Achievemath High School Readiness Sample

AchieveMath Instructional Intervention

High School Readiness SAMPLE LESSONS

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AchieveMath HS Math Readiness— Lesson 39

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High School Readiness – Lesson 39

AchieveMath

Objective and Standards Add positive and negative integers (6.NS.5, 6.NS.7, 7.NS.1, 7.EE.3, PS.2, PS.3, PS.4)

Word Problem Objective Use a diagram and chart to draw a conclusion and solve a word problem

High School Readiness – Lesson 39 Bill

Ted

Sara

Eddy

Sara has shaken everyone’s hand by now. There are 6 handshakes total.

Materials/Manipulatives two-colored counters, Concept Development Integer Mat (student worksheets), dry-erase boards/markers/erasers, pencils, loose-leaf paper

Corresponding Vocabulary Teacher: Write the following vocabulary words on a board. Discuss these words and their meanings throughout the lesson.

Welcome (3 min.)

integer, positive, negative, addend

Brief Review and Practice (10 min.)

Concept Development (10 min.)

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Skill: Compare positive and negative integers.

Teacher: Write the following problems on the board. Students will solve the problems as a group. Write the correct symbol in the box. 1) 1 (>) -6

2) -5 (<) 2

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3) 3 (<) 4

4) -8 (=) -8

Write the following sets of integers in order from smallest to largest. 5) -8, 10, -16, 24, -38, 74

(-38, -16, -8, 10, 24, 74)

6) 51, -2, 83, -32, 62, -100

(-100, -32, -2, 51, 62, 83)

Word Problem

Teacher: Write the following problem on the board. Read it out loud as the students read it silently. You may want to act out this problem as well as give the set-up of the diagram to the students. This problem is to be discussed as a group. Bill, Tedd, Sara, and Eddy are in a group. All four of them shake hands with each other. No two people shake hands more than once. How many handshakes were there all together?

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Teacher: Show the students one yellow and one red counter.

Say: “Today we’re going to learn how to add integers. We’ll be using two-color counters. The red side will represent negative. The yellow side will represent positive. The important part to remember is that positive one and negative one cancel each other out and their value is zero. These counters represent a pair of yellow and red counters, canceling one another. Let’s think of what this means in a money situation. You have $1 in your pocket. What number does this represent?”

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(positive one)

Say: “You owe someone $1. What number does this represent?” (negative one)

Say: “When you pay off your debt, how much will you have left?” (0)

Say: “So a positive one and a negative one equal zero.”

Teacher: Pass out thirty counters to each student. Have students find the Concept Development Integer Mat in their portfolios.

Say: “We will use the counters to represent positive and negative numbers in our problems. Let’s try the first one.” Teacher: Write on the board: 3 + 2

Bill shakes hands with Tedd, Eddy, and Sara (3 handshakes so far). Bill

Ted

Say: “What’s the sum?”

Sara

Eddy

Say: “What color counters would we use?”

(5)

Tedd has already shaken Bill’s hand. Tedd shakes Sara’s and Eddy’s hand (2 more handshakes). Bill

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(3 yellow and 2 yellow counters)

Say: “Place the three yellow counters on the positive side of your mat.”

Ted

Teacher: Allow students time to place 3 yellow counters on the mat.

Sara

Eddy

Eddy has already shaken Bill’s and Teddy’s hands. Eddy shakes Sara’s hand (1 more handshake). AchieveMath

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High School Readiness – Lesson 39

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High School Readiness – Lesson 39

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Say: “What cancels here?”

Say: “What represents 2?”

(nothing, everything is red)

(2 yellow counters)

Say: “What is our sum?”

Say: “Place those counters on the positive side of the mat.” Teacher: Allow the students time to place two more counters on the mat, positive side.

Say: “How many counters do we have in all?”

Negative

Positive

(5, all yellow)

(-12)

Say: “What did you notice about the sign of the answer when you have more yellow counters than red?” (It is positive.)

Say: “What do you notice about the sign of the answer when there are more red counters than yellow?” (It is negative.)

Say: “This represents our answer; positive 5. Now let’s look at a problem where we add a negative to a positive.”

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Teacher: Write on the board: -4 + 1 = ?

Say: “What color counters do we place on the mat for –4 and where are they placed?” (4 red counters are placed on the negative side of the mat)

Say: “What do we use for positive 1?”

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(one yellow counter on the positive side)

Say: “Remember we mentioned that a positive and a negative cancel each other out. Since we have both colors on the mat we need to pair up one red counter with one yellow counter to represent elimination.” Teacher: The students’ mats should reflect the following:

Say: “What can we remove from the mat?”

Negative

Positive

Say: “What do you notice if all of the counters are red?”

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(The answer is negative.)

Guided Practice (15 min.)

Teacher: The students will work with partners. Give the students two-color counters and dry-erase boards/markers/ erasers. Have the students write the integer addition sentence on their boards.

