Integers & Number Lines
1.) Place 0, 4, –6, –1, -8, & 7 on a horizontal number line.
2.) Which number is furthest from zero?
1.) Correctly labeled number line: (-8, -6, -1, 0, 4, 7)
2.) -8 is furthest from zero. It is 8 away.
Calculate: -7 + 12
5
Add: 3/4 + 2/5
23/20 or 1 & 3/20
Evaluate: -5 + 3 × 2
1
A student calculates 5 + -8 = 3. Identify and correct the error.
The student added 8 to 5 instead of adding -8 to 5.
The answer is -3.
Pro tip: when adding integers, circle and change signs next to signs.
-- & ++ become + and -+ & +- become -
1. The temperature was -5°F the morning before school. By midday lunch it had risen 12°F. What was the temperature then?
2. The temperature then got 11°F warmer by the time school let out. But, by dinner time it had dropped 15°F. At bedtime it had fallen 4°F more. What temperature was it then?
1. 7°F
2. -1°F
Calculate: -18 - -35
17
Subtract: 7.6 - 4.65
2.95
Evaluate: (8 - 3)2 * -4
-100
A student says 7 - (-3) = 4. Identify and correct the mistake.
The student subtracted 3 from 7 instead of changing the two negatives into a plus, and then adding 3 to 7. The correct solution is 7 - (-3) becomes 7 + 3 = 10.
A submarine is at -250 m below sea level. It descends another 75 m. Then, it dives twice as deep before rising 100 m. What is its final position?
1.) Multiply: -6 × 7 and Divide: -42 ÷ -6
2.) If Mr. Murphy doesn't dislike caramel, then does he like it or not?
1. -42 and 7
2. Doesn't dislike caramel is a double negative. It actually means he likes caramel :9, because he doesn't dislike it.
Multiply: 2 ⅔ × 9/4
6
Simplify: 12 ÷ (1/2)2 + 19
67
A student computes 2/3 × 9/4 = 11/12. Identify, explain, and correct the error.
The student added the numerators, but did multiply the denominators. The answer is 3/2.
Match each vocabulary term to its correct definition and record the number→letter pairs.
| Terms | Definitions |
|---|---|
| 1.) Absolute value | a.) A number greater than zero; found to the right of 0. |
| 2.) Coordinate | b.) Two numbers that are the same distance from zero but on different sides. |
| 3.) Negative number | c.) The distance a number is from zero; always positive. |
| 4.) Opposites | d.) A visual model showing numbers placed in order from left to right. |
| 5.) Number line | e.) A whole number, its opposite, or zero (…, –3, –2, –1, 0, 1, 2, 3 …). |
| 6.) Positive number | f.) The position of a number on a number line. |
| 7.) Integer | g.) A number less than zero; found to the left of 0. |
1→b 2→c 3→f 4→a 5→d 6→g 7→e
Match each vocabulary term to its correct definition and record the number→letter pairs.
| Terms | Definitions |
|---|---|
| 1.) SADS rule (+ & -) | d. The rule for adding/subtracting signed numbers: same signs → add & keep sign; different signs → subtract smaller absolute value from larger & keep the sign of the number farther from zero. |
| 2.) Product | e. The answer to a multiplication problem. |
| 3.) Opposite | c. Two numbers that are the same distance from zero but with different signs. |
| 4.) Sum | a. The answer to an addition problem. |
| 5.) Quotient | f. The answer to a division problem. |
| 6.) SADS rule (* & /) | g. The rule for multiplying/dividing signed numbers: same signs → positive; different signs → negative. |
| 7.) Difference | b. The answer to a subtraction problem. |
1→a 2→b 3→e 4→f 5→c 6→d 7→g
Match each vocabulary term to its correct definition and record the number→letter pairs.
