7 th Grade Math Integers 1 of 42

7 th Grade Math Integers 1 of 42 © Boardworks Ltd 2004

Contents Integers A Adding Integers and Signed Numbers 2 of 42 © Boardworks Ltd 2004

Adding Integers using Counters • Red Chips are Negative (─) • White Chips are Positive (+) ─ + • What is Additive Inverse? • What is the value of the red chip + the white chip? Red + White = ? 3 of 42 © Boardworks Ltd 2004

Adding Integers using Counters • This is called a “Zero Pair” because added together they make zero! ─ + • We can use these to add integers. 4 of 42 © Boardworks Ltd 2004

Adding Integers using Counters • Let’s Try: 5+2=? 5 Positives + 2 Positives + + + 5 of 42 + ─ + + © Boardworks Ltd 2004

Adding Integers using Counters • Let’s Try: -4 + -1 = ? 4 Negatives + 1 Negative 6 of 42 ─ ─ + ─ ─ © Boardworks Ltd 2004

Adding Integers using Counters • Let’s Try: -5 +3=? 5 Negatives + 3 Positives ─ ─ + + ─ ─ 7 of 42 © Boardworks Ltd 2004

Adding Integers using Counters • Let’s Try: 6 + -2 = ? 6 Positives + 2 Negatives + + + 8 of 42 + ─ ─ ─ © Boardworks Ltd 2004

Adding Integers • Let’s practice a few with your counters. -5 + 6 7 + -2 8+3 -7 + -1 10 + -3 -4 + -2 9 of 42 © Boardworks Ltd 2004

Homework • Carnegie – Page 219 - 220 10 of 42 © Boardworks Ltd 2004

Adding integers on a number line Before we begin, you and your group must complete the following task: You have 5 minutes to formulate the process of adding integers using a number line as your manipulative. Use the example of -5 + 3 = ? 11 of 42 © Boardworks Ltd 2004

Adding integers What directions can you move on a number line? How do you determine distance on a number line? Direction: The way you are moving on a number line (positive direction or negative direction) Distance: How far you are moving on a number line (ex. 5 places, 7 places, etc. ) 12 of 42 © Boardworks Ltd 2004

Adding integers KEY POINTS!!!! Positive number, move When adding a ____ to the ____ on the number line. Right Negative number, move When adding a ____ Left to the ____ on the number line. 13 of 42 © Boardworks Ltd 2004

PROCESS for Adding on a Number Line: Step 1 Zero • ALWAYS, start at _______! Direction Distance • Move the _____ and Addend first _____. Step 2 ______ of the • FROM THAT POINT, move the Distance Direction ______ and _____ of Step 3 the second ______. Addend 14 of 42 © Boardworks Ltd 2004

Adding integers PROCESS for Adding on a Number Line: 1. Start at zero – Always! 2. Move the direction and distance of the 1 st Addend 3. From that point, move the direction and distance of the 2 nd Addend How close was your group to the correct steps? 15 of 42 © Boardworks Ltd 2004

Adding integers – 2 + 5 = 3 -2 3 1. Start at zero 2. Go to first addend 3. Move in the direction and distance of the second addend 16 of 42 © Boardworks Ltd 2004

Adding integers – 3 + – 4 = – 7 -7 -3 1. Start at zero 2. Go to first addend 3. Move in the direction and distance of the second addend 17 of 42 © Boardworks Ltd 2004

Examples: (Show process on provided # lines) = 11 1. 6 + 5 (Do together) = -9 2. -7 + -2 3. 5 + (-3) =2 = -1 4. -3 + 2 5. 6 + (-7) 6. -9 + 4 18 of 42 = -1 = -5 © Boardworks Ltd 2004

Practice • Complete “Adding Integers Number Line” worksheet 19 of 42 © Boardworks Ltd 2004

Let’s Discover/Develop a Rule… • Use the “Developing a Rule” Organizer 20 of 42 © Boardworks Ltd 2004

Adding Signed Numbers Rule If both are Positive: - Add and the sum is positive (Ex. 8 + 4 = 12) If both are Negative: - Add and the sum is negative (Ex. -6 + -5 = -11) If they have different signs: - Subtract the absolute values, and - the sum will have the sign of the larger absolute value. (Ex. -7 + 4 = -3) Remember counters and # line Do you have more + or -? 21 of 42 7 -4=3 © Boardworks Ltd 2004

“Row, Row Your Boat!” or “Add, Add Your Integers!” • Operations with Integers song 22 of 42 © Boardworks Ltd 2004

Independent Practice • Glencoe Textbook – – Page 98 - #1 – 8 – Page 98 - #10 – 27 – Page 98 - #28 – 36 1. Write the actual problem on your paper 2. Use the rule to solve it. 23 of 42 © Boardworks Ltd 2004

1. 3. 5. 7. 9. 11. 13. 15. 17. 19. 21. 23. 25 24 of 42 3+2 -5 + 5 -10 + 5 5+3 -5 + -4 -6 + 13 -35 + 10 -5 + 9 -8 + -7 -50 + 30 -7 + 17 -6 + 3 -30 + 10 5 minute Challenge 2. 4. 6. 8. 10. 12. 14. 16. 18. 20. 22. 24. 26. -1 + 3 -9 + 3 -15 + 32 -4 + 7 -3 + 9 -30 + -15 6+7 -3 + 2 -10 + 4 0+7 -7 + 13 -12 + -1 -34 + 16 © Boardworks Ltd 2004

