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Grade 6 Module4 Math
Expressions, Equations, and more
| Question | Answer |
|---|---|
| Build a tape diagram with 10 squares. Remove six squares. Add six squares . Write this expression. | 10-6+6 |
| 10-6+6= | 10 (because β 6 +6 is like adding a 0) |
| π β π + π= | π (because β x + x is like adding a 0) |
| 25 - ____ +10=25 | 10 (because β 10 + 10 is like adding a 0) |
| b-b = | 0 (b-b=0) |
| -x +x= | 0 (-x +x=0) |
| π + π β _____ = π | π (because β b + b is like adding a 0) |
| π β π + π = _____ | π (β π + π is like adding a 0) |
| π + _____ β π = π | π (+f-f is like adding a 0) |
| _____β π + π = g | g (β π + π is like adding a 0) |
| When you add and subtract the same number, the overall change to the expression is | 0 (Adding and subtracting the same number) |
| When you subtract and then add the same number, the overall change to the expression is | 0 (Subtracting then adding the same number) |
| Numbers like -3 and 3 are opposites, which have the sum of | 0 (-3 +3=0) |
| when asking for the sum of two numbers, you are supposed to | add (sum of 3 and 4 = 3+4=7) |
| Addition and Subtraction | are inverse (or opposite) operations -2+2 = 2-2 = 0 |
| Multiplication and Division | are inverse (or opposite) operations (Γ· 3 Γ3 = Γ3Γ· 3 is like multiplying by 1) |
| 9 Γ· 3 Γ 3 | 9 (Γ· 3 Γ3 is like multiplying by 1) |
| When we divide by one number and then multiply by the same number, we end up | with our original number (9 Γ· 3 Γ 3 = 9) |
| π Γ· π Γ π = | a (Γ· π Γ π is like multiplying by 1) |
| π Γ π Γ· π = | a (Γ π Γ· π is like multiplying by 1) |
| 12 Γ· 3 Γ ______ =12 | 3 (Γ· 3 Γ3 is like multiplying by 1) |
| π Γ β Γ· β = ______ | π |
| 45 Γ ______ Γ· 15 = 45 | 15 (x15Γ·15 is like multiplying by 1) |
| ______ Γ· π Γ π =p | p (Γ· r Γ r is like multiplying by 1) |
| 4 Γ 5 Γ· 5 = | 4 (Γ 5 Γ· 5 is like multiplying by 1) |
| 132 Γ· π Γ π= _____ | 132 (Γ· 3 Γ3 is like multiplying by 1) |
| How is the relationship of addition and subtraction similar to the relationship of multiplication and division? | Both relationships create identities. (Identity for addition and subtraction is 0) (Identity for multiplication and division is 1) |
| Why is identity for addition 0? | Because 0+ any number will equal that number. (4+0=4) |
| Why is identity for multiplication 1? | Because 1 times any number =that number. (5 x 1 = 5) |
| Multiplication is repeated __________ | addition |
| Multiplication is repeated addition, so 4 x 2 = | 4 + 4 or 2+2+2+2 |
| g + g + g = | 3π |
| 1x +1x+1x+1x+1x = | 5x |
| 2x + 4x = | 6x |
| 8x-5x | 3x |
| 4x-4x= | 0x = 0 |
| 4π Γ·1π = | 4π Γ·1π =4 |
| πy knowing that multiplication is the same as repeated addition | y+y+y+y+y+y |
| h+h+h+h+h knowing that repeated addition is the same as multiplication | 5h |
| use the relationship of division and subtraction to determine that 12 Γ· π₯ = 4 means | 12-x-x-x-x=0 |
| use the relationship of division and subtraction to determine that 20 Γ· 5 = 4 | 20 β 4 β 4 β 4 β 4 β 4 = 0 |
| use the relationship of division and subtraction to determine that π5 Γ·y=5 | π5 β π β π β π β π βπ =0 |
| If 12 Γ· π = π, how many times would π have to be subtracted from 12 in order for the answer to be zero? | 3 times, so x=4 |
| If 24 Γ· π = 12, which number is being subtracted 12 times in order for the answer to be zero? | Two |
| What is the inverse operation of addition? | Subtraction is the opposite or inverse of addition |