| Terms | Definitions |
|---|---|
| 1.) Decimal | a.) The top number in a fraction, showing how many parts are counted. |
| 2.) Improper fraction | b.) A number written with a whole part and a fraction part (e.g., 2 ¾). |
| 3.) Mixed number | c.) A number written with a numerator over a denominator (e.g., 3/4). |
| 4.) Fraction | d.) A number with a decimal point (e.g., 0.75). |
| 5.) Equivalent fraction | e.) The bottom number in a fraction, showing how many equal parts the whole is divided into. |
| 6.) Numerator | f.) A fraction that has the same value as another fraction but different numbers (e.g., 1/2 = 2/4). |
| 7.) Denominator | g.) A fraction whose numerator is larger than its denominator (e.g., 7/4). |
1→b 2→e 3→c 4→g 5→f 6→a 7→d
Match each vocabulary term to its correct definition and record the number→letter pairs.
| Terms | Definitions |
|---|---|
| 1.) Grouping symbols | a. A combination of numbers, variables, and operations (no equal sign). |
| 2.) Exponent | b. Symbols such as parentheses or brackets used to group parts of an expression. |
| 3.) Multiply | c. The operation of repeated addition (×). |
| 4.) Divide | d. The operation of separating a quantity into equal parts (÷). |
| 5.) Add | e. The operation of combining numbers to find a total (+). |
| 6.) Subtract | f. The operation of finding the difference between numbers (–). |
| 7.) Expression | g. A shorthand way to show repeated multiplication (e.g., 3² = 3 × 3). |
1→b 2→g 3→c 4→d 5→e 6→f 7→a
Match each vocabulary term to its correct definition and record the number→letter pairs.
| Terms | Definitions |
|---|---|
| 1.) Estimate | a.) The process of making an expression as simple as possible. |
| 2.) Sign | b.) To find the value of an expression by performing all operations correctly. |
| 3.) Correction | c.) A rough calculation to get an approximate answer. |
| 4.) Reasoning | d.) An error made while calculating or thinking. |
| 5.) Simplify | e.) A number’s positive or negative property. |
| 6.) Mistake | f.) The action of fixing a mistake to make it correct. |
| 7.) Check | g.) The thought process used to solve a problem or explain a solution. |
1→e 2→f 3→d 4→a 5→b 6→c 7→g
Starting at -8 on a number line, move 3 steps to the right, then 10 steps to the left, then 4 steps right. What is the opposite number of where you are now?
11
A hiker loses 12 meters going down a hill, then gains 5 meters climbing. Repeat this sequence 3 times. What is the net change in height?
-21 meters
Sort the following numbers from least to greatest:
3/2, 3/4, -0.6, 7/10, 0.67, -0.625, 0
-0.625, -0.6, 0, 0.67, 7/10, 3/4, 3/2
-7 + 23 + 10*((3.5 + 2.2) ÷ 3)
-7 + 23 + 10*((3.5 + 2.2) ÷ 3)
Step 1: 3.5 + 2.2 = 5.7.
Step 2: 23 = 2*2*2 = 8
Step 3: 5.7 * 10 = 57.
Step 4: 57 ÷ 3 = 19
Step 5: -7 + 8 = 1
Step 6: 1 + 19 = 20.
A student evaluates: 3 - 5 * (6 – 2)² ÷ 4. Identify the student's three computational errors. Then evaluate the expression correctly.
Student’s Work:
1.) (6 – 2) = 4
2.) 4² = 8
3.) 5 × 8 = 40
4.) 40 ÷ 4 = 10
Student’s Answer: 10
Errors:
1.) 42 = 4*4 = 16
2.) 5*8 = 40 should be -5*8 = -40
3.) After dividing by 4, the student still had to add the initial 3 in order to finish.
Correction: 3 - 5 * (6 – 2)² ÷ 4
Steps:
1.) (6 – 2) = 4
2.) 4² = 16
3.) -5 × 16 = -80
4.) -80 ÷ 4 = -20
5.) -20 + 3 = -17
Answer: -17