## Addition Facts Through 10

Kindergarten children begin work with addition by building on their knowledge of numbers and their interest in representing and composing them. They explore the meaning of addition as they join or combine groups of children or sets of blocks or beads—for example, three children meet four others, or five red blocks are linked together with three blue ones. In such cases, children typically begin by counting the number for each addend, combining the objects, and counting the resulting groups to find how many in all.

Children also learn that addition can be represented by increasing one group of objects—two or more pennies added to a stack of three; another link added to four links already joined. Increasing one quantity leads children to the idea of counting on to find the sum. Some children will need to practice this skill many times. Other children will want to recount the beginning group and then count on. Adding cups of water to that previously poured into a bowl may help to bridge this gap since children must remember how many cups of water are already in the bowl and then count on saying, “4 cups in the bowl, 5; 5 cups of water in all.”

Children must learn the vocabulary and symbols associated with addition. As they act out and discuss addition situations, children use words and phrases such as **altogether**, **how many in all**, **total**, and **sum**. Children are introduced to the plus sign (+) and the equals sign (=) as they record results of modeling addition of numbers. Children begin writing number sentences, such as 3 + 1 = 4, to match situations with physical objects. Writing number sentences in horizontal form is natural for children because they have been exposed to writing words and sentences “across” the paper, from left to right. After modeling addends in vertical form with manipulatives, children also learn to record addition vertically; this vertical form will be used later for efficient paper-and-pencil computation of multidigit addends.

After children have developed some ideas about the meaning and process of addition, they begin to learn strategies for addition. They count on to add one or two to numbers zero through eight. This process is reinforced by practice in oral counting and use of the number line. Children also model “addition doubles” (e.g., 1 +1, 2 + 2, 3 + 3, 4 + 4, and 5 + 5), the sums of which are easy for many children to commit to memory. Through modeling, children explore adding zero to other numbers. Some children may be able to generalize that the sum of zero and another number is that number. Using concrete objects increases children's confidence with addition strategies. Plenty of practice with manipulatives assists children in answering quickly and committing some facts to memory. Finally, children use modeling, drawing, and pictures for finding the sum for other facts with addends 10 or less.

**Teaching Model:** Addition Facts Through 10