| repeated subtraction can be represented by which operation? | Division can be represented by repeated subtraction |
| Which operation is the inverse of division? | Multiplication is the inverse of division. |
| Explain why 30 Γ· π = π is the same as 30 β π βπ β π β π β π β π =π. | 30 Γ·5 = π , so π = π. When I subtract π from π0 six times, the result is zero. Division is a repeat operation of subtraction. |
| 2 raised to the power of 3 (2 is the base and 3 is the exponent or power) | 2 x 2 x 2 =8 |
| g x g x g written as an exponent | g to the power of 3 |
| 5 x 5 x 5 x 5 (repeated multiplication--write as an exponent, then solve) | 5 to the power of 4 = 625 (On calculator 5^4 = 625) |
| 6 squared is the same as 6 to the power of 2, which equals | 6 x 6 =36 (On calculator 6^2 = 36) |
| 4 cubed is the same as 4 to the 3rd power, which equals | 4 x 4 x 4 = 64 (On calculator 4^3 = 64) |
| Adding 1/2 +1/2 on your calculator | 1 (A b/c) 2 + 1 (A b/c) 2 = 1 |
| What is the difference between 6π§and π§ to the power of 6? | ππ = π + π + π + π + π + π or π times π; π to the power of π = π Γ π Γ π Γ π Γ π Γ z |
| Write 10 to the power of 3 as a multiplication expression having repeated factors. | 10 x 10 x 10 |
| Write π Γ π Γ π using an exponent. | 8 to the power of 3 (on calculator, 8^3) |
| Why do whole numbers raised to an exponent get greater? | As whole numbers are multiplied by themselves, products are larger because there are more groups. |
| Why do fractions raised to an exponent get smaller? | A part of a part is less than how much we started with. |
| The powers of π that are in the range π through 1000 | 2 raised to the 1st, 2 raised to the second, and so on.... 2, 4, 8, 16, 32, 64, 128, 256, 512 |
| Find all the powers of π that are in the range π through 1000 | 3 raised to the 1st, 3 raised to the second, and so on.... 3,9,27,81,243,729 |
| Find all the powers of π in the range π through π, πππ | 4 raised to the 1st, 4 raised to the second, and so on.... 4,16,64,256 |
| W raised to the power of b. What is w? | W is the base. Also, π is the factor that will be repeatedly multiplied by itself |
| W raised to the power of b. What is b? | b is called the exponent or you could call it a power. Also, π is the number of times π will be multiplied by itself. |
| What is the advantage of using exponential notation? | It is a shorthand way of writing a multiplication expression if the factors are all the same. |
| PEMDAS is an acronym to help you remember the order of operations. What does it stand for? | 1) Complete work inside Parentheses 2) evaluate Exponents 3)Add or Subtract left to right 4) Multiply or divide left to right |
| 3+4x2 | Multiply first! 3+4x2 = 3+8 = 11 |
| sum of two numbers | add the numbers |
| difference of 8 and 7 | 8-7=1 |
| product of 2 and 3 | 2 x 3 =6 |
| quotient of 8 and 4 | 8 divided by 4 is 2 |
| twice 6 | 6 x2 |
| twice 8 | 8x2 |
| 8 more than 1 | 1+8 |
| 6 less than 12 | 12-6 |
| What operations are always evaluated last? | Addition and subtraction are always evaluated last, from left to right. |
| π + π^π Γ· π Γ π β 2. What is completed first? ( π^π means 9 to the power of 2) | Exponents (π^π = π Γπ =81) |
| π + π^π Γ· π Γ π β 2. After first step is π + 81 Γ· π Γ π β 2. What is the next step | Multiplication and division, from left to right (81 Γ·π = π7; then 27 Γ π = 54) |
| π Γ (π + π^π) ( π^π means 4 to the power of 2) | =π Γ (π +16)= 2 x 19 = 38 |
| x + 7 = ____ , when x=2 | Substitute the 2 in place of the x, now 2 + 7 = 9 |
