1. Problem Solving in Kindergarten Math November 30, 2016

2. Growth Mindset
It used to be believed that the brains people were born with couldn’t really be changed, but this idea has now been resoundingly disproved. Study after study has shown the incredible capacity of brains to grow and change within a really short period (Abiola & Dhindsa 2011; Maguire, Woollett, & Spiers, 2006; Wollett & Maguire, 2011)

3. Brain Research
These researchers have documented that when we learn something deeply, the synaptic activity will create lasting connections in your brain, forming structural pathways, but if you visit an idea only once or in a superficial way, the synaptic connections can “wash away” like pathways made in the sand.

4. Mistakes are Valuable
Please take one sheet of white paper and crumble it up into a ball.
I would like each of you to throw it against this board and describe how you felt about making mistakes in math when you where in school.
Then ask participants to retrieve a paper ball and smooth it out. Take a marker and trace all the crumpled lines on the paper. These lines represent the brain growth that happens every time you make a mistake.

5. The Power of Mistakes and Struggle
Every time a student makes a mistake in math, they grow a synapse*.
A junction between two nerve cells a small gap at the end of a neuron that allows a signal to pass from one neuron to the next.

6. Table Discussion How can we change the ways students view mistakes?
In your groups list ways we could encourage young students to embrace mistakes instead of fearing them.

7. Counter-Off Game Materials: 1-20 Number Path 1 die 1 cup per team
10 counters per team
Game goal: to have the most counters in your team cup at the end of the game.
Directions:
Each team will begin with 10 counters.
Decide which team will go first. That team will roll the die and count forward the number of spaces shown on the die and place one of their counters there.
The second team will roll and count forward the number of spaces shown on the die. If there is another counter of either color on the number at which the count ends, the counting team will put that counter into their cup and leave their counter in that space. (Additional rules as play continues: if a move ends on 10, the team will put that counter in their cup; if the counter ends on 20, they will put that counter in their cup. All counts must end at 20 without going over. If the number rolled creates a count that goes beyond 20 the counter must remain in place).
The game ends when a team does not have any more counters to move. The winning team is the one with the most counters in their cup.

8. Number Jigsaw
Directions: Arrange the puzzle pieces so that the numbers shown on all sides match.

9. “Out to Dry” Materials: 12 Clothes pins numbered 1-12
“Out to Dry” game cards
Clothes Line game board
Game goal: To hang all of your
clothes pins first.
Directions: Play with 2 to 4 players. Students will randomly select clothes pins until all are taken. Shuffle the game cards and place face down in a pile in the center of the table. Player 1 will turn over the top card on the deck and display it for all to see. The student who has the clothes pin that represents the quantity of the card will take the card and pin it with the matching clothes pin. Play continues in the same manner until a player has “pinned” all of their clothes pins to the clothes line.

10. Ten Little Fish
Say…This book told a story of how 10 little fish were swimming in the sea and one by one they left the group. Let’s see how many different ways we can separate our 10 little fish into two groups. Work with your partner to see how many different ways you can find. I have given each group paper to record your findings.
Say… Fish are a lot like people, they come in different sizes, shapes, and colors. Using your fish cut outs, how might you group these fish by size? I would like you to work with your partner to group your fish by size. Please be able to explain your reasoning.
Say… A group of students had a outing at the beach. All of the children were picking up sea shells. The graph shows the number of shells that the boys collected and how many sea shells the girls collected. Take a moment to view the graph by yourself. Now with your elbow partner, discuss different questions this graph might be able to answer. Now, I would like you to discuss the questions you have discussed with your table group. Invite tables to share with the class. Ex: How many more seashells did the girls collect than the boys? Who collected the least amount of shells? How many seashells were collected in all? How many seashells did the boys collect? After each questions shared, ask the group to explain how they know this information.
Discuss what mathematical concepts each of the activities focused on.
Ask table groups to discuss additional open ended problem solving experiences students have using the characters, setting, illustrations, or theme of the book Ten Little Fish?

