# 2.5 - Missing Addends and Practical Problems

The student will

a)  recognize and use the relationships between addition and subtraction to solve single-step practical problems, with whole numbers to 20; and

b)  demonstrate fluency with addition and subtraction within 20.

### BIG IDEAS

• So that I can have the mental facts to enable understanding of higher level operations

• We add/subtract every day so that if I know my facts, I will be able to use them accurately

• So I can use inverse relationships in operations  to check my own work

### UNDERSTANDING THE STANDARD

• Computational fluency is the ability to think flexibly in order to choose appropriate strategies to solve problems accurately and efficiently.
• Addition and subtraction should be taught concurrently in order to develop understanding of the inverse relationship.
• Concrete models should be used initially to develop an understanding of addition and subtraction facts.
• Recognizing and using patterns and learning to represent situations mathematically are important aspects of primary mathematics.
• An equation (number sentence) is a mathematical statement representing two expressions that are equivalent. It consists of two expressions, one on each side of an 'equal' symbol (e.g., 5 + 3 = 8, 8 = 5 + 3 and 4 + 3 = 9 - 2).
• Equations may be written with sums and differences at the beginning of the equation (e.g., 8 = 5 + 3).
• An equation can be represented using balance scales, with equal amounts on each side (e.g., 3 + 5 = 6 + 2).
• An expression is a representation of a quantity.  It contains numbers, variables, and/or computational operation symbols.  It does not have an equal sign (e.g., 5, 4 + 3, 8 - 2).   It is not necessary for students at this level to use the term ‘expression.’
• The patterns formed by related facts facilitate the solution of problems involving a missing addend in an addition sentence or a missing part in a subtraction sentence.
• Provide practice in the use and selection of strategies. Encourage students to develop efficient strategies. Examples of strategies for developing the addition and subtraction facts include counting on;
• counting back;
• “one more than,” “two more than”;
• “one less than,” “two less than”;
• “doubles”  (e.g., 2 + 2 =  ; 3 + 3 =  );
• “near doubles” (e.g., 3 + 4 = (3 + 3) + 1 =  );
• “make 10” facts (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., 4 + 3 is the same as 3 + 4);
• use of related facts (e.g., 4 + 3 = 7 , 3 + 4 = 7, 7 – 4 = 3, and 7 – 3 = 4);
• use of the additive identity property (e.g., 4 + 0 = 4); and
• use patterns to make sums (e.g., 0 + 5 = 5, 1 + 4 = 5, 2 + 3 = 5, etc.)
• Grade two students should begin to explore the properties of addition as strategies for solving addition and subtraction problems using a variety of representations.
• The properties of the operations are “rules” about how numbers work and how they relate to one another.  Students at this level do not need to use the formal terms for these properties but should utilize these properties to further develop flexibility and fluency in solving problems.  The following properties are most appropriate for exploration at this level:
• The commutative property of addition states that changing the order of the addends does not affect the sum (e.g., 4 + 3 = 3 + 4).
• The identity property of addition states that if zero is added to a given number, the sum is the same as the given number (e.g., 0 + 2 = 2).
• The associative property of addition states that the sum stays the same when the grouping of addends is changed (e.g., 4 + (6 + 7) = (4 + 6) + 7).
• Addition and subtraction problems should be presented in both horizontal and vertical written format.
• Models such as 10 or 20 frames and part-part-whole diagrams help develop an understanding of relationships between equations and operations.

### ESSENTIALS

• Recognize and use the relationship between addition and subtraction to solve single-step practical problems, with whole numbers to 20. (a)
• Determine the missing number in an equation (number sentence) (e.g., 3 +   = 5 or  + 2 = 5; 5 –  = 3 or 5 – 2 =  ). (a)
• Write the related facts for a given addition or subtraction fact (e.g., given 3 + 4 = 7, write 7 – 4 = 3 and 7 – 3 = 4). (a)
• Demonstrate fluency with addition and subtraction within 20. (b)

### KEY VOCABULARY

Updated: Aug 22, 2018