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Say: “Write an addition sentence for the information given. Use the two-color counters to help you add the integers. Solve the problems as a pair.” 1) 2 red, 3 red (-2 + (-3) = -5)

2) 4 red, 2 red (-4 + (-2) = -6)

3) 5 red, 2 red (-5 + (-2) = -7)

4) 2 red, 3 yellow (-2 + 3 = 1)

5) 3 red, 1 yellow (-3 + 1 = -2)

6) 6 red, 2 yellow (-6 + 2 = -4)

Say: “Who can develop a rule for the numbers we’re adding if the signs are the same?” (If the addends have the same sign, add the numbers, keep the same sign.)

(one yellow and one red to make a pair)

Say: “Who can develop a rule for adding a positive and a negative integer?”

Say: “What does this pair represent?”

(Subtract the numbers. The answer has the sign of the higher number.)

(-1 + 1 = 0)

Say: “What do we have left?”

Independent Practice/Application (7 min.)

(3 red counters or -3)

Say: “So, -4 + 1 = -3. If we rewrote the problem with the positive number first, it would be 1 + (-4). The negative

Teacher: Write the problems on the board. Students will solve the problem independently on their dry-erase boards. Students may use counters if they choose. Check all results.

number after the addition sign is put in parentheses so that we keep track of the negative sign. Redo this problem as 1 + (-4) and see what you get.”

1) -8 + (-3) = (-11)

2) 4 + (-11) = (-7)

3) -6 + 7 = (1)

4) -5 + (-7) = (-12)

5) 3 + (-2) = (1)

6) -8 + 2 = (-6)

7) -7 + 3 = (-4)

8) -2 + (-5) = (-7)

Teacher: Allow students to redo problem. They will still have a negative 3 as the sum.

9) -3 + (-4) = (-7)

10) -3 + 7 = (4)

Say: “Let’s look at adding 2 negatives.” Teacher: Write on the board: -8 + (-4) = ?

Say: “How many counters of what color do we put down?” (8 red, then 4 red, all go in the negative section) AchieveMath

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Closure (15 min.)

High School Readiness – Lesson 39

Daily Lesson Assessment

Name: _____________________________________________________________________________________

•Lesson Summary – (1 minute) What did we do today?

Date ____________________________

SKILL: Add positive and negative integers

Provide a real life application of this skill. • Administer Daily Lesson Assessment – (8 minutes) Check all answers. Score and record responses on the Math Group Skills Sheets. 1) 9 + 5 = (14)

1) 9 + 5 =

2) 4 + (-8) = (-12) 3) 7 + (-6) = (1) 4) -8 + 3 = (-5)

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5) -10 + 3 = (-7) •Tokens/Token Tracker/Awards Center – (6 minutes)

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2) -4 + (-8) =

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3) 7 + (-6) =

4) -8 + 3 =

5) -10 + 3 =

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Activity Sheet

Name: _____________________________________________________________________________________

Date ____________________________

Concept Development Integer Mat Negative

Positive

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High School Readiness – Lesson 40

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High School Readiness – Lesson 40

AchieveMath

Objective and Standards

Say: “My example of this type is: -5 + (-2) = -7.”

Add positive and negative integers (6.NS.5, 6.NS.7, 7.NS.1, 7.EE.3, PS.1, PS.2, PS.3)

Teacher: As you are mentioning the examples, write them on the board. Addends with same sign

Word Problem Objective Use a diagram and chart to draw a conclusion

2 + 3 = 5

Materials/Manipulatives

-5 + (-2) = -7

deck of playing cards (face cards removed), dry-erase boards/markers/erasers, 15 sheets of copy paper

Welcome (3 min.)

Say: “What do you notice about the sign of the sum?” (It’s the same sign as the addends.)

Say: “Now let’s have two volunteers create two examples – one with two positive addends and a problem with two

Brief Review and Practice (10 min.)

negative addends.”

Skill: Add positive and negative integers

Teacher: Choose two students to create the examples. One example should add two positive integers, while the other adds two negative integers. Have the examples written on the board. The whole group should help solve their examples.

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Teacher: Pass out dry-erase boards/markers/erasers to the students. Write the following problems on the board. Have the students solve the problems independently on their dry-erase boards. 1) -8 + 6 = (-2)

2) 8 + (-3) = (5)

5) -9 + (-7) = (-16)

6) -18 + 1 = (-17)

3) -4 + 7 = (3)

4) -4 + 10 = (6)

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Word Problem

Teacher: Write the problem on the board. Have the students read the problem silently. Have 15 pieces of copy paper laid out on the floor to represent each rung of the ladder. Students will act out climbing up/down a certain number of rungs until the sum is found. Once this is done, work with the students to get an addition problem to represent the scenario. Tom started at the bottom of a ladder. He climbed up 8 rungs and went down 3 rungs. Then he climbed up 5 rungs and went down 7 rungs. Finally, he climbed 12 rungs to the top. How many rungs are on the ladder? (15)

(Addends can have different signs.)

