Lesson Menu Main Idea and New Vocabulary NGSSS Example 1:Add Integers with the Same Sign Key Concept:Add Integers with the Same Sign Example 2:Add Integers with the Same Sign Key Concept:Additive Inverse Property Example 3:Add Integers with Different Signs Example 4:Add Integers with Different Signs Key Concept:Add Integers with Different Signs Example 5:Add Integers with Different Signs Example 6:Add Integers with Different Signs Example 7:Add Integers with Different Signs Example 8:Real-World Example Five-Minute Check

Main Idea/Vocabulary Add integers. opposites additive inverse

NGSSS MA.7.A.3.1 Use and justify the rules for adding, subtracting, multiplying, dividing, and finding the absolute value of integers. Also addresses MA.7.A.3.2.

Example 1 Add Integers with the Same Sign Find –6 + (–3). Start at 0. Move 6 units to the left to show –6. From there, move 3 units to the left to show –3. Answer: So, –6 + (–3) = –9. –6–3

Example 1 CYP A.–4 B.–2 C.0 D.4 Find –2 + (–2).

Key Concept 2

Example 2 Find –34 + (–21). Add Integers with the Same Sign – 34 + ( – 21) = –55Both integers are negative, so the sum is negative. Answer: So, –34 + (–21) = –55.

Example 2 CYP A.22 B.6 C.–6 D.–22 Find –14 + (–8).

Key Concept 3

Example 3 Add Integers with Different Signs Find 8 + (–7). Answer: So, 8 + (–7) = –7

Example 3 CYP A.–4 B.–2 C.2 D.4 Find 3 + (–1).

Example 4 Find – Add Integers with Different Signs Answer: So, –5 + 4 = –1. –5 +4

Example 4 CYP A.–11 B.–7 C.7 D.11 Find –9 + 2.

Key Concept 6

Example 5 Add Integers with Different Signs Find 2 + (–7). 2 + (–7) = –5Subtract absolute values; 7 – 2 = 5. Since 7 has the greater absolute value, the sum is negative. Answer: So, 2 + (–7) = –5.

Example 5 CYP A.14 B.2 C.–2 D.–14 Find 6 + (–8).

Example 6 Add Integers with Different Signs Find – – = –3Subtract absolute values; 9 – 6 = 3. Since 9 has the greater absolute value, the sum is negative. Answer: So, –9 + 6 = –3.

Example 6 CYP A.12 B.10 C.–10 D.–12 Find –

Example 7 Add Integers with Different Signs Find 11 + (–4) + (–11) (–4) + (–11) = 11 + (–11) + (–4)Commutative Property (+) = [11 + (–11)] + (–4)Associative Property (+) = 0 + (–4)Additive Inverse Property = –4Additive Identity Property Answer: The solution is –4.

Example 7 CYP A.–12 B.–10 C.–7 D.–2 Find 5 + (–7) + (–5).

Example 8 FINANCIAL LITERACY Small businesses manage their inventory using integers. The cost of goods sold is calculated as starting inventory plus cost of items bought during the year plus a negative value on the ending inventory for the year. For example, a small horse farm owner might have a starting inventory of horses valued at $9,500, purchase a colt during the year for $2,000, and have an ending inventory value of $6,000. What is the cost of goods sold? Write an addition sentence to describe this situation. Then find the sum and explain its meaning.

Example 8 $9,500 + $2,000 + (–$6,000) = $11,500 + (–$6,000)$9,500 + $2,000 = $11,500 = $5,500Subtract the absolute values. Since $11,500 has the greater absolute value, the sum is positive. Answer: The cost of goods sold is $5,500.

Example 8 CYP A.Point E is 4 feet lower than point A. B.Point E is 6 feet lower than point A. C.Point E is 8 feet lower than point A. D.Point E is 10 feet lower than point A. ROLLER COASTERS The graphic shows the change in height at several points on a roller coaster. Write an addition sentence to find the height at point E in relation to point A (–32) (–10) = –6

A.0 B.1 C.–8 D.8 Find – Five Minute Check 1

A.15 B.–15 C.1 D.–1 Find 8 + (–7). Five Minute Check 2

A.–8 B.8 C.–2 D.2 Find –3 + (–5). Five Minute Check 3

A.– = –40; the bird is 40 feet below where it started. B.50 + (–10) = 40; the bird is 40 feet above where it started. C = 60; the bird is 60 feet above where it started. D.–50 + (–10) = –60; the bird is 60 feet below where it started. Write an addition expression to describe the situation. Then find the sum and explain the meaning. A bird flies up 50 feet and swoops back down 10 feet. Five Minute Check 4

A.– = –4; Teresa still owes her brother $4. B.–14 – 10 = –24; Teresa still owes her brother $24. C.14 + (–10) = 4; Teresa’s brother now owes her $4. D = 24; Teresa’s brother now owes her $24. Write an addition expression to describe the situation. Then find the sum and explain the meaning. Teresa owes her brother $14. She finds $10 and gives it to him. Five Minute Check 5

A.–12 B.–6 C.6 D.12 Evaluate x + y if x = –3 and y = –9. Five Minute Check 6