7.EE.A.2Common CoreMathExpressions and EquationsGrade 7
7.EE.A.2: Rewriting Expressions to Understand a Problem
In plain English: 7.EE.A.2 is the Common Core grade 7 math standard that asks students to rewrite an expression from a real situation in an equivalent form and explain what the new form shows. The official example is a + 0.05a = 1.05a: increasing by 5% is the same as multiplying by 1.05. Factored forms and combined terms can also reveal a cost per person or a rate.
Understand that rewriting an expression in different forms in a problem context can shed light on the problem and how the quantities in it are related. For example, a + 0.05a = 1.05a means that "increase by 5%" is the same as "multiply by 1.05."
Common Core State Standards for Mathematics · Domain: Expressions and Equations (EE) · Cluster: Use properties of operations to generate equivalent expressions. Also written as 7.EE.2 · Official standard
Students learn that one quantity can be written in more than one way, and that each way can tell a different part of the story. An expression is a group of numbers, letters and operation signs with no equal sign, such as p - 0.3p. Two expressions are equivalent when they are equal for every value of the letter. In 7.EE.A.1, students learned to rewrite expressions with the properties of operations. In 7.EE.A.2, they ask a new question: what does the new form tell us about the situation?
The official example is a + 0.05a = 1.05a. The left side says "the price a, plus 5% of a." The right side says "multiply the price by 1.05." Because the two are equivalent, a 5% increase is the same as multiplying by 1.05. The number 1.05 is called the multiplier: the single number the original amount is multiplied by. Students also see that a factored form (a number times a sum, such as 6(f + 2.50)) can show the cost for one person, and that combining like terms (terms with the same letter part) can show a total rate, such as dollars saved per week.
Learning Objectives
By the end of this lesson, students will be able to:
Rewrite a percent increase or decrease, such as a + 0.05a or p - 0.3p, as one multiplication, and explain what the multiplier means
Explain why "increase by 5%" is the same as "multiply by 1.05" using the official example a + 0.05a = 1.05a
Factor an expression from a word problem and explain what the factored form shows, such as the cost for each person
Combine like terms in a word problem and explain what the new coefficient (the number multiplied by the letter) says, such as a rate per week
Choose the form of an expression that answers a given question most directly
Prior Knowledge Required
Students should already be comfortable with:
Finding a percent of a quantity, for example 30% of 50 6.RP.A.3
Deciding whether two expressions are equivalent 6.EE.A.4
Adding, subtracting, expanding and factoring linear expressions with rational coefficients 7.EE.A.1
Post the question. Give students 3 minutes to find the sale price in two different ways.
Warm-Up Prompt
"A $40 hoodie is on sale for 25% off. Find the sale price in two different ways. Do both ways give the same price?"
Collect both methods. Some students find the discount first: 25% of 40 is 0.25 × 40 = 10, and 40 - 10 = $30. Others say: "25% off means I pay 75%," so 0.75 × 40 = $30. Write the two methods with a letter p for any price: p - 0.25p and 0.75p. Ask: "Will these two always give the same price?" Yes: p - 0.25p = 1p - 0.25p = (1 - 0.25)p = 0.75p by the distributive property. The first form shows the discount. The second shows the part you pay.
Direct Instruction20 minutes
Part 1: Two forms, two stories. When we rewrite an expression, the value stays the same, but the form can answer a different question. Work each example on the board. For each one, ask: "What does each form tell us?"
Percent increase, the official example
A store raises every price by 5%. An item costs a dollars before the increase. Write the new price two ways.
Equation: a + 0.05a = (1 + 0.05)a = 1.05a. The first form shows the old price plus the increase; the second shows that "increase by 5%" is the same as "multiply by 1.05." A $20 item becomes 20 + 1 = $21, and 1.05 × 20 = $21.
Percent decrease
A game costs p dollars and is 30% off. Write the sale price two ways.
