Algebra Do-Nows

Objective: Students will be able to write statements of equality in the form of equations.

Number 1 Tell students that: “I’m thinking of a number. Two times this number is 4. What is the number?” Give other word problems and tell students to write as math problems. Eight times some number equals twenty-four.

Objective: To solve equations of the form x – b = c.

Number 1 The Franklin School allows each class a monthly budget of $50 for miscellaneous supplies. The current budget balance for Ms. Limon’s class is $24.20. The receipt for the purchases was lost. However, the treasurer remembers buying 20 notebooks to use a math journal and that the notebooks were either $1.29, $1.39, or $1.49. How much did each notebook cost? (answer-$1.29) Students will solve the problem and prepare a storyboard or comic strip showing how they found the cost of one notebook. Tell them that they nee d to use equations to describe the problem. Encourage students to assign jobs such as storyboard designer, artist, and writer. One student can be responsible for obtaining the materials needed to produce the storyboard.

Objective: Students will be able to use multiplication by reciprocals to solve multiplication equations.

Number 1 Give the following problems for the students to work on: Three times what number is equal to 1? (answer-1/3) Five times what number is equal to 1? (answer-1/5) N times what number is equal to 1? (answer-(1/N) Stress that any number times its reciprocal equals one.

Number 2 Students work in groups to produce a five-minute “How To” segment for Math Improvement television show. Encourage students to present step-by-step directions for solving multiplication equations using either multiplication by reciprocals or division. Encourage students to assign tasks to group members such as scriptwriter, artist, director, and announcer.

Objective: Students will be able to solve equations requiring more than one step.

Number 1 Give the students a brain teaser to solve: “I’m thinking of a number. Three times that number minus seven equals twenty. What is the number?” (answer-9) Students write how they found the number.

Number 2 Students work in groups to solve the following problem. The following information about the student lunch program at Jefferson Elementary School is given.

Tuesday , October 14

Cost per lunch $0.40

Uneaten lunches 43

Total spent on lunches $62.80

The school orders enough lunches for all students but does not pay for any uneaten lunches. How many students are in Jefferson Elementary School? answer {0.40(x) – 0.40(43) = $62.80; x = 200}

Objective: Students will be able to use the Pythagorean theorem to solve for the value of the third side of a right triangle.

Number 1 Students will use unit cubes to solve: a2 + b2 = c2 Groups work with 3 squared + 4 squared = 5 squared. Groups draw and label the corresponding right triangle. Within the group, they discuss the equation in terms of the Pythagorean theorem. To prove the theorem, they build a model of the square of each number, they combine the cubes in 3 squared and 4 squared, and compare to the number of cubes in 5 squared. They repeat this for a 6, 8, 10 triangle. They next draw a right triangle and label one leg 8, one leg a, and the hypotenuse 10. They write the equation a squared + 8 squared = 10 squared. They build models of 8 squared and 10 squared. They discovered how to find a squared. They form a rule to find the length of leg a.

Number 2 Students at Grant School plan to plant 22 oak trees around the perimeter of the school. Each tree needs to be braced with three wires. Each wire is attached 3 ½ feet from the ground and 2 ½ feet from the base of the trunk. What is the minimum amount of wire the students will need? (answer the square root of 3.5 squared + 2.5 squared = 4.3 ft. per wire, 3 x 4.3 = 12.9 ft./tree, 13 ft./tree x 22 trees = 286ft.)

Objective: Students will be able to write statements of equality or inequality based on information on a number line.

Number 1 Students write the mathematical sign to make the statements true.

Problems Answers

4 + 2 + 3 ___ _ 4 + 4 >

6 + 2 + 3 ____ 4 + 6 >

7 + 2 + 3 ____ 4 + 7 >

Number 2 Students are given the following pairs of numbers. They use =, <, or > to make the numbers into a statement that is true or false.

Problems Answers

4, 3 true (4>3)

4, 3 false (4 = 3, 4 < 3)

17, 15 true (17 > 15)

32, 0 false (32 = 0 OR 32 < 0)

5, 9 true ; (5 < 9)

Number 3 Students prepare five cards, each showing one of the signs =, <. >. >, and <, and place the cards face down in a pile. One partner rolls two number cubes and chooses one card. That partner then writes a statement using the numbers on the cubes and the symbol on the card. The other partner reads the statement aloud and determines whether it is true or false. Partners change roles after each turn.

Number 4 Students prepare a truth table for the following statements. The table should give the truth-values for p, q, and the disjunction “p or q.”

P = all birds have feathers

Q = most birds can fly

P = the sun rises in the east

Q = fish can sing

P = baseball is played on ice

Q = hockey is played with a puck

P = bowling balls are light

Q = Ping-Pong balls are heavy

Example truth table:

P Q P or Q

T T T

T F F

F T F

F &nbs p; F F

Number 5 Students work in groups. Each group has two number cubes. Two students roll the number cubes and then use either the > or the < symbol to write statements using the numbers from a single toss. Remaining group members identify the statements as either true or false. Groups might try to form only true or only false statements.