Kristine Kellenberger
September 18, 2012
Problem #1
Topic: Number and Number Sense: Whole Number Concepts – Kindergarten
SOL K.1
The student, given two sets, each containing 10 or fewer concrete objects, will
identify and describe one set as having more, fewer, or the same number of
members as the other set, using the concepts of one-to-one correspondence.
Expected Heuristics: Make a model, Draw a picture, Use manipulatives, Act it out
Slipper Day Problem
Kindergarten had Slipper Day. Everyone brought slippers to wear to school. Each child
measured his/her slippers with rainbow cubes. Chelsea’s pink slippers were 6 cubes long.
Connor’s Batman slippers were 9 cubes long. How much longer were Connor’s slippers?
Answer:
Connor’s slippers were 3 cubes longer than Chelsea’s slippers.
Possible Method:
Make a model:
Chelsea’s Slippers
Connor’s Slippers
Extension:
How do you know that Connor’s slippers are longer than Chelsea’s slippers?
Carroll County Public Schools. (2002). Kindergarten problem solving. Retrieved from
http://www2.carrollk12.org/instruction/elemcurric/math/tkproblemsolving.htm.
Kristine Kellenberger
September 25, 2012
Problem #2
Topic: Patterns, Functions, and Algebra: Attributes and Patterning – Kindergarten
SOL K.16
The student will identify, describe, and extend repeating patterns.
Expected Heuristics: Draw a picture, Make a model, Find a pattern
Missing Beads Problem
I want to make a bracelet with a pattern. First I’ll put a red bead, then a blue bead and then
another blue bead. I have room on the string for 13 beads altogether. How many of each color
bead will I need?
Answer:
5 Red beads
8 Blue beads
Possible method:
Draw a picture:
Extension:
I want to make a necklace with red and blue beads to match my bracelet. What kind of pattern
can I make that is not an ABB pattern?
Adapted from:
Carroll County Public Schools. (2002). Kindergarten problem solving. Retrieved from
http://www2.carrollk12.org/instruction/elemcurric/math/tkproblemsolving.htm.
Kristine Kellenberger
October 9, 2012
Problem #3
Topic: Number and Number Sense: Whole Number Concepts – Kindergarten
SOL K.1
The student, given two sets, each containing 10 or fewer concrete objects, will
describe one set as having more, fewer, or the same number of members as the
other set, using the concept of one-to-one correspondence.
Expected Heuristics: Use manipulatives, Draw a picture, Make a model
Pet Problem
Amber has 2 cats, 1 rabbit, and 1 bird. Josh has 1 dog and 4 fish. How many pets does Amber
have? How many pets does Josh have? Who has more pets?
Answer:
Amber has 4 pets. Josh has 5 pets. Josh has more pets than Amber.
Possible method:
Draw a picture:
Amber’s pets
Josh’s pets
Extension:
How many legs do Amber’s pets have? How many legs do Josh’s pets have? Whose pets have
more legs?
Kellenberger, K. (2012).
Kristine Kellenberger
October 23, 2012
Problem #4
Topic: Patterns, Functions, and Algebra: Attributes and Patterning – Kindergarten
SOL K.15
The student will sort and classify objects according to attributes.
Expected Heuristics: Use Logical Reasoning, Make an Organized List/Group, Make a Model
Button Problem
Given a large box of buttons; how can you sort these buttons?
Answer:
Students will all have a different correct answer because they will each have different
manipulatives to work with and have their own categories. It will be correct if they have all of
their manipulatives sorted into different groups based on attributes and can explain why they
sorted the buttons the way they did.
Possible method:
Make an Organized List/Group
Below is an image of one student’s method of sorting the buttons found on the blog I found the
problem on. It is considered a correct response because the student was able to explain his/her
method of sorting, in this case, by color.
Extension:
Can you find a way to sort your buttons that is different from anyone else at your table?
Kathryn. (2010, July 17). Math problem-solving week 3: Attributes and sorting [Web log post].
Retrieved from http://www.kindergartenkindergarten.com/2010/07/math-problemsolvingweek-3-attributes-and-sorting.html
Kristine Kellenberger
October 30, 2012
Problem #5
Topic: Number and Number Sense: Place Value and Fractions – 3rd Grade
SOL 3.1.a
The student will read and write six-digit numerals and identify the place value and
value of each digit.
Expected Heuristics: Make a model, Use Logical Reasoning, Guess & Check
Three Other Ways Problem
What are three different ways that you can record 463 with base-ten materials?
