Problem Solving

Kindergarten Mathematics

Problem Solving

"Students act out adding and subtracting situations by representing quantities in the situation with objects, their fingers, and math drawings. To do this, students must mathematize a real-world situation, focusing on the quantities and their relationships rather than non-mathematical aspects of the situation. Situations can be acted out and/or presented with pictures or words. Math drawings facilitate reflection and discussion because they remain after the problem is solved. These concrete methods that show all of the objects are called Level 1 methods.

Students learn and use mathematical and non-mathematical language, especially when they make up problems and explain their representation and solution. The teacher can write expressions (e.g., 3 - 1) to represent operations, as well as writing equations that represent the whole situation before the solution (e.g., 3 -1 - ?) or after (e.g., 3 - 1 - 2). Expressions like 3 - 1 or 2 + 1 show the operation, and it is helpful for students to have experience just with the expression so they can conceptually chunk this part of an equation."

Common Core Tools Links to an external site.

 

Methods Used for Solving Single-Digit Addition and Subtraction Problems

The following suggested solving problem methods have been retrieved from Common Core Tools Links to an external site..

  • Level 1 - Direct Modeling by Counting All or Taking Away. Represent situation or numerical problem with groups of objects, a drawing, or fingers. Model the situation by composing two addend groups or decomposing a total group. Count the resulting total or addend.
  • Level 2 - Counting On. Embed an addend within the total (the addend is perceived simultaneously as an addend and as part of the total). Count this total but abbreviate the counting by omitting the count of this addend; instead, begin with the number word of this addend. Some method of keeping track (fingers, objects, mentally imaged objects, body motions, other count words) is used to monitor the count. For addition, the count is stopped when the amount of the remaining addend has been counted. The last number word is the total. For subtraction, the count is stopped when the total occurs in the count. The tracking method indicates the difference (seen as an unknown addend).
  • Level 3 - Convert to an Easier Problem. Decompose an addend and compose a part with another addend.

 

Developing Problem Solvers

Addition and subtraction problems can be posed in many different ways. Students must be able to solve problems of any situation. Problem solving is not an isolated activity. It doesn't occur every Friday. Instead, problem solving is a skill that favors every mathematics lesson. Problem solving is more than just one-step word problems. It should feature risk tasks, authentic purposes, and multiple ways to be solved.

 

Problem Solving Structures.png

The four Kindergarten problem subtypes are:

  • Result Unknown, Add To
  • Result Unknown, Take From
  • Total Unknown, Put Together/Take Apart
  • Both Addends Unknown, Put Together/Take Apart.

 

For students that are ready for Grade 1 instruction, they can work with all subtypes and variants. The following problems are the four difficult subtypes or variants that students should work with in Grade 1 but need not master until Grade 2-level instruction:

  • Start Unknown, Add To
  • Start Unknown, Take From
  • Bigger Unknown, Compare
  • Smaller Unknown, Compare

Download Start  Change  End Organizer

 

 

Avoiding Key Words

  1. Key words are misleading. Some key words typically mean addition or subtraction. But not always. Consider: There were 4 jackets left on the playground on Monday and 5 jackets left on the playground on Tuesday. How many jackets were left on the playground? "Left" in this problem does not mean subtract.
  2. Many problems have no key words. For example, How many legs do 7 elephants have? This example does not have a key word. However, any 1st grader should be able to solve the problem by thinking and drawing a picture or building a model.
  3. It sends a bad message. The most important strategy when solving a problem is to make sense of the problem and to think. Key words encourage students to ignore meaning and look for a formula. Mathematics is about meaning (Van de Walle, 2012).
  4. Solving Problems Relies on Thinking and Making Sense. Context Helps Make Meaning. Context helps students make meaning to solve problems. The story problems below can be connected to a variety of children's literature titles to build context. There are examples of each story structure for each context/theme. Please use numbers that are appropriate for the instructional standard. Story structures adapted from CGI, 1998.

 

Story Problems

Download Apples Problem Solving.docx Download Birds Problem Solving.docx Download Books:Library Problem Solving.docx
Download Clothing Problem Solving.docx Download Dental Health Problem Solving.docx Download Ducks Problem Solving.docx
Download Farm Problem Solving.docx Download Forest Animals Problem Solving.docx Download Friends Problem Solving.docx
Download Insects Problem Solving.docx Download Mice Problem Solving.docx Download Ocean Problem Solving.docx
Download Penguins Problem Solving.docx Download Rainforest Problem Solving.docx Download Space Problem Solving.docx
Download Teddy Bears Problem Solving.docx Download Transportation Problem Solving.docx Download Valentines Problem Solving.docx
Download Winter I Problem Solving.docx Download Winter II Problem Solving.docx Download Zoo Problem Solving.docx

 

Other exemplary resources for problem solving include ThinkTank by Origo, Read It, Draw It, Solve It, and Groundworks.