11. A Fishy Race Materials: 5 different colors of counters
Deck of Fishy Race cards
A Fishy Race Game board
Directions: Place one fish counter on each bubble. Each player will guess which color will win the race. Multiple students may guess the same color. Shuffle cards and place them face down in a stack. The first player will draw the top card and move the color of the number draw that many spaces. The next player will draw a card and move the color that is represented by the card that many spaces. Play continues until a fish (counter) moves beyond its row of squares.
What mathematical ideas does this game develop? How might you change this game to accommodate struggling learners?

12. The 4-Triangle Problem Materials:
Two squares- fold on the diagonal and make a crease, cut along the crease to make 2 triangles from each square piece.
Rules:
You can only put sides with the
same length together.
You must use all 4 triangles.
As a table group you will be exploring how many different shapes can be made by putting four paper triangles together. When everyone has had the opportunity to create a different shape, have participants post their shapes using tape, to a piece of chart paper. Discuss the different possibilities there are using 4 triangles. Using post-it notes – each table will write 2 questions they might ask to further student thinking.
Have teachers count off by Ask the 1s to go find a random place in the room spread apart from other 1s. Then invite 2s to join a 1, then 3s to join the group pf 1 & 2s. Ask everyone to take 30 seconds each to share their questions. Then ask the 2s to move to the next 1 going clockwise. 3s will move 2 groups down.

13. Number Relationships
Application of number relationships to the real world marks the beginning of making sense of the world in a mathematical manner (Van de Walle, 2010).
How can I use different combinations of numbers to represent the same quantity?
Numbers are related to each other through a variety of number relationships. The number 6, is 2 more than 4, two less than 8, can be composed of 3 and 3, as well as 5 and 1, and can quickly be recognized in several patterned arrangements of dots.
Introduce our next task:

14. Domino Discoveries
Little Red Riding Hood loved to play dominoes with her Grandma. She had one domino in her red cape. The sum of the pips on her domino was 5. What could the domino in Little Red Riding Hood’s cape look like?
Introduce students to the task of 5 pips. Comment: there are more squares provided for the task to 5, this is done so to make sure students justify that they have found all of the possible cominations. Many times students are just trying to “fill” the spaces provided without thinking about the task.

15. Reflection
How many number combinations could the students make with 5? 10?
What should they notice about the combinations?
Did they identify any patterns or rules?
How did you know when you found all of the dominoes?

16. A Fishy Problem

17. The Goldfish problem works because it:
builds upon the “big idea” of quantity by asking students to decompose the number 9;
helps students to recognize numbers as different combinations of other, smaller numbers (e.g., 10 is 0 and 10, 1 and 9, 2 and 8, 3 and 7, 4 and 6, or 5 and 5), an ability that will allow students to be more flexible when working with operations;
involves the meaningful use of mathematics;
allows learners of varying abilities to enter into solving the problem (through the use of manipulatives, the open-ended nature of the problem, and the potential for students to use their own experiences to solve the problem);
is developmentally appropriate; that is, it is a reasonable problem
for Kinder students to solve;
is active – the student is able to decide how to approach the
problem and to decide what materials to use;
is collaborative – the student can interact with other students or the
teacher in order to solve the problem.

18. You’ve got Your Own Problems
A good instructional problem captures students’ interest and imagination and satisfies the following criteria:
• The solution is not immediately obvious.
The context of the problem is meaningful to students.
There may be more than one solution.
The situation requires decision making above and beyond the choosing of a mathematical operation.
The solution time is reasonable.
The situation may encourage collaboration in seeking solutions.
I would like each table to create a problem situation that aligns to a kindergarten TEKS.

19. You’ve Got Your Own Problems
Problematic situation that aligns to at least one kindergarten student expectation.
Allows learners of varying abilities to enter into solving through the use of manipulatives.
Allows the student to decide how to
approach the problem and to decide
what materials to use.
Tables will post their problem ideas on chart paper and be ready to present.