Answer:
Students will all have a different correct answer because they will each have different methods of
organizing their base-ten materials. It will be correct if they have base-ten materials that add up
to 463 in three different ways and can show how each one equals 463.
Possible Method:
Make a Model
Below are three different ways a student could represent 463 with base-ten materials.
Extension:
Can you show 463 with 31 pieces of base-ten materials?
Van De Walle, J., Karp, K., & Bay-Williams, J. (2013). Elementary and middle school
mathematics: Teaching developmentally. Upper Saddle River, NJ: Pearson Education.
Kristine Kellenberger
November 6, 2012
Problem #6
Topic: Number and Number Sense: Whole Number Concepts – Kindergarten
SOL K.3
The student, given an ordered set of ten objects and/or pictures, will indicate the
ordinal position of each object, first through tenth, and the ordered position of
each object.
Expected Heuristics: Use manipulatives, Draw a picture, Make a model
Racing Bears Problem
Three bears were in a race. The red bear crossed the finish line after the blue bear. The green
bear crossed the finish line before the blue bear. Which bear came in first place? Which bear
came in second place? Which bear came in third place? How do you know which bear won the
race?
Answer:
The green bear came in first place. The blue bear came in second place. The red bear came in
third place. The green bear came in first place because it crossed the finish line before the blue
bear and the red bear.
Possible method:
Draw a picture:
Finish
Line
3rd
2nd
1st
Extension:
If the yellow bear crossed the finish line before the blue bear but after the green bear, what
position would the bears have come in?
Kellenberger, K. (2012).
Kristine Kellenberger
November 13, 2012
Problem #7
Topic: Patterns, Functions, and Algebra: Attributes and Patterning - Kindergarten
SOL K.16
The student will identify, describe, and extend repeating patterns.
Expected Heuristics: Use manipulatives, Draw a picture, Make a model, Find a pattern
This problem should be presented prior to any instruction on patterns. Show the following to
students. Do not tell them that it is called a pattern or point out the base pattern to students.
What Comes Next? Problem
What comes next?
.
Answer:
Possible method:
Use manipulatives:
Extension:
What comes next?
Kellenberger, K. (2012).
Kristine Kellenberger
November 20, 2012
Problem #8
Topic: Patterns, Functions, and Algebra: Attributes and Patterning – Kindergarten
SOL K.15
The student will sort and classify objects according to attributes.
Expected Heuristics: Use Logical Reasoning, Draw a picture, Make a model
Which Doesn’t Belong? Problem
Draw a cat, a fish and a dog. Which one does not belong?
Answer:
Students may all have different correct answers because they could pick any of the animals as
not belonging, based on their different attributes. It will be correct if the student can explain why
the animal they selected did not belong in a logical way.
Possible method:
Use Logical Reasoning:
Here are some of the solutions students gave on the blog where I found the problem:
Students could reason that the fish doesn’t belong because it doesn’t have legs. The cat might not
belong because it can’t swim. The fish might not belong because it lives in the water. The cat
might not belong because the dog would chase the cat and the cat would eat the fish, but the dog
and the fish would get along just fine.
Extension:
Can you think of another animal that would fit in your group from above? (For example, if you
said the cat doesn’t belong because it can’t swim but the other ones can, can you think of an
animal to add to the group that does swim?)
Kathryn. (2010, July 13). Math problem-solving notebooks week 2: Sharing during
mathematician’s chair [Web log post]. Retrieved from http://www.kindergartenkinder
garten.com/2010/07/math-problemsolving-notebooks-week-2-sharing-duringmathematicians-chair.html
Kristine Kellenberger
Problem #9
Topic: Number and Number Sense: Whole Number Concepts – Kindergarten
SOL K.5
The student will identify the parts of a set and/or region that represent fractions
for halves and fourths.
Expected Heuristics: Use manipulatives, Draw a picture, Make a model
Cookie Problem
My mom sent me to school with six cookies today. She told me to give ½ of them to my sister.
How many do I need to give my sister? How do I know that that answer is ½ of the cookies?
Answer:
I will give my sister 3 cookies.
Possible method:
Use Manipulatives:
My Cookies:
My Sister’s Cookies:
Extension:
My mom sent me to school with eight cookies today. She told me to give ¼ of them to my older
sister, ¼ of them to my older brother, and ¼ of them to my younger sister. How many do I need
to give each of my siblings? How do I know that that answer is ¼ of the cookies?
Kellenberger, K. (2012).