Addition and subtraction is hard to explain in words, and simply writing out the numbers does little better to illustrate a mathematical concept: it is not visual enough. Students need to be able to see what it means to add and subtract in the real world by manipulating objects. Furthermore, different students learn in different ways and need different mental strategies. Including plenty of variety and number arrangements in your math lessons will give you the best chance to help every child achieve addition and subtraction fluency.
To get you started, here are a few techniques you can try:
For instant comprehension of how different combinations of numbers can be put together to get the same answer, this six-color rainbow shows the pairs of numbers that equal ten.
For more advanced comprehension of how different combinations of numbers can be put together to get the same answer, students can play Shut the Box with special sets of cards (0–5 for adding; 0–10 for subtracting). It's just like the rainbow above, except students must figure out a number combination themselves when they draw a card. For instance, if they draw a number 4 from the addition pile, they can either flip up 4, or 3 and 1. If they draw a number 6 from the subtraction pile, they can flip up 10 and 4; 9 and 3; 8 and 2; 7 and 1, or 6.
A pair of paper hands teaches your students how to use their fingers to add or subtract. Lift fingers up to add, fold fingers down to subtract.
A little gumball machine with numbered gumballs (0–5 for adding; 0–10 for subtracting) is a fun way for students to practice basic sums (as long as they remember these gumballs have marker on them and are not meant to be chewed). Have the first student release two balls and (if subtracting) subtract the lesser number from the greater number. When all students have gone though the subtraction exercise, remove the balls numbered 6–10 and have them repeat the process with the balls numbered 1–5 to practice addition.
Students can visualize adding and subtracting by helping a toy frog “hop” forward and backward on a number line. This is an example to show how they would hop forward for 3+2.
In a game of bowling, students can use scorecards to add or subtract the pins they knock down for each frame. If they are practicing addition, they add the pins they knock down. (If they knock down three the first time, they color in three pins on their scorecard. If they knock down seven pins the second time, they color in seven pins.) Then they add the two numbers.
Likewise with subtraction, they subtract the pins they knock down. (If they knock down three the first time, they cross off three pins. If they knock down seven pins the second time, they cross off seven pins.) Then they subtract the remaining number (in this case, 0) from ten. Color in the pins to add; cross out the pins to subtract.
As kindergarten teachers know, a number story is literally a story with a number problem. For instance, "I walked into a pet store and saw five fish and four turtles. I saw nine animals in all." Multiple pictures on craft sticks make easy puppets to act out number stories.
Using two ten frames together help students see that numbers higher than ten are just ten ones plus some other ones, or twenty ones minus some other ones.
LEGO bricks are a way to show groups of tens and ones vertically.
Chains of two colors of links work well for visualizing that two parts added together make a whole — or that if you start with a whole and two parts, and take away one part, you still have one part left.
To solve equations written on the outside of plastic eggs, students break them apart to count the buttons inside.
In this building game, students compete against each other to be the first to construct and deconstruct a tower of Unifix cubes. They take turns rolling the dice and adding the total number of cubes, and when they get to twenty, they roll the dice and subtract the total number of cubes until their towers are completely disassembled.