Contents Integers A Subtracting Integers and Signed Numbers 25 of 42 © Boardworks Ltd 2004

Use Sticky Notes: • 3 – 1= (Questions for following problems) – Think of a time when you could experience this subtraction problem. – How would you write an equivalent addition problem? • 6– 5= – Think of a time when you could experience this subtraction problem. – How would you write an equivalent addition problem? • 14 – 8 = – Think of a time when you could experience this subtraction problem. – How would you write an equivalent addition problem? 26 of 42 © Boardworks Ltd 2004

Let’s Discover/Develop a Rule… • Use the “Developing a Rule” Organizer 27 of 42 © Boardworks Ltd 2004

Contents Just remember, … EVERY SUBTRACTION PROBLEM CAN BE MADE INTO AN ADDITION PROBLEM!!! (The inverse of subtraction is addition. Also helps with commutative and associative properties!) 28 of 42 © Boardworks Ltd 2004

Contents JUST REMEMBER THREE WORDS… LITTLE, BITTY, TINY ADD THE OPPOSITE! This is the Rule!! 29 of 42 © Boardworks Ltd 2004

Contents 1. 2. 3. 4. 5. 30 of 42 Make each of these subtraction problems an equivalent addition problem: 5 -3= 6 -4= 10 – (-1) = -5 – 4 = -2 – (-7) = © Boardworks Ltd 2004

Subtracting integers We can use a number line to help us subtract positive and negative integers. 5 – 8 = – 3 5 + (-8) = – 3 -3 31 of 42 5 © Boardworks Ltd 2004

Subtracting integers We can use a number line to help us subtract positive and negative integers. 3 – – 6 = 9 3+6=9 3 3 – – 6 32 of 42 is the same as 9 3+6 © Boardworks Ltd 2004

Subtracting integers We can use a number line to help us subtract positive and negative integers. – 4 – – 7 == 3 – 4 + 7 = 3 -4 – – 7 33 of 42 3 is the same as – 4 + 7 © Boardworks Ltd 2004

Examples: 1. 8 – 13 2. 6 – 14 3. - 10 – 1 4. 1 – (-2) 5. 4 – (-8) = -5 = -8 = -11 =3 = 12 6. -3 – (-5) 7. -7 – (-4) 34 of 42 =2 = -3 © Boardworks Ltd 2004

Independent Practice • Glencoe Textbook – – Page 105 - #1 -11 – Page 105 - #13 -28 – Challenge - #37 -40 35 of 42 © Boardworks Ltd 2004

Subtraction Card Game • Either “Subtract One” or “Partner Play” 36 of 42 © Boardworks Ltd 2004

Dazzling Line Designs • “Paper Folding” – Integer Subtraction 37 of 42 © Boardworks Ltd 2004

Signed Rational Numbers • “Fraction, Decimal and Integer Practice” Worksheet • Buckle Down – page 23 38 of 42 © Boardworks Ltd 2004

Exercise Work out the following 1) 4 – 6 9) 3 – 6 2) +5 – 6 10)– 2 – 3 3) 4 – 10 11) – 3 4) 2 – 6 12) 0 – 5 5) 3 – 3 13)5 – 11 – 2 5 minute Challenge 6) 4 – (-2) 7) 5 - -4 8) -9 – (-5) 39 of 42 © Boardworks Ltd 2004

Extra Practice Below 40 of 42 © Boardworks Ltd 2004

Exercise B 1) – 8 + 9 9) 5 – 9 16) 4 + – 2 2) – 6 + 10 10) – 8 + 8 17) 2 + – 3 3) – 2 + 8 11)6 – 12 – 4 18) 4 – (– 2) 4) 0 – 8 12)7 – 10 + 3 19) 5 – (– 4) 5) 3 – 10 13)– 3 + 10 – 7 20) 15 – (– 3) 6) 8 – 10 14) 6 – 12 + 6 21) 4 – (– 6) 7) 7 – 9 15)8 – 16 – 3 22) – 9 – (– 5) 8) 4 – 10 41 of 42 23) – 10 + – 7 © Boardworks Ltd 2004

Exercise C Work out the following 1) 4 + – 2 2) 2 + – 3 3) 4 – – 2 4) 5 – – 4 5) 15 – – 3 6) 4 – – 6 7) – 9 – – 5 8) – 10 + – 7 42 of 42 © Boardworks Ltd 2004

Exercise E 43 of 42 © Boardworks Ltd 2004

Ordered addition square Copy the grid and work out the numbers in the empty squares 44 of 42 © Boardworks Ltd 2004

Ordered subtraction square Copy the grid and work out the numbers in the empty squares 45 of 42 © Boardworks Ltd 2004

Mixed subtraction square Copy the grid and work out the numbers in the empty squares 46 of 42 © Boardworks Ltd 2004

Integer cards - addition and subtraction Complete the sums 47 of 42 © Boardworks Ltd 2004