Equation: p - 0.3p = (1 - 0.3)p = 0.7p. The first form shows the discount taken away; the second shows that you pay 70% of the price. For a $50 game: 50 - 15 = $35 and 0.7 × 50 = $35.
Factoring to see the cost for one person
Six players each pay an entry fee of f dollars and $2.50 for a team shirt. The coach writes the total as 6f + 15.
Equation: 6f + 15 = 6(f + 2.50). The factored form shows that each player pays f + 2.50 dollars, and there are 6 players.
Combining like terms to see a rate
Maya has $20 in a jar. Each week she adds $5 and her brother adds $3. After w weeks the jar holds 20 + 5w + 3w dollars.
Equation: 20 + 5w + 3w = 20 + 8w. The new form shows that the jar grows by $8 each week, starting from $20.
Combining like terms to see profit
A club sells shirts for $15 each. Each shirt costs the club $9, and the design costs $40 once. The profit (money earned minus costs) for s shirts is 15s - 9s - 40.
Equation: 15s - 9s - 40 = 6s - 40. The new form shows that each shirt adds $6 of profit, and the club starts $40 behind.
Part 2: Reading a multiplier. Diagram 2 shows the two percent examples as bars drawn to scale. A multiplier greater than 1, such as 1.05, means an increase. A multiplier less than 1, such as 0.7, means a decrease. To find the percent, compare the multiplier with 1: 1.05 is 0.05 more than 1, so the increase is 5%; 0.7 is 0.3 less than 1, so the decrease is 30%.
Part 3: Choosing a form. No form is always best. The expanded form (a sum of terms, such as 6f + 15) is quick for the total. The factored form, 6(f + 2.50), shows one person's share. Diagram 1 shows a counting problem with three equivalent forms, where each form matches a different way of counting. Students use it in Activity 2.
Guided Practice15 minutes
Pairs rewrite each expression, then write one sentence about what the new form shows. One pair shares each answer, and the class checks it with a number.
Guided practice problems with answers
Problem
Answer
A restaurant bill is b dollars, and the family adds an 18% tip: b + 0.18b
1.18b: the total is 118% of the bill. For a $50 bill, 1.18 × 50 = $59.
A jacket's price j drops by 27%: j - 0.27j
0.73j: the new price is 73% of the old price.
A rectangular pen is x meters long and 4 meters wide. Its perimeter (distance around) is x + 4 + x + 4
2x + 8 = 2(x + 4): the perimeter is two copies of one length plus one width.
Two plants are 12 cm and 8 cm tall. They grow 1.5 cm and 2 cm per week. Their total height after w weeks is (12 + 1.5w) + (8 + 2w)
20 + 3.5w: together they start at 20 cm and gain 3.5 cm each week.
Listen for students who write 0.18b as the total bill: 0.18b is only the tip. Ask: "Is the total more or less than the bill? So should the multiplier be more or less than 1?"
Independent Practice10 minutes
Students rewrite each expression and write one sentence about what the new form shows.
Independent practice problems with answers
Problem
Answer
A toy costs p dollars plus 7% sales tax: p + 0.07p
1.07p: multiply the price by 1.07
A coat is 40% off: c - 0.4c
0.6c: you pay 60% of the price
A monthly bill m drops by 10%: m - 0.1m
0.9m: the new bill is 90% of the old one
Five friends each buy a sandwich for n dollars and a $4 drink: 5n + 20
5(n + 4): each friend pays n + 4 dollars
A recipe makes x cookies. A bigger batch makes 30% more: x + 0.3x
1.3x: the bigger batch is 130% of the recipe
Jen earns $12 per hour, plus a $3 per hour bonus on weekends. For h weekend hours: 12h + 3h
15h: she earns $15 for each weekend hour
Closure5 minutes
Exit ticket: (1) Rewrite q + 0.09q as one term and say what it means. (Answer: 1.09q; an increase of 9% is the same as multiplying by 1.09.) (2) A sale price is 0.65p. What percent is taken off? (Answer: 35%.) (3) Four friends each buy a ticket for t dollars and pay a $1.50 fee each. Which form shows the cost for one friend: 4t + 6 or 4(t + 1.50)? (Answer: 4(t + 1.50), since t + 1.50 is one friend's cost.)
