Foundations Sampler 2024

53 Lesson Plans 35 ©MathTeachersPress, Inc. Reproduction by anymeans is strictly prohibited. 35 An equation may be written from words. The sum of three times a number and 4 is 10. 3 n + 4 = 10 An equation is a sentence with an equal sign. In a mathematical sentence, the words “is equal to” are replaced by the equal sign.The equal sign tells you that both sides of the equation have the same value. Summeans to add. Write an equation for each picture. Use x as the variable. 1. ________ 3. ________ 5. ________ + = = = 2. ________ 4. ________ 6. ________ = + = = 7. Anumber plus 5 is 8. 9. 10 more than a number is 45. 11. Anumber minus 20 is 80. 13. Anumber divided by 2 is 12. 15. Twice the number is 12. 17. Anumber decreased by 4 is 50. 8. Anumber less 6 is 34. 10. Anumber increased by 6 is 58. 12. 2 times a number less 5 is 7. 14. 3 times a number decreased by 4 is 23. 16. 11 less than a number is 7. 18. 4 times a number is 40. An equation can be written from a model or picture of a model. – x + 4 = 5 n + 5 = 8 = Joan had some money in her purse. She went to the store and bought a CD for $18. When she got home, Joan had $10 left. Pick the equation that shows what happened. A n – 18 = 10 C 18 + n = 10 B 18 – 10 = 8 D 28 – 18 = 10 Answer Writing Equations from Models or Words x – 3 = 4 2 x +2=8 x +3+ x =–2 x +3 2 x +2 x –4=4 x –4 2 x +2=3 x –4 3 x +4=–2 n –6=34 n +10=45 n +6=58 n –20=80 2 n –5=7 =12 3 n –4=23 2 n =12 n –11=7 n –4=50 4 n =40 n 2 Objective: To write equations from models or from sentences. Materials: Rectangular rods (or positive rectangular rods, Master 5), black and white cubes (or positive and negative integer squares, Master 5), equal sign index card (Master 5) Vocabulary: equation, phrase, equality symbol Comparing a Phrase to an Equation In these activities, students write equations from prose and models. In equations, the variable represents a specific unknown number. Write on the board: x + 4 Display 1 brown bag marked x (or one rectangular rod) and 4 black cubes to model the expression. What is the value of x ? (The value can be any number.) Write on the board: x + 4 = 6 Next to the 1 rectangular rod and 4 black cubes, put an equal sign followed by 6 black cubes. Ask a student volunteer to explain the meaning of the models in his/her own words. (We start with an unknown number, add 4 to the number and it equals 6.) What number would you add to 4 and get 6? (2) Is there any other number? (no) How many different values of x will make the statement true? (only one, x = 2) Emphasize that the equal sign turns the phrase into a sentence or equation in which only one value of x will make the equation true. Display other combinations with rectangular rods and cubes and an equal sign, asking students to guess and check to find the value of x that makes the statement true. = Read and model the explanation at the top of the page together. Use one rectangular rod, black cubes, and an equal sign to model and simplify the equation. Have student volunteers use rods and cubes to model problems 1 and 2 before they are recorded. Ask student volunteers to read and identify key operational words in problems 7–18 before they are assigned. Using Guess and Check Students enjoy solving problems in a variety of ways. Explain that one way of solving an equation is to keep substituting different numbers for the variable until you find the one that makes the equation true. Ask students to use guess and check to solve several problems. Skill Builders 50-1 Equations Sample of Scripting (Bold Type) Wha number would you add to 4 and get 6? (2) Is there any other number? (no) How many different values of x will make the statement true? (only one, x = 2) Emphasize that the equal sign turns the phrase into a sentence or equation in which only one value of x will make the equation true. Display other combinations with rectangular rods and cubes and an equal sign, asking students to guess and check to find the value of x that makes the statement true. MH5 Lesson Plan Students solve one-step equations.