Dr. Monica Hartman

 Each person takes a turn. Roll the die and answer the question that corresponds to the number on the die. The other members, in turn, will ask you probing questions for more information.  Prepare to introduce one of the teachers in your group, using what you learned about that person from this activity.

1. Who is someone you most admire? 2. What is your favorite movie or book? 3. What accomplishment are you most proud of? 4. What was the most exciting event in your life? 5. What are you looking forward to the most this school year? 6. What is your most memorable vacation experience?

 In your journal, write down your answer to this question.

 Make a list of numbers that begin with a “start number” and increase by a fixed amount we call the “jump number”.  First try 3 as the start number and 5 as the jump number. Write the start number at the top of your list, then 8, 13, and so on, “jumping” by 5 each time until your list extends to about 130.  Examine this list and find as many patterns as you can. Share your ideas with the group and write down every pattern you agree really is a pattern.

 Try an idea that was shared that you have not tried.  Change the start number but keep the jump number equal to 5. What is the same and what is different?  Keep the same start number and try different jump numbers. How does the pattern of the length change as the jump number changes?  Discuss how it felt to “do mathematics”. How does it compare to what you wrote down before the activity? How does it compare to traditional mathematics classrooms?

 CommonCorePowerPoint_NCTM.ppt

Number and Operations: Representing, comparing, and ordering whole numbers and joining and separating sets Children use numbers, including written numerals, to represent quantities and to solve quantitative problems, such as counting objects in a set, creating a set with a given number of objects, comparing and ordering sets or numerals by using both cardinal and ordinal meanings, and modeling simple joining and separating situations with objects. They choose, combine, and apply effective strategies for answering quantitative questions, including quickly recognizing the number in a small set, counting and producing sets of given sizes, counting the number in combined sets, and counting backward.

Number and Operations and Algebra: Developing understandings of addition and subtraction and strategies for basic addition facts and related subtraction facts Children develop strategies for adding and subtracting whole numbers on the basis of their earlier work with small numbers. They use a variety of models, including discrete objects, length-based models (e.g., lengths of connecting cubes), and number lines, to model “part-whole,” “adding to,” “taking away from,” and “comparing” situations to develop an understanding of the meanings of addition and subtraction and strategies to solve such arithmetic problems. Children understand the connections between counting and the operations of addition and subtraction (e.g., adding two is the same as “counting on” two). They use properties of addition (commutativity and associativity) to add whole numbers, and they create and use increasingly sophisticated strategies based on these properties (e.g., “making tens”) to solve addition and subtraction problems involving basic facts. By comparing a variety of solution strategies, children relate addition and subtraction as inverse operations.

Number and Operations: Developing an understanding of whole number relationships, including grouping in tens and ones Children compare and order whole numbers (at least to 100) to develop an understanding of and solve problems involving the relative sizes of these numbers. They think of whole numbers between 10 and 100 in terms of groups of tens and ones (especially recognizing the numbers 11 to 19 as 1 group of ten and particular numbers of ones). They understand the sequential order of the counting numbers and their relative magnitudes and represent numbers on a number line.

 Fostering the Development of Whole-Number Sense  Read pages  If time, continue to page 277

 Sharon Griffin: In order to teach math, you need to know three things: 1. Where are you now? 2. Where do you want to go? 3. What is the best way to get there? Three principles from How People Learn 1. Eliciting, building upon, and connecting to student knowledge 2. Building learning paths and networks of knowledge 3. Building resourceful, self-regulating mathematical thinkers and problem-solvers

 In Grade Level Groups, discuss the understandings of the age group you teach.  Choose a partner and practice giving the Knowledge Test

 Number at the Concept Level Number at the Concept Level  s.shtml s.shtml  Blackline Masters for Number 1.Writing Numbers 2.Unifix Number Station 3.Two –Sided Beans 4.Peek Through the Wall 5.Lift the Bowl

 Unifix cubes in two colors  Each child in the group uses two colors to make different patterns with the number being explored. The teacher asks the child to describe the stacks of cubes by determining the total number of each color that is grouped together as they read from left to right.

 Two-sided beans and paper cup  Each child takes a given number of beans and shakes them from a paper cup. The beans are spilled out onto the table and the children read the combinations. For consistency, have the children read the painted beans first.

 Pattern Blocks in two different shapes  A group of children arrange a given quantity of pattern blocks. The teacher encourages the children to describe the pattern in a variety of ways.

 One-inch Tiles  A group of children work together exploring the possible arrangements of a given quantity of tiles. Every tile must touch a corner or at least part of a side of another tile. Encourage the children to describe the pattern in a variety of ways.

 Wooden Cubes (1 inch or 2 cm)  Children take a given quantity of cubes and arrange them in many different designs. They have an opportunity to build multi-layer patterns. The teacher should encourage the children to describe their arrangements in different ways as they build.

 When the children have explored a given number using many different materials and arrangements, they are ready to record their explorations of that number. Unifix Worksheet Two Sided Beans

 When children know the routine and are confidently exploring their results at the number stations, take a small group of children at a time and teach the three games.  The children have explored three, moved on to four, and are ready to record patterns for four. ◦ The Hand Game ◦ Peek Through the Wall ◦ Lift the Bowl

 Beans or other small manipulatives  Teacher asks children to take four beans and put three in one hand and one in the other.  When it is your turn, open your hand, one at a time, and tell the group how many beans you see.  For example, child says, “Three and one.”  The next time, they decide how many beans to put in each hand.

 Blocks, a piece of acetate with tape around the edges, one work space per child.  Ask children to arrange four blocks on their work space in a vertical line with about an inch between each block.  Have children first use their hands as a wall. To “wall off three” means to place your wall do you can see the three blocks closest to your body.  Teacher says “peek”.  Children say the number behind the wall and then the number in front of the wall. “One and three”  When children know how to play the game. Choose one to give directions.

 Children work together in a small group walling off the blocks and describing the combinations formed.  For a vertical line, suggest the children point the line at their stomachs.  For a horizontal line, ask them to make a line like their arms when they are stretched out to each side.

 A bowl and wooden blocks for each child.  In a small group, teacher asks students to take four blocks and put them under their bowl.  Then she asks them to take one from underneath and place it on top of the bowl.  When it is your turn, tell how many blocks are on top of the bowl and then tell how many are under the bowl.  The next time, the student decides how many of the four blocks to put on top.

 More stations and games and a further description of these activities can be found in Chapter 7: Number at the Connecting Level Chapter 7

 Number Worlds Number Worlds  Number Line Movie - Teddy Bear Path Number Line Movie - Teddy Bear Path  Plus Pups Plus Pups  Count and Compare (More and Less) Count and Compare

 Give Knowledge Test to at least three of your students  Try one of the activities from today and prepare to share what happened next time

 Three things that I learned today that I will use in my classroom are….  For the next time, I would like to learn more about….