Differentiation Strategies
For Struggling Students
Draw a bar for the original amount before writing any expression, as in Diagram 2, and shade the part added or taken away
Start with percents that are easy to picture, such as 10%, 50% and 25%, and test each form with a price of $100
Give sentence frames: "The first form shows ___. The second form shows ___."
For Advanced Students
Ask whether a 10% increase followed by a 10% decrease returns to the starting price. Students write 1.1p, then 0.9(1.1p) = 0.99p, and explain the result (going further than this standard)
Ask students to write two different word problems that both lead to 4(x + 3), then explain what 4 and x + 3 mean in each
Give 3n - 12 = 3(n - 4) in a profit context and ask what the 4 tells the seller
Assessment Guidance
What to Look For
Check that students can say in words what each form shows, not only rewrite it. For percent problems, look for multipliers greater than 1 for an increase and less than 1 for a decrease, and for students who can turn 1.07 back into "a 7% increase." For factored forms, students should name what the number outside and the sum inside stand for, with units. A strong answer explains why the two forms are equal (with a property) and why one form answers the question more directly.
02
Classroom Activities
3 Activities
1
Percent Change Match
15 minPairs
Each pair gets 12 index cards: 4 word cards, 4 expanded cards (the original plus or minus the change) and 4 multiplier cards. Pairs make 4 sets of 3 cards that mean the same thing, then check each set with x = 50.
Cards (answer key, one set per line)
"Increase by 20%", x + 0.2x, 1.2x (check: 60)
"Decrease by 20%", x - 0.2x, 0.8x (check: 40)
"Increase by 2%", x + 0.02x, 1.02x (check: 51)
"Decrease by 8%", x - 0.08x, 0.92x (check: 46)
Procedure
Mix the 12 cards and lay them face up
Match each word card with one expanded card and one multiplier card
Rewrite the expanded card as the multiplier card, naming the property you use
Substitute x = 50 into both expressions of each set and compare
Discussion Questions
Two of the multipliers are less than 1. Which word cards do they match, and why?
Why is "increase by 20%" not the same as "multiply by 0.2"? What does 0.2x stand for?
A student matched "increase by 2%" with 1.2x. What would you tell them?
Modification for Distance Learning
Put the 12 cards on a shared slide. Pairs drag the cards into 4 rows and type the check with x = 50 next to each row.
2
Garden Border Tiles
20 minPairs
A square garden is n tiles long on each side. A border one tile wide goes all the way around it. Pairs build or draw the border with square tiles or on grid paper, count the border tiles in their own way, and write an expression that matches their way of counting.
Procedure
Build or draw gardens with n = 3, n = 5 and n = 8, and count the border tiles (16, 24 and 36)
Color the tiles to show how you counted, as in Diagram 1
Write an expression in n that matches your coloring
Find a pair with a different expression, test both with n = 8, and show with properties that they are equivalent
Expressions Students Often Find (answer key)
4n + 4: four sides of n tiles, plus 4 corner tiles
4(n + 1): four groups of n + 1 tiles, in a pinwheel
2(n + 2) + 2n: top and bottom rows of n + 2 tiles, plus two side columns of n tiles
4(n + 2) - 4: four sides of n + 2 tiles, minus the 4 corners that were counted twice
Discussion Questions
In 4n + 4, what do the 4 in 4n and the + 4 stand for in the picture?
Why does 4(n + 2) - 4 subtract 4? Show the corners that were counted twice.
Use the distributive property to show that all four expressions equal 4n + 4.
Challenge Variation
Change the garden to a rectangle that is n tiles long and 3 tiles wide. Write two expressions for the border tiles and show they are equivalent. (2n + 10 and 2(n + 5))
3
Which Form Helps?