| Area = length x width can be written with variables A = l x w. Let l = 2 and w = 13. What is the Area? | A = l x w. Substitute l=2 and w = 13. Now, A = 2 x 13 = 26 square units |
| If l = length and w = width of a rectangle, What does the expression π+ π + π + π represent? | Perimeter of the rectangle, or the sum of the sides of the rectangle |
| Area of a square. Take the side length and multiply it by the side length again. What is the area of a square with a side of 4 inches | 4 x 4 = 16 square inches |
| Volume of a right rectangular prism is Volume = length x width x height or V=l x w x h. Let l=2 w=3 and h=4. What is the volume? | V=l x w x h V=2x 3 x 4=24 cubic units |
| What is an Equation An equation says that two things are equal. It will have an equals sign "=" like this: | x + 2 = 6 This is an equation. |
| Here we have an equation that says 4x β 7 equals 5. What is the coefficient of x? | 4 is the coefficient of 4x |
| Here we have an equation that says 4x β 7 equals 5. What is the variable? | The variable is x |
| Here we have an equation that says 4x β 7 equals 5. What is the constant? | 5 is the constant |
| Division by zero is undefined | means that you cannot divide by 0 |
| A letter in an expression can represent a number. Think about x+4. If we know that x=3, we can state the value of the expression. | x+4 , when x=3 3 +4 = 7 |
| Multiplicative Identity Property of One means anything times 1 equals itself so... | g x 1 = g shows Multiplicative identity property |
| Commutative Property of Addition and Multiplication (you can add two numbers in any order/numbers move) | 3 + 4 = 4+3 3 x 4 = 4 x 3 |
| additive property of zero (Identity for addition) means you can add 0 to any number to get that number | example of additive property of 0 16 + 0 =16 |
| State the commutative property of addition, and provide an example using two different numbers | Any two different addends can be chosen, such as ππ + ππ = ππ + ππ. |
| State the commutative property of multiplication, and provide an example using two different numbers | Any two different factors can be chosen, such as ππ Γ ππ = ππ Γ ππ. |
| State the additive property of zero, and provide an example using any other number. | Any nonzero addend can be chosen, such as π + π = π. |
| State the multiplicative identity property of one, and provide an example using any other number. | Any nonzero factor can be chosen, such as 12 Γ π = 12 |
| State the commutative property of addition using the variables a and b | a +b = b+a (variables change places or move-commute means move) |
| State the commutative property of multiplication using the variables a and b | a x b = b x a (variables change places or move-commute means move) |
| State the additive property of zero using the variable π. | b + 0 = b |
| State the multiplicative identity property of one using the variable π | b x 1 = b |
| Why is there no commutative property for subtraction or division? Show examples. | 8 - 2 does not equal 2 - 8. 8Γ· 2 does not equal 2 Γ· 8 |
| Both π + π and π + π have a sum | sum of 8 |
| write an expression to show π less than a number π | We are taking π away from the unknown number. The expression is π β π. |
| Write an expression to show π minus the sum of π and b | π β (π + π) c minus sum of a and b |
| Write two expressions to show π increased by 4 | π + π and π + w |
| Write an expression and a model showing π less than π. | p - 3 |
| Write an expression to show π decreased by the sum of π and π. | π β (π+ π) 4 minus the sum of g and 5 |
| π +k | the sum of π and k |