Say: “Here’s my first example with different signs: -3 + 5 = 2. The next example is: 7 + (-10) = -3. How are these two

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examples different?”

(The first one adds positive to a negative. The second one adds negative to a positive.) Teacher: Write the examples on the board as you say them. Addends with different signs -3 + 5 = 2

7 + (-10) = -3

Say: “Now it’s your turn to make up two more examples.”

8 + (-3) + 5 + (-7) + 12 =

5 + 5 + (-7) + 12 =

Teacher: Choose two students to each make up one example. One example should add a positive to a negative and the other example should add a negative to a positive. The group should help solve their examples.

10 + (-7) + 12 =

3 + 12 = 15

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Say: “What other type of addition problem can we have?”

15 rungs on the ladder.

Say: “We have examples for both types of addition problems. Let’s talk about the rules. What is the rule for adding integers with the same sign?” (The sum is the same sign as the addends.)

Corresponding Vocabulary Teacher: Write the following vocabulary words on a board. Discuss these words and their meanings throughout the lesson. addends, integer, sum, digit

Say: “What’s the rule for adding integers of different signs?” (The sum has the sign of the larger digit.)

Concept Development (10 min.) Say: “We have worked with different types of integer addition problems. Let’s go through the types. First, we have the addition problem where the addends are the same sign. My example is: 2 + 3 = 5. What other addition problem can we have where the signs are the same?”

Teacher: Write these rules on the board.

Guided Practice (15 min.) Teacher: Have playing cards ready.

(Both addends are negative) AchieveMath

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Say: “We’re going to use playing cards to help us practice our addition problems. In this deck, the red cards represent

High School Readiness – Lesson 40

AchieveMath

Closure (15 min.)

a negative integer and the black cards represent a positive integer. Each of you will receive two cards from the deck. Your job is to add the two cards that you have. We will then ask each person to tell the group their sum. The student who has the greatest sum is the winner of that round and gets all of the cards from the other students. We’ll keep playing until we run out of cards.”

•Lesson Summary – (1 minute)

Teacher: The charts below represent all possible combinations of problems as well as solutions.

• Administer Daily Lesson Assessment – (8 minutes) Check all work. Score and record student results on the Math Group Skills Sheet.

Addends with same signs (for negatives, just include negative with answer) + 1 2 3 4 5 6 7 8 9 10

1 2 3 4 5 6 7 8 9 10 11

2 3 4 5 6 7 8 9 10 11 12

3 4 5 6 7 8 9 10 11 12 13

4 5 6 7 8 9 10 11 12 13 14

5 6 7 8 9 10 11 12 13 14 15

6 7 8 9 10 11 12 13 14 15 16

7 8 9 10 11 12 13 14 15 16 17

8 9 10 11 12 13 14 15 16 17 18

9 10 11 12 13 14 15 16 17 18 19

10 11 12 13 14 15 16 17 18 19 20

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1 0 -1 -2 -3 -4 -5 -6 -7 -8 -9

2 1 0 -1 -2 -3 -4 -5 -6 -7 -8

3 2 1 0 -1 -2 -3 -4 -5 -6 -7

4 3 2 1 0 -1 -2 -3 -4 -5 -6

5 4 3 2 1 0 -1 -2 -3 -4 -5

6 5 4 3 2 1 0 -1 -2 -3 -4

7 6 5 4 3 2 1 0 -1 -2 -3

8 7 6 5 4 3 2 1 0 -1 -2

9 8 7 6 5 4 3 2 1 0 -1

Provide a real life application of this skill.

1) -6 + 6 = (0)

2) 5 + (-16) = (-11)

4) 6 + (-3) + 11 = (3 + 11 = 14)

5) -4 + (-10) + 3 = (-14 + 3 = -11)

3) 15 + (-23) = (-8)

•Tokens/Token Tracker/Awards Center – (6 minutes)

Addends with different signs (can reverse order: ex. -3 + 4 = 4 + (-3) = 1) + -1 -2 -3 -4 -5 -6 -7 -8 -9 -10

What did we do today?

10 9 8 7 6 5 4 3 2 1 0

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Independent Practice/Application (7 min.) Teacher: Write problems on the board. Pass out dry-erase boards/markers/erasers. Students are to work on the problems independently. Discuss the solutions. 1) -9 + (-2) = (-11)

2) 8 + (-8) = (0)

3) -6 + (-8) = (-14)

4) 12 + (-3) = (9)

5) -7 + (-12) = (-19)

6) -20 + 6 = (-14)

7) -6 + (-7) = (-13)

8) -16 + 8 = (-8)

9) -15 + 9 = (-6)

10) -17 + (-9) = (-26)

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Daily Lesson Assessment

Name: _____________________________________________________________________________________

Date ____________________________

SKILL: Add positive and negative integers 1) -6 + 6 =

2) 5 + (-16) =

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3) 15 + (-23) =

4) 6 + (-3) + 11 =

5) -4 + (-10) + 3 =

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