15 minGroups of 3-4
Each group gets 6 context cards. Each card gives a situation, two equivalent expressions and a question. The group decides which form answers the question more directly and explains why in one sentence.
Context Cards
C1: A video game costs p dollars plus 8% tax: p + 0.08p or 1.08p. Question: what single number do you multiply the price by?
C2: Twelve team shirts cost s dollars each plus $3 each to print a name: 12s + 36 or 12(s + 3). Question: what does one printed shirt cost?
C3: Two siblings share a jar that starts with $30. One adds $4 a week and the other adds $6 a week: 30 + 4w + 6w or 30 + 10w. Question: how fast does the jar grow?
C4: A hotel room costs x dollars plus a 14% fee and $10 for parking: x + 0.14x + 10 or 1.14x + 10. Question: the room and fee together are what percent of the room price?
C5: A club sells cookies for $1.50 each and spent $24 on supplies. Its profit for c cookies is 1.5c - 24 or 1.5(c - 16). Question: how many cookies must it sell to break even (make a profit of $0)?
C6: A lamp costs p dollars and is 22% off: p - 0.22p or 0.78p. Question: what fraction of the price do you pay?
Answer Key
C1: 1.08p, multiply by 1.08
C2: 12(s + 3), one shirt costs s + 3 dollars
C3: 30 + 10w, the jar grows $10 per week
C4: 1.14x + 10, the room and fee are 114% of the room price
C5: 1.5(c - 16), the profit is $0 when c = 16 cookies
C6: 0.78p, you pay 78/100 of the price
Discussion Questions
On which cards did the factored form help, and on which did combining terms help?
On C5, what happens to the profit when c is less than 16? Try c = 10.
03
Diagrams & Visual Aids
2 diagrams
Diagram 1: Three Ways to Count Border Tiles
A 5-by-5 garden has 24 border tiles. The numbers 1 to 4 show one way to count them: four groups of n + 1 = 6 tiles, which is 4(n + 1). Counting four sides plus four corners gives 4n + 4, and counting two long rows and two short columns gives 2(n + 2) + 2n. All three forms equal 24 when n = 5, and they are equivalent for every n.
Diagram 2: Percent Change as a Multiplier
Top: the price a plus 5% of a makes a bar 105% as long, so a + 0.05a = 1.05a. Bottom: taking 30% off the price p leaves 70% of the bar, so p - 0.3p = 0.7p. The bars are drawn to scale, 4 pixels per percent.
04
Homework Assignment
~30 min
7.EE.A.2 Homework: What Does Each Form Tell You?
Directions: Rewrite each expression in the form asked for. Then write one full sentence that explains what the new form tells you about the situation. Check your forms by substituting a number.
Part 1: Percent Change (Problems 1-2)
(a) A town's population is t people and grows by 28%. Rewrite t + 0.28t as one term. (b) A price is multiplied by 0.88. What percent change is this? (c) A price p goes up by 3%. Write the new price in two forms.
A bike costs b dollars and is on sale for 32% off. Write the sale price in two forms. Explain what each form shows, and show that both give the same sale price when b = $250.
Part 2: Factoring and Combining in Context (Problems 3-4)
Each of the 11 players on a soccer team pays a registration fee of r dollars and $6 for socks. Write the total cost in an expanded form and in a factored form. Which form shows the cost for one player?
A car wash charges $8 per car and spent $36 on soap and sponges. Its profit for c cars is 8c - 36. Rewrite it as 8(c - 4.5). What does the 4.5 tell you? How many cars must be washed before the car wash makes a profit?
Part 3: Explaining Equivalent Forms (Problems 5-6)
A rectangular patio is 6 tiles long and w tiles wide, with a border one tile wide around it. Ana counts the border tiles as 2(6 + 2) + 2w. Ben counts them as 2(w + 8). Show that both expressions are equivalent, and describe how each student counted.
Mia runs x km on Monday. On Tuesday she runs 40% farther than on Monday. Write her total distance for both days as x + 1.4x, then rewrite it as one term. What does the new coefficient tell you?
