grade Math

1. Developing understanding of addition, subtraction within 20

2. Developing understanding of whole number relationships and place value, including grouping in tens and ones

3. Developing understanding of linear measurement and measuring lengths in units

4. Reasoning about attributes of, and composing and decomposing geometric shapes

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.

Importance of Writing About MathReflection 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.

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)

Exploring the Eight Mathematical Practices

Advanced Organizer1) Count off to make eight groups2) 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.

Exploring the Eight Mathematical Practices Activity

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

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.

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)

888 + 88 + 8 + 8 + 8 = 1,000

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!

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.

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?

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

Subitizing Simulation

• Directions: In your math journal, write the title “Subitizing” at the top of the page. Number the page from 1-10. 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!

Make Your Own Subitizing Cards• Materials: index cards (20 per person), colored adhesive dots,

hole punchers, metal rings• Directions: 1. Make cards for the numbers 1-9 in a linear fashion (i.e.

straight horizontal or vertical lines, four square, t-squares, etc.).

2. Then, use the rest of the cards to makes the numbers 1-9 but in a non-linear fashion.

3. Once finished, punch a hole in the top of each card and place on metal ring.

4. Ask a partner to practice subitizing.

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).

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.

Five Frame

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

Ten Frame

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

Dot Card and Ten Frame Activities

• For more activities with dot cards and ten frames, visit:

http://www.edplus.canterbury.ac.nz/literacy_numeracy/maths/numdocuments/dot_card_and_ten_frame_package2005.pdf

Or

http://bit.ly/1cJz3H6

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.

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

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 6+6+1 =12+1=13)

How Many Under the Shell? http://illuminations.nctm.org/ActivityDetail.aspx?ID=198

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

Strategies for Addition Facts• Near Doubles facts for addition (i.e. 7+7 to find 8+7)

There are only 10 doubles facts from 0 + 0 to 9 + 9- 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.”

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.

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.

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.

Using Literature to Build Mathematical Thinking and Writing: The Grapes of Math

by Greg Tang

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.

Measuring with Connecting CubesMaterials: connecting cubes and math journalsDirections: 1. Use connecting cubes to measure the length of three different

objects in the classroom2. In your journal, use pictures, numbers and words to show what

you measured and how many connecting cubes you used.3. What was the shortest object you measured? What was the

longest object you measured? 4. What was the difference in length between the shortest and

longest objects you measured?

Exploring Standards1.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.

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.

Fold a SquareMaterials: paper squares, scissorsDirections:1. Fold a square in half in two different ways.

2. Cut your square along the fold lines so that you have four pieces.

3. How many different ways can you put the pieces back together? (Rule: Sides that touch must be the same length)

4. Draw the shapes in your math journal and describe using math vocabulary words.

Skeletal Models of 3D ShapesMaterials: toothpicks, playdough ballsDirections: 1. Choose one of the three-dimensional shapes below2. Make a skeletal model of the shape using the toothpicks and

playdough balls3. In your math journal, sketch the shape you made4. Describe the shape you made using math vocabulary

Work Time

Make and Take Options:1) Create additional subitizing cards to add to your stack2) Make a set of ten-frame cards3) Explore websites and bookmark activities you want to share with others4) Make some of the activities you used in small group/center time. 5) Explore additional small group/center activities you were not able to

previously6) Use chart paper to create number riddles- see The Grapes of Math by

Greg Tang7) 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%2C3547876-%2C00.html