| Write an expression showing the sum of 8 and z | 8 + z |
| Write an expression showing π less than the number π. | π-5 |
| Write an expression showing the sum of a number π and a number π minus ππ | h + w - 11 sum of h and w minus 11 |
| 6 fewer than 9 | 9 - 6 = 3 |
| π decreased by 13 | h-13 |
| π less than π, plus π. | y - 5 +g |
| π less than the sum of π and π. | (y+ g) -5 |
| Product of 7 and 8 | 7 x 8 = 56 |
| Product of 2 and 10 | 2 x 10 = 20 |
| Quotient of 12 and 2 | 12 divided by 2 = 6 |
| Half of twenty | Half of 20 means 20 divided by 2 = 10 |
| -(x+17)= (Distribute the negative to x and to 17 | -x -17 (Notice each term changed signs) |
| Is π + π equivalent to π + π? Is π β π equivalent to π β π? | π + π equivalent to π + π. π β π is not equivalent to π β π |
| 6 x b | 6b |
| 17 x c | 17c |
| 2 x 2 x 2 x a x b | 8ab |
| 5 x m x 3 x p | 15mp |
| Factor | A number or variable that is multiplied to get a product |
| Variable | A letter used to represent a number |
| Product | The solution when two factors are multiplied |
| Coefficient | The numerical factor that multiplies the variable |
| 3 β 3 β 3 β 2 β π β π β t (expanded form) | 54πpt (standard form) |
| Rewrite the expression in standard form (use the fewest number of symbols and characters possible). 5π β 7β | 35gh |
| Name the parts of the expression 14b+2. | 14 is the coefficient, π is the variable, and 14b is one term, 2 is the constant that is also another term. |
| Name the parts of the expression 14b. Then, write it in expanded form. | 14 is the coefficient, π is the variable, and 14b is a term that is also the product of 14 and b. |
| write 20yz in expanded form | 20 β π β π or π β π β π β π β z |
| Find the product. 12ab β πcd | 36abcd is the product in standard form. |
| Find the greatest common factor of 3f + 3g | The GCF is 3. |
| 3f + 3g in expanded form | π β π + π β g |
| How can we use the GCF to rewrite 3f + 3g | π goes on the outside, and π + π will go inside the parentheses. The factored expression is 3(f+g) |
| Factor 6x+9y | 3(2x+3y) |
| Factor 2x + 8y | 2(x+4y) |
| Factor 13ab +15ab | ab(13+15) (notice this also =28ab if gathering like terms) |
| Factor 20g +24h | 4(5g +6h) |
| Factor 4d+12e | 4(d+3e) |
| Factor 18x+3y | 3(6x+y) |
| 21a+28y | 7(3a +4y) |
| 24f+56g | 8(3f+7g) |
| Use distributive property for 2(b+c) | 2b+2c |
| 5(7h +3m) | 35h +15m |
| e(f+g) | ef +eg |
| 4(x+y) | 4x+4y |
| 8(a+3b) | 8a +24b |
| 3(2x+11y) | 6x+33y |
| 9(7a+6b) | 63a+54b |
| c(3a+b) | 3ac+bc |
| y(2x+11z) | 2xy+11yz |
| dividend Γ· divisor | dividend is the numerator divisor is the denominator. |
| Write an expression showing π Γ· π without the use of the division symbol. | Write a fraction with a in the numerator and b is the denominator |
| π Γ· (β + 3) | g is the numerator (h+3) is the denominator |
| The quotient of π and 7 | π Γ· π or m is the numerator 7 is the denominator |
| Five divided by the sum of π and b | π Γ· (π + π) or 5 is the numerator (π + π) is the denominator |
| The quotient of (π decreased by π) and 9 | (π β π) Γ· π or (π β π) is the numerator π is the denominator |
| Write the division expression (π + 12) Γ· h in words and as a fraction | The sum of π and 12 divided by π,or(π + 12)is the numerator h is the denominator |
| Write the following division expression using the division symbol and as a fraction: π divided by the quantity (π minus π) | fΓ· (π β π) or f is the numerator (π β π) is the denominator |
| The top number in a fraction | the numerator |