Rubric
Criterion
Full Credit (2 pts)
Partial Credit (1 pt)
No Credit (0 pts)
Rewriting
Both forms correct and equivalent
One form has a small error
Forms missing or not equivalent
Meaning of Each Form
A clear sentence for each form that uses the situation and units
Meaning given for only one form, or no units
No explanation
Percent Multipliers
Multiplier and percent change match (above 1 for increase, below 1 for decrease)
Correct multiplier but percent misread
Multiplier confused with the change
Checking
A substitution check shown for each rewrite
Some checks shown
No checks
05
Quiz: 20 Questions
Interactive, with answers
Instructions
Work through the questions in order. Your score updates as you answer, and Reset quiz clears everything so you or your students can try again.
Multiple choice: pick an option to check it. Short answer: write your answer, then reveal the model answer.
0 of 20 answered · 0 correct
Question 1 of 20 · Multiple Choice
A price p increases by 6%. Which expression gives the new price?
Answer: C
The new price is p + 0.06p = (1 + 0.06)p = 1.06p. Choice A is only the increase, not the new price. Choice B adds 6 dollars instead of 6% of the price. Choice D uses 0.6, which is 60%, not 6%.
Question 2 of 20 · Multiple Choice
A store writes the sale price of every item as 0.62x, where x is the regular price. What does this mean?
Answer: B
0.62x means you pay 62% of the price, so 100% - 62% = 38% is taken off: x - 0.38x = 0.62x. Choice A confuses the part you pay with the part taken off. Choice C reads 0.62 as 6.2%. Choice D reads 0.62 as dollars instead of a multiplier.
Question 3 of 20 · Multiple Choice
A backpack's price m is lowered by 16%. Which single term equals m - 0.16m?
Answer: D
m - 0.16m = (1 - 0.16)m = 0.84m, so the new price is 84% of the old one. Choice A adds 0.16 instead of subtracting. Choice B keeps only the amount taken off. Choice C writes 84% as 84 instead of 0.84.
Question 4 of 20 · Multiple Choice
Which sentence matches w + 0.12w = 1.12w?
Answer: A
w + 0.12w is the amount w plus 12% of w, an increase of 12%, and it equals 1.12w. Choice B confuses the increase, 0.12w, with the new amount. Choice C reads the multiplier 1.12 as the percent change. Choice D calls it a decrease, but the multiplier is greater than 1.
Question 5 of 20 · Multiple Choice
Eight students each buy a ticket for t dollars and a $2 snack. The total is 8t + 16. Which equivalent form shows the cost for one student?
Answer: C
8(t + 2) shows 8 students who each pay t + 2 dollars, a ticket and a snack. Choices A and B are equivalent to 8t + 16, but 4t + 8 and 0.5t + 1 are not one student's cost. Choice D is not equivalent: it expands to 8t + 128, because it does not divide the 16 by 8.
Question 6 of 20 · Multiple Choice
Two candles are lit at the same time. Candle A is 20 cm tall and burns 1.5 cm per hour. Candle B is 15 cm tall and burns 1 cm per hour. Their total height after h hours is (20 - 1.5h) + (15 - h) = 35 - 2.5h. What does the 2.5 tell you?
Answer: B
Combining like terms, -1.5h - h = -2.5h, so the total height drops 1.5 + 1 = 2.5 cm each hour. Choice A describes a difference in height, but the heights differ by 5 cm at the start. Choice C mixes up the rate with a time. Choice D compares the heights by division, which the expression does not do.
Question 7 of 20 · Multiple Choice
A club makes bracelets for a fundraiser. It spent $60 on beads and sells each bracelet for $4. Its profit (money earned minus costs) for b bracelets is 4b - 60, which equals 4(b - 15). What does the 15 tell the club?
Answer: D
When b = 15, 4(15 - 15) = 0, so the profit is $0: selling 15 bracelets pays back the $60. Each bracelet after that adds $4. Choice A confuses the 15 with the profit per bracelet, which is $4. Choice B reads 15 as a cost per bracelet, but the only cost is the $60 for beads. Choice C also reads 15 as a count of bracelets made, which the problem does not give.
