To introduce the idea of finding a missing number to 1st and 2nd graders, first review simple math facts that students should be able to quickly recall, along with the idea that addition and subtraction are opposites. After collecting a few addition or subtraction facts that all students recognize immediately, write one on the board, replacing one of the numbers with a blank square. Many students will be able to identify the missing number. Have them turn and talk with a neighbor to discuss their thinking. After ample discussion, practice as a class, recalling the importance of knowing the original math fact and recognizing opposite operations. This introductory activity will set the foundation for advanced algebraic thinking in later grades.
A fact family triangle creates a visual representation of the relationship between specified numbers and reinforces the notion of operational opposites. The bottom two corners of a drawn triangle represent the two numbers that are used to “build” the number in the top corner. The operation used to build the bigger number can be either addition or multiplication. For example, if 3 and 4 are on the bottom, and the operation is multiplication, the top number will be 12. As an extension, students can be given triangles that have all 3 corners numbered and be asked which operations were used. Fact family triangles make it easy to show how numbers are built, as well as how they are broken down by looking in the opposite direction.
For this game, students will need a deck of index cards with operational instructions on them (i.e., add 3 to your number), dry erase markers and erasers, and a small white board or laminated surface. In pairs, students will take turns playing each role of the game. Student A picks a card but does not show it to Student B, who writes a number on the left side of the board. Student A must use that number and the operational rule on the card to come up with a number to write on the right side of the board. Player B picks another number, and student A solves again using the same card. The process is repeated until student B can guess the rule. Players switch roles and repeat the process; the “winner” is whomever guesses the rule in the least number of guesses.
This whole classroom activity combines aspects from all of the previous activities, and challenges students to be creative with their algebraic thinking. The teacher simply picks two numbers (labeled A and B) on a large number line and asks students to create different operational paths to get from A to B. Because students are free to explore and experiment with numbers, it is beneficial to the class as a whole to be able to hear different explanations and “pathways.” For example, a student that picks a simple path such as 10+2=12 may begin to expand his thinking if a neighbor picks a more complicated path such as 4x5-8=12. By giving students permission to create their own number sentences, the teacher creates a classroom of autonomous algebraic thinkers.