| The bottom number in a fraction | the denominator |
| Words for Addition | SUM, ADD, MORE THAN, TOTAL, ALTOGETHER, IN ALL, INCREASED BY, PLUS |
| Words for Subtraction | DIFFERENCE, SUBTRACT, FEWER THAN, MINUS,LESS THAN,HOW MANY MORE,LEFT ,DECREASED BY |
| Words for Multiplication | PRODUCT,MULTIPLY, TIMES,EVERY, DOUBLE, TRIPLE,OF,AS MUCH,EACH |
| Words for Division | QUOTIENT, DIVIDE, EACH, PER, SPLIT |
| Words for Exponents | POWER, SQUARED, CUBED, Repeatedly multiplying by same number |
| Write two word expressions for each problem using different math vocabulary for each expression. 5d-10 | 10 fewer than the product of 5 and d |
| aΓ· (b+2) | a divided by the sum of b and 2 |
| List five different math vocabulary words that could be used to describe each given expression. π(π β π) + 10 | difference (for d-2), subtract(for d-2, product for π(π β π), times for π(π β π), quantity for + 10, add for + 10, sum for + 10 |
| abΓ· c | for division: quotient, divide, split, for multiplication : product, multiply, times, per, each |
| Omaya picked π amount of apples, then picked π more. Write the expression that models the total number of apples picked. | x+v apples picked in total |
| A number π is tripled and then decreased by π. | 3h-8 |
| Sidney brought π carrots to school and combined them with Jenanβs π carrots. She then split them equally among π friends. | (π + π) Γ· 8 |
| 15 less than the quotient of π and d | π Γ· π β 15 |
| Marissaβs hair was 10 inches long, and then she cut π inches. | 10-h |
| π squared | d to the power of 2 |
| A number π increased by π, and then the sum is doubled. | 2(x+6) |
| The total of π and π is split into π equal groups. | (π + π) Γ· 5 |
| Jasmin has increased her $45 by π dollars and then spends a third of the entire amount. | (45 +m) Γ·3 dollars spent |
| Bill has π more than (π times the number of baseball cards as Frank). Frank has π baseball cards. | d+3f |
| Gregg has two more dollars than Jeff. How much money does Gregg have if j represents Jeffβs money in dollars? | j+2 dollars |
| j+2 when j=12 | j+2 = 12+2= 14 |
| Joe has two fewer dollars than Greg. How much money does Joe have if g represents Greg's money in dollars? | g-2 dollars |
| g-2 if g=14 | g-2=14-2=12 |
| Abby read π more books than Kris. How many books did Abby read if k= number of books Kris read? | k+8 books |
| k+8 if k=9 | k+8=9+8=17 |
| Kelly read 6 fewer books than Amy. If a = the number of books Amy read, write an expression for number of books Kelly read. | a-6 |
| a-6 if a=20 | a-6 = 20-6 = 14 |
| Daryl has been teaching for one year longer than Julie. Let π =number of years Julie taught. How long has Daryl taught? | j+1 |
| j+1 if j=28 | j+1 = 28+1 = 29 |
| Ian scored π fewer goals than Jay. Let π represent the number of goals Jay scored. How many did Ian score? | j-4 |
| Izzy scored π fewer goals than Julia. Let π represent the number of goals scored by Izzy. How many did Julia score? | π + 3 |
| Write an expression to represent the number of teeth Cara has lost. Let π² represent the number of teeth Kathleen lost. | k-4 |
| Write an expression to represent the number of teeth Kathleen lost. Let πͺ represent the number of teeth Cara lost. | c+4 |
| c+4 if c=3 | c+4 = 3+4 = 7 |
| Jenna and Allie work together and were hired on January 3, but Jenna was hired in 2005, and Allie was hired in 2009. | Jenna has worked 4 more years than Allie. |
| If Jenna has worked 4 more years than Allie, and Allie has worked for 20 years, how long will Jenna have worked? | 20 + 4=24 years |