Question 8 of 20 · Multiple Choice
A shirt costs p dollars. Which expression is NOT the price after 60% off?
Answer: A
After 60% off you pay 40%: p - 0.6p = 0.4p = (2/5)p. So choice A, 0.6p, is not the sale price; it is the amount taken off. Choices B, C and D are all equal to 0.4p.
Question 9 of 20 · Multiple Choice
A $75 pair of shoes goes up in price by 4%. Use the multiplier 1.04 to find the new price.
Answer: A
1.04 × 75 = 78, so the new price is $78. Check: 75 + 0.04(75) = 75 + 3 = 78. Choice B adds $4 instead of 4%. Choice C is only the increase. Choice D multiplies by 1.4, a 40% increase.
Question 10 of 20 · Multiple Choice
A rectangle is x cm long and 3 cm wide. Its perimeter is x + 3 + x + 3. Which form shows the perimeter as two copies of one length plus one width?
Answer: B
2(x + 3) is 2 copies of x + 3, one length plus one width. Choices A and C are equivalent, but they add the lengths and the widths separately. Choice D is not equivalent: it counts the length 4 times.
Question 11 of 20 · Multiple Choice
Sam says, "Increasing a number by 50% is the same as multiplying it by 0.5." Is Sam right?
Answer: C
An increase of 50% is the number plus half of it: n + 0.5n = 1.5n. Multiplying by 0.5 gives half the number, a decrease. Choice A mixes up the increase, 0.5n, with the new amount. Choice B reads 50% as 50. Choice D adds 0.5 instead of 50% of the number.
Question 12 of 20 · Multiple Choice
Two hoses fill a pool. One pours 12 gallons per minute and the other pours 8 gallons per minute. After m minutes the pool has 12m + 8m = 20m gallons. What does the 20 tell you?
Answer: D
Combining like terms, 12m + 8m = 20m, so the two hoses together add 20 gallons every minute. Choice A reads the rate as a time. Choice B reads it as the size of the pool. Choice C would be a difference, and 12 - 8 is only 4.
Question 13 of 20 · Multiple Choice
Which expression shows a decrease of 12.5%?
Answer: A
x - 0.125x = (1 - 0.125)x = 0.875x. Choice B is an increase of 12.5%. Choice C is the amount of the decrease, not the new amount. Choice D subtracts 12.5 units instead of 12.5% of x.
Question 14 of 20 · Multiple Choice
A store buys a jacket for w dollars and sets its price 40% higher, so the price is w + 0.4w = 1.4w. The store buys a jacket for $35. What is its price?
Answer: A
1.4 × 35 = 49, so the price is $49. Check: 35 + 0.4(35) = 35 + 14 = 49. Choice B is only the amount added. Choice C adds $40 instead of 40%. Choice D reads 0.4w as $4.
Question 15 of 20 · Short Answer
Rewrite k + 0.35k as one term. Then explain what the new form means in words.
k + 0.35k = (1 + 0.35)k = 1.35k. Increasing an amount by 35% is the same as multiplying it by 1.35, so the new amount is 135% of the original.
Question 16 of 20 · Short Answer
A shirt costs s dollars and is 24% off. Write the sale price in two forms, and find the sale price of a $25 shirt.
s - 0.24s and 0.76s. The first shows the discount taken away; the second shows you pay 76%. For s = 25: 0.76 × 25 = $19 (and 25 - 6 = 19).
Question 17 of 20 · Short Answer
Each of the 9 members of a swim team pays a fee of f dollars and $5 for a swim cap. The coach writes 9f + 45. Write an equivalent factored form and explain what each form shows.
9(f + 5). The expanded form 9f + 45 shows the total fees (9f) plus the total for caps ($45). The factored form shows that each of the 9 members pays f + 5 dollars.
