Common Core Standards: Grade 7

7.RP. Ratios and Proportional Relationships

Analyze proportional relationships and use them to solve realworld and mathematical problems.

7.RP.1. Compute unit rates associated with ratios of fractions, including ratios of lengths, areas and other quantities measured in like or different units.

7.RP.2. Recognize and represent proportional relationships between quantities.

7.RP.3. Use proportional relationships to solve multistep ratio and percent problems. Examples: simple interest, tax, markups and markdowns, gratuities and commissions, fees, percent increase and decrease, percent error.



Given one term and a ratio, find the other term

Given the total amount and a ratio, find each term

Given one term and a ratio of fractions, find the other term

Solving word problems by changing twoterm ratios into a threeterm ratio

Given one term and a ratio, find the total amount

Given two terms, a ratio, and a total amount, find the missing term

Given the total amount and a ratio of fractions, find each term

Given the total amount and a ratio, find each term

Given one term and a ratio, find the other term and use it to solve a word
problem


Find the percentage profit given cost and sales

Find the discount and percentage discount given original
price and selling price

Find the percentage discount given the original price
and sale price

Find the total commission given a commission percentage and selling price

Find the total tax given total income and income tax
rate

Find the Price after Tax, price before tax, and GST amount

Find the Percent Loss given cost and sales

Find the selling price and discount given original price
and percentage discount

Find the savings amount given the original price and
percentage discount

Find the number of units sold given base salary, commission percentage, and
selling price

Find the percentage of tax given the original price and
posttax price

Find the better discount

Find the cost given sales and percentage profit

Find the original price and percentage discount given
selling price and discount

Find the sale price given the original price and
percentage discount

Find the total salary and units sold

Find the posttax price given the selling price and tax
rate

Find the total amount and total GST given a percentage discount on the second
item

Find the selling price given sales and Percent Loss

Find the original price given the savings amount and
percentage discount

Find the original price given the posttax price and tax
rate

Find the total amount remaining after taxes, tips, and shipping fees

Find the percentage profit given sales and total profit

Find the sale price given the original price and two
consecutive percentage discounts

Find the original price, GST, and percentage decrease

Find the market price given cost, percentage profit, and percentage gain

Find the total cost of the breakeven deal



7.NS. The Number System

Apply and extend previous understandings of operations with fractions to add, subtract, multiply, and divide rational numbers.

7.NS.1. Apply and extend previous understandings of addition and subtraction to add and subtract rational numbers; represent addition and subtraction on a horizontal or vertical number line diagram.

7.NS.2. Apply and extend previous understandings of multiplication and division and of fractions to multiply and divide rational numbers.

7.NS.3. Solve realworld and mathematical problems involving the four operations with rational numbers.

7.EE. Expressions and Equations

Use properties of operations to generate equivalent expressions.

7.EE.1. Apply properties of operations as strategies to add, subtract, factor, and expand linear expressions with rational coefficients.

7.EE.2. 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 â€œincrease by 5%â€ is the same as â€œmultiply by 1.05.â€)

Solve reallife and mathematical problems using numerical and algebraic expressions and equations.

7.EE.3. Solve multistep reallife and mathematical problems posed with positive and negative rational numbers in any form (whole numbers, fractions, and decimals), using tools strategically. Apply properties of operations to calculate with numbers in any form; convert between forms as appropriate; and assess the reasonableness of answers using mental computation and estimation strategies. (For example: If a woman making $25 an hour gets a 10% raise, she will make an additional 1/10 of her salary an hour, or $2.50, for a new salary of $27.50. If you want to place a towel bar 9 3/4 inches long in the center of a door that is 27 1/2 inches wide, you will need to place the bar about 9 inches from each edge; this estimate can be used as a check on the exact computation.)

7.EE.4. Use variables to represent quantities in a realworld or mathematical problem, and construct simple equations and inequalities to solve problems by reasoning about the quantities.

7.G. Geometry

Draw, construct, and describe geometrical figures and describe the relationships between them.

7.G.1. Solve problems involving scale drawings of geometric figures, including computing actual lengths and areas from a scale drawing and reproducing a scale drawing at a different scale.

7.G.2. Draw (freehand, with ruler and protractor, and with technology) geometric shapes with given conditions. Focus on constructing triangles from three measures of angles or sides, noticing when the conditions determine a unique triangle, more than one triangle, or no triangle.

7.G.3. Describe the twodimensional figures that result from slicing threedimensional figures, as in plane sections of right rectangular prisms and right rectangular pyramids.

Solve reallife and mathematical problems involving angle measure, area, surface area, and volume.

7.G.4. Know the formulas for the area and circumference of a circle and use them to solve problems; give an informal derivation of the relationship between the circumference and area of a circle.

7.G.5. Use facts about supplementary, complementary, vertical, and adjacent angles in a multistep problem to write and solve simple equations for an unknown angle in a figure.

7.G.6. Solve realworld and mathematical problems involving area, volume and surface area of two and threedimensional objects composed of triangles, quadrilaterals, polygons, cubes, and right prisms.

7.SP. Statistics and Probability

Use random sampling to draw inferences about a population.

7.SP.1. Understand that statistics can be used to gain information about a population by examining a sample of the population; generalizations about a population from a sample are valid only if the sample is representative of that population. Understand that random sampling tends to produce representative samples and support valid inferences.

7.SP.2. Use data from a random sample to draw inferences about a population with an unknown characteristic of interest. Generate multiple samples (or simulated samples) of the same size to gauge the variation in estimates or predictions.

Draw informal comparative inferences about two populations.

7.SP.3. Informally assess the degree of visual overlap of two numerical data distributions with similar variabilities, measuring the difference between the centers by expressing it as a multiple of a measure of variability. (For example, the mean height of players on the basketball team is 10 cm greater than the mean height of players on the soccer team, about twice the variability (mean absolute deviation) on either team; on a dot plot, the separation between the two distributions of heights is noticeable.)

7.SP.4. Use measures of center and measures of variability for numerical data from random samples to draw informal comparative inferences about two populations. For example, decide whether the words in a chapter of a seventhgrade science book are generally longer than the words in a chapter of a fourthgrade science book.

Investigate chance processes and develop, use, and evaluate probability models.

7.SP.5. Understand that the probability of a chance event is a number between 0 and 1 that expresses the likelihood of the event occurring. Larger numbers indicate greater likelihood. A probability near 0 indicates an unlikely event, a probability around 1/2 indicates an event that is neither unlikely nor likely, and a probability near 1 indicates a likely event.

7.SP.6. Approximate the probability of a chance event by collecting data on the chance process that produces it and observing its longrun relative frequency, and predict the approximate relative frequency given the probability. (For example, when rolling a number cube 600 times, predict that a 3 or 6 would be rolled roughly 200 times, but probably not exactly 200 times.)

7.SP.7. Develop a probability model and use it to find probabilities of events. Compare probabilities from a model to observed frequencies; if the agreement is not good, explain possible sources of the discrepancy.

7.SP.8. Find probabilities of compound events using organized lists, tables, tree diagrams, and simulation.