| Anna charges $8. 50 per hour to babysit. Write an expression describing her earnings for working h hours. | 8.50h |
| Anna charges $8. 50 per hour to babysit. How much will she earn if she works for 3.5 hours? | 8.50 β π. π =$29.75 |
| Anna charges $8. 50 per hour to babysit. How long will it take Anna to earn $π1. ππ? | π1 Γ· π. π = π. It will take Anna π hours to earn $π1. |
| A Cell Phone Company charges $π per month for service plus $π.10 for each text. If t=number of texts, what is the bill? message sent. | 5+0.1t |
| Given 5+0.1t and t=10 | 5+0.1t=5+0.1(10) = 6 |
| Given 5+0.1t=10, what is t? | t=50 |
| Naomiβs allowance is $2.00 per week. If she her parents doubled her allowance each week , what will her allowance be in 8 weeks? | 2 x2x2x2x2x2x2x2, doubling each week= 2 to the power of 8 or 2^8 = $256 that week. |
| Naomiβs allowance is $2.00 per week. If she her parents doubled her allowance each week , what will her allowance be in w weeks? | 2 to the power of w |
| 15aβ₯ 75. Substitute 5 for π. | When π is substituted in for π, the number sentence is true. |
| 23+b=30. Substitute 10 for π. | When 10 is substituted in for π, the number sentence is false |
| 20 > 86-h. Substitute 46 for π. | When 46 is substituted in for π, the number sentence will be false |
| 32 β₯ πm. Substitute π for π. | When π is substituted in for π, the number sentence is false |
| 5g>45 | g>9 |
| 14=5+k | k=9 |
| 26-w<12 | w>14 |
| Is equal to | = |
| β | Is not equal to |
| > | Is greater than |
| Is less than | < |
| 32 β€ π + 8 | Subtract 8 from both sides to solve. The inequality is true when πβ₯24 |
| π π β€ 16 | Divide both sides by 2 to solve. π β€ 8 |
| VARIABLE: | A variable is a symbol (such as a letter) that is a placeholder for a number or set of numbers. |
| Constant | A number that does not vary in value |
| EXPRESSION: | It can be the result of replacing some (or all) of the numbers in a numerical expression with variables |
| EQUATION: | Has an equals sign in it: An equation is a statement of equality between two expressions. |
| 7f=49 | Divide both sides by 7 to solve. f=7 |
| 1=r/12 | Multiply both sides by 12 to solve. r=12 |
| 1.5 =d+0.8 | Subtract 0.8 from both sides to solve. d=0.7 |
| 9 ^2 = h (9 to the power of 2 equals h) | 9 times 9 = 81 |
| q=45-19 | q=26 |
| 40 = (1/2) p | Multiply both sides by 2 to solve. p=80 |
| j+12 = 25 | Subtract 12 from both sides to solve. j=13 |
| k-16=4 | Add 16 to both sides to solve. k=20 |
| r/10 = 4 | Multiply both sides of the equation by 10. r=40 |
| 64 = 16u | Divide both sides by 16. u = 4 |
| 12 = 3v | Divide both sides by 3. v=4 |
| Alyssa is twice as old as Brittany, and Jazmyn is 15 years older than Alyssa. If Jazmyn is 35 years old, how old is Brittany? | Jazmyn's age of 35-15 = 20= Alyssa's age. Her age of 20 is twice Brittany's age, which is 10. |
| Byron orders the same amount of "b" bird food as "h" hamster food. b=h and b=75 | h=75 |
| Byron buys four times as much "d" dog food as "b" bird food. 4b=d and b=75 | d=300 |
| Byron needs half the amount of "c" cat food as dog food. (1/2)d= c and d=300 | c=150 |
| The total amount of pet food Byron ordered was 600packages such that π + π + πb + πb=600 | b=75 |
| Acute angle | Less than 90Β° |
| Obtuse angle | Between 90Β° and 180Β° |
| Right | Exactly 90Β° |
| Straight | Exactly 180Β° |
| How are these two complementary angles related? | The two angles have a sum of 90Β°. |
| How are these two supplementary angles related? | The two angles have a sum of 180Β°. |
