Lesson: Only Like Terms Can Be Combined
Colored markers/pencils/crayons for student to color code
Attached Note transparency
Attached Guided Practice transparency
Soft, bouncy ball
8-12A 1.0 Students identify and use the arithmetic properties of subsets of integers and rational, irrational, and real numbers, including closure properties for the four basic arithmetic operations where applicable:
A1.1 Students use properties of numbers to demonstrate whether assertions are true or false.
Launch: Present 3 problems that review recently acquired skills, provide 3-5 minutes for solving, solicit answers, guide student-led clarification if needed
Write on overhead projector (or use adhesive items on a white board if no projector) :
What do we have here? (Simplify with student input.)
2x + 4x
xx + xxxx
5x + 2x + 3y
xxxxx + xx + yyy
4x + 3y + 8 + 2y + 2
xxxx + yyy + 8 + yy + 2
Draw the contents of each term (use the word term) and demonstrate that when we combine x’s and y’s, we just have some x’s and y’s. We don’t have something that has one total, so that doesn’t work. This makes sense to us, but let’s learn the rules that we are following.
Guide students through note-taking, soliciting examples of each category, constants, variables, coefficients. Clarify that these are all terms.
The exception to clarify is that although 2 + 3x can not be simplified because we do not know what x is, 2 * 3x can be simplified, because it will always be 6x, whatever x is. Run through some examples of multiplication and division, but stress that these work when addition and subtraction do not.
Model color-coding and simplification. Students can call out instructions or demonstrate on overhead, complete problems with increasing independence. Stress that when we simplify, we are not necessarily solving. We might not get an “answer,” but we will get a simpler way of showing knowns and unknowns. Variables are unknowns.
Distribute 3-5 index cards to each student. Instruct students to randomly choose one term to write on each card. IT IS IMPORTANT THAT IF THEY USE VARIABLES, THE WHOLE CLASS ONLY USE 2 VARIABLES, for example, x and y.
Go Fish: In table groups of 3-5 students, shuffle and distribute cards. Students ask a student of their choice if they have a like term for what they have, and if so, they combine the like terms and set them down. If they do not have a matching term, the first student “goes fish” and has to draw another term card. The first student to match all of their terms wins. Play several rounds.
Match Ball: Take students to spacious place with soft, bouncy ball. Students tape terms to their chests or stomachs where they are visible. Students stand in a circle. They have to bounce the ball to a like term (for the term they are wearing). If they bounce it to a non-like term, they are out. If someone grabs the ball that is not a like term, they are out. The circle will shrink until often it is stuck, then restart.
7x + 3y – x + 4 - 2
Scale 1 - 5