MBT Sampler Flipbook

42 Level D Solving Addition and Subtraction Equations with Models To solve addition or subtraction equations with models Objective: To solve addition or subtraction equations with models. Materials: Algebra Tools (Master 20) or Algebra Tiles Equations with Addition or Subtraction Model the equation x + 4 = 8 with rods or lunch bags and cubes as shown. The activity may also be modeled using black and white squares and rectangular rods from Master 18. = Ask a student to translate the equation shown into words. ( x + 4 = 8) What must be done to an equation to keep it balanced? (Whatever operation is done on one side of the equal sign must be repeated on the other side of the equal sign.) The easiest way to solve an equation is to get the variable by itself on one side of the equal sign. What is on the same side as the variable x ? (4) How can we get rid of the 4? (Add – 4.) If we add 4 to the left side, what must be done on the right side of the equal sign? (Add – 4.) Model this by placing 4 white cubes on each side. Now how does the equation read? ( x + 4 – 4 = 8 – 4) If we put together the like terms on both sides of the equal sign, what do we get? ( x = 4) Let us check our answer. If we put 4 in for x , is the equation true? (Yes) Why? (because 4 + 4 = 8) Model the equation x – 3 = – 5 with rods and cubes as shown below. = Ask a student to translate the equation shown into words. ( x – 3 = – 5) What must we get rid of to get x by itself on one side of the equal sign? ( – 3) How can we do this? (Add +3.) If we add +3 to the left side, what must be done on the right side of the equal sign? (Add +3.) Model this by placing 3 black cubes on each side. Now how does the equation read? ( x – 3 + 3 = – 5 + 3) Simplify the equation by putting the like terms together on both sides of the equal sign. What are we leftwith? ( x = – 2) If we put – 2 in for x , is the equation true? Show the check on the board: (2) – 3 = – 5 – 2 + ( – 3) = – 5 – 5 = – 5 Model the two examples at the top of the page. Ask student volunteers to translate the models in problems 1 and 2 to words. For example, for problem 1, a student might say “when a number x has 2 added to it, the result is 4.” Then the equation x + 2 = 4 can be written by the class and solved together. Have students use models to solve the problems. Answer Key 1. 2 2. 9 3. 3 4. 9 5. 8 6. 6 7. – 3 8. 7 Pattern: Add or subtract the same number on both sides so that the variable will be by itself. - Have students check problems by mentally substituting the answer for the variable in the equation. Ex. 1: x + 2 = 4, x = 2 Check: 2 + 2 = 4 Student-Authored Equations Give each student a half-sheet of paper. Ask students to think of a number, write a true sentence about the number using a plus or minus sign, and draw a picture of the sentence or a sketch of a balance scale. Exchange equations and pictures with the students in the class. Journal Prompt: Lynn said she had a can with black or white cubes in it. Ric wanted to guess the number and color of the cubes in the can. Lynn said, “If you add 2 white cubes to the can, you will have a value of 3.” Decide the color and number of cubes in the can. Draw a picture and tell how you know. Page 48 48 ©MathTeachersPress, Inc. Reproductionby anymeans is strictlyprohibited = Adda2 to a ¯2 toget asum zero. = To solvean equation, find the value for the variable thatwillbalance theequation. You canusemodels tohelp find the solution. 3. Simplify bymatching positive andnegative pairs. x =5 x =7 Example: x + 3=8 Example: x – 2= 5 Usemodels tosolve theequations. 1. = x =_____ 2. = x = _____ 3. x + 3=6 x = _____ 6. x – 3=3 x =_____ 4. x –4=5 x =_____ 7. 4+ x = 1 x =_____ 5. x –2=6 x =_____ 8. ¯4+ x =3 x = _____ = = = = Solving Addition and Subtraction Equations with Models 2. Isolate x byusing the sum zero pattern. Make the same changeon theother side of theequation. 1. Build the equation with rods and cubes. Steps: Adda2on thisside also. Can you find the pattern for solving equationswith additionand subtraction? Adda ¯3on theother sidealso. Adda ¯3 to a3 toget asum zero. Lesson Uses: Algebra Tiles Level D Sample Lesson Plan