| ππΒ° + ππΒ° + πΒ° = 180Β° | Add like terms 110Β° + πΒ° = 180Β°. Now subtract 110 from both sides and πΒ° = 70Β°. |
| Alejandro is repairing a stained glass window. He needs to solve this equation 40Β° + πΒ° + 30Β° = 180Β° | Add like terms πΒ° + 70Β° = 180Β°. Now subtract 70 from both sides and πΒ° = 110Β°. |
| Hannah is putting in a tile floor. She needs to solve this equation πΒ° + 38Β° = 90Β° | subtract 38 from both sides and πΒ° = 52Β°. |
| The independent variable changes, and when it does, it affects the dependent variable. | So, the dependent variable depends on the independent variable. |
| Kyla spends 60 minutes of each day exercising. Let π be the number of days that Kyla exercises, and let π =min exercised | Independent variable =Number of Days and Dependent variable=Total Number of Minutes. π = 60d |
| . A taxicab service charges a flat fee of $π plus an additional $1.50 per mile. Relationship between cost and miles driven. | Independent variable =Number of miles. Dependent variable=Total cost, in dollars. π = 1.50m+8 |
| Generally, the independent variable is measured along the π₯-axis. Which axis is the π₯-axis? | The π₯-axis is the horizontal axis. Start at the origin. Then think of running x units forward or backward. |
| Generally, the dependent variable is measured along the y-axis. Which axis is the y-axis? | the π¦-axis travels vertically, or up and down. Start at the origin. Then x units forward or backward. Then y units up or down. |
| Enoch can type 40 words per minutes. Let π be the number of words typed and π be the number of minutes spent typing. | The independent variable is the number of minutes spent typing. The dependent variable is the number of words typed. |
| Enoch's equation is w=40m. If number of minutes is m=0, 1, 2, 3, 4, 5 | w=40m. If number of minutes is m=0, 1, 2, 3, 4, 5. # words respectively is w=0, 40, 80, 120, 160, 200 |
| When graphing (0,0) , (1,40), (2, 80), (3, 120), (4, 160), and (5, 200) | Start at the origin. Then look at the point (x, y). Always complete the x movement left or right, and y movement up or down. |
| β₯ | greater than or equal to |
| less than or equal to | β€ |
| (1/3) f=4 | Multiply both sides by 3. f=12 |
| (1/3) f<4 Choose possible answers from this list {3, 4, 7, 9, 12, 18, 32}. | {π, π, π, π} |
| π + π = 20. Do any answers in this list work? {3, 4, 7, 9, 12, 18, 32}. | There is no number in the set that will make this equation true. |
| π + π β₯ 20. Choose possible answers from this list {3, 4, 7, 9, 12, 18, 32}. | {18, 32}. |
| How are inequalities different from equations? | Inequalities can have a range or interval of possible values that make the statement true, where equations do not. |
| Does the phrase βat mostβ refer to being less than or greater than something? | βAt mostβ means that you can have that amount or less than that amount. You cannot go over. or fewer than 3 TV shows. |
| At least 13 | π β₯ 13 To graph, fill in the circle at 13 and then draw a line from there toward the right (where greater numbers are) |
| Less than 7 | π < 7 To graph, draw an open (not filled in) circle around the number 7, then draw a line to the left (toward smaller numbers) |
| Chad will need at least 24 minutes to complete the πK race. However, he wants to finish in under 30 minutes | 24 β€ π < 30. x is between 24 and 30. It also includes 24. Fill in circle at 24, open circle at 30. Draw line between 2 circles. |
| 8m+1m+2m | 11m |
Created by:
Mrs.Cantrell
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