# 1.6 - Practical Problems with Addition and Subtraction within 20

The student will

• create and solve single-step story and picture problems using addition and subtraction within 20.

### BIG IDEAS

• So that by knowing how to solve every day math problems will help me to learn how to solve higher level problem solving
• So that I can understand addition problems in many different forms in everyday life

### UNDERSTANDING THE STANDARD

• Addition and subtraction should be taught concurrently in order to develop understanding of the inverse relationship.
• The problem-solving process is enhanced when students:
• create their own story problems;
• visualize the action in the story problem and draw a picture to show their thinking; and
• model the problem using manipulatives, representations, or number sentences/equations.
• The least number of steps necessary to solve a single-step problem is one.
• In problem solving, emphasis should be placed on thinking and reasoning rather than on key words.  Focusing on key words such as in all, altogether, difference, etc.,encourages students to perform a particular operation rather than make sense of the context of the problem.  A key-word focus prepares students to solve a limited set of problems and often leads to incorrect solutions as well as challenges in upcoming grades and courses.
• Provide practice in the use and selection of strategies. Encourage students to develop efficient strategies. Examples of strategies for developing the basic addition and subtraction facts include:
• counting on;
• counting back;
• “one more than,” “two more than”;
• “one less than,” “two less than”;
• “doubles” (e.g., 6 + 6 =__);
• “near doubles” (e.g., 7 + 8 = (7 + 7) + 1 =  or (8 + 8) – 1);
• “make ten” (e.g., 7 + 4 can be thought of as 7 + 3 + 1 in order to make a 10 );
• “think addition for subtraction” (e.g., for 9 – 5 = __, think “5 and what number makes 9?”);
• use of the commutative property (e.g., 14 +3 is the same as 3 + 14);
• use of related facts (e.g., 14 + 3 = 17 , 3 + 14 = 17, 17 – 4 = 13, and 17 – 13 = 4);
• use of the additive identity property (e.g., 14 + 0 = 14); and
• use patterns to make sums (e.g., 0 + 15 = 15, 1 + 14 = 15, 2 + 13 = 15, etc.).
• Students at this level are not expected to use the parentheses or to name the properties.
• Students should develop fluency with facts to 10 and then use strategies and known facts to 10 to determine facts to 20.
• Flexibility with facts to 10 should be applied to facts to 20 (e.g., when adding 4 + 7, it is appropriate to think of 4 as 3 + 1 in order to combine 3 and 7 to make a 10 whereas adding 4 + 8, it is appropriate to think of 4 as 2 + 2 in order to combine 8 and 2 to make a 10).
• Extensive research has been undertaken over the last several decades regarding different problem types. Many of these studies have been published in professional mathematics education publications using different labels and terminology to describe the varied problem types.
• Students should have exposure to a variety of problem types related to addition and subtraction.  Examples are represented in the chart below.  It is important to note that Join Problems (with start unknown), Separate Problems (with start unknown), Compare Problems (with larger unknown – using “fewer”) and Compare problems (with smaller unknown – using “more”) are the most difficult and should be mastered in grade two.