Question 18 of 20 · Short Answer
A rectangle is (2x + 1) cm long and x cm wide. Write its perimeter as 2(2x + 1) + 2x, then as a sum of two terms. How much does the perimeter grow when x grows by 1?
2(2x + 1) + 2x = 4x + 2 + 2x = 6x + 2. The coefficient 6 shows that the perimeter grows by 6 cm each time x grows by 1 cm.
Question 19 of 20 · Short Answer
Use the expression z - 0.45z to explain why "decrease by 45%" is the same as "multiply by 0.55."
z - 0.45z = 1z - 0.45z = (1 - 0.45)z = 0.55z by the distributive property. Taking away 45% of z leaves 55% of z, so both descriptions give the same amount for every z.
Question 20 of 20 · Short Answer
Kai's rule for a tip: "Find 10% of the bill b, then find half of that. Add both amounts to the bill." Write his rule as an expression, rewrite it as one term, and say what percent tip he leaves.
b + 0.1b + 0.05b = 1.15b. Kai multiplies the bill by 1.15, so he leaves a 15% tip.
0 of 20 answered · 0 correct
06
Frequently Asked Questions
10 Questions
What does 7.EE.A.2 mean?
7.EE.A.2 means students understand that writing an expression in a new, equivalent form can show something new about a problem. For example, p - 0.3p and 0.7p give the same sale price, but the first shows the 30% discount and the second shows that you pay 70%.
What does a + 0.05a = 1.05a mean in 7.EE.A.2?
It means that increasing an amount by 5% gives the same result as multiplying it by 1.05. The left side is the amount a plus 5% of a. By the distributive property, a + 0.05a = (1 + 0.05)a = 1.05a. This is the official example in the standard.
How is 7.EE.A.2 different from 7.EE.A.1?
7.EE.A.1 is about how to rewrite an expression, and 7.EE.A.2 is about why the new form is useful. In 7.EE.A.1, students add, subtract, expand and factor. In 7.EE.A.2, they use those skills inside a story and explain what each form says about the quantities.
Which form of an expression is the best one?
It depends on the question. A factored form such as 3(n + 7) shows 3 equal groups of n + 7, which helps when you want one group's value. An expanded form such as 3n + 21 shows the total of each kind of quantity. A single term such as 1.2x shows the multiplier for a percent change.
How do you turn a multiplier back into a percent change?
Compare the multiplier with 1. If it is more than 1, the amount above 1 is the increase: 1.07 means an increase of 7%. If it is less than 1, the amount below 1 is the decrease: 0.93 means a decrease of 7%.
What mistakes do students make with percent expressions?
A common mistake is writing only the change, such as 0.25x, when the problem asks for the new amount, which is 1.25x after a 25% increase. Other frequent errors are writing 7% as 0.7 instead of 0.07, and using a multiplier greater than 1 for a discount.
How does factoring help in a word problem?
Factoring can show a value for one group or a break-even point. For example, a profit of 3n - 12 dollars can be written as 3(n - 4). The factored form shows that the profit is $0 when n = 4, and that each item after that adds $3.
What grade is 7.EE.A.2, and what comes next?
It is a grade 7 standard in Expressions and Equations. It connects to percent problems in grade 7 (7.RP.A.3). In high school, students choose an equivalent form of an expression to reveal a property of a quantity (HSA.SSE.B.3), for example to show a rate of growth or a starting amount.
Do students need to solve equations for 7.EE.A.2?
No. The standard is about rewriting and explaining expressions. Students may substitute numbers to check or to find a value, for example a price after a discount, but solving equations belongs to 7.EE.B.4.
How can parents help with 7.EE.A.2 at home?
Use shopping. When you see a sign such as "20% off," ask your child to say the price two ways: the price minus 20% of it, or 80% of the price. Then ask which way is quicker on a calculator and why both give the same answer.
07
Related Standards
6 standards
These standards connect to 7.EE.A.2: prerequisites to review first, parallel standards at the same level, and next steps that build on it.
