In 7th grade, students focus on using their understanding of ratios and rates to solve real-world problems involving proportional relationships, solving problems involving positive and negative rational numbers, and working with mathematical expressions and linear equations.

##### Real World Problems

Solve real-world rate, ratio, proportion and percent problems involving discounts, markups, markdowns, interest, taxes, tips, commissions, percent increase or decrease.

• At a “25% Off” sale, Marissa buys a skirt for \$40.50. What was the original price of the skirt? Adding sales tax of 6%, what is the total cost of the skirt?
• The recipe calls for 34 cup of cream for every 2 cups of milk. If the amount of milk is increased to 8 cups, how many cups of cream are needed?
##### Unit Rate of Change

Understand variables as symbols for numbers, or values, not yet known – for example, x and y are the variables in y = 2x + 6. Using equations, tables, graphs, and descriptions, identify the unit rate of change – a ratio comparing the change in one quantity to a 1-unit change in another quantity.

• Anthony reads 36 pages in one hour. The following hour, he reads 42 pages. What is the rate of change in the number of pages he can read in an hour? Explain your reasoning.
• Using the table, what is the rate of change in the height of this teenager over three years? Explain your reasoning. ##### Calculating Unit Rates

Calculate unit rates associated with ratios of fractions including ratios of lengths and areas and quantities measured in different units.

• If a person walks 12 mile in each ¼ hour, what is the (unit) rate at which the person is walking, expressed in miles per (1) hour?
• It takes 18 of a liter of water to fill 19 of the fish tank. How many liters of water are needed to fill the tank?
##### Multi-Step Real World Problems

Add, subtract, multiply, and divide with positive and negative rational numbers in any form – including whole numbers, fractions, or decimals. Understand that numbers cannot be divided by 0. Use these skills to solve multi-step real-world problems.

• If a babysitter is paid \$13.00 an hour and gets a 15% raise, what will her new hourly wage be?  What will she now make for 5½  hours of babysitting? Explain or illustrate your reasoning.
• In Halifax, the low temperatures (in Fahrenheit) for seven days in January were:  -12°, -3°, 6°, -14°, -8°, 9°, -1°.  What was the average temperature for that week? Explain or illustrate your reasoning.

Tip: Encourage Savvy Spending
Shopping continues to be one of the best opportunities for your child to practice the math concepts she is learning. She can practice percentages and subtraction by calculating the exact amount you’ll save when something goes on sale and the final cost of discounted items. Have her help you calculate the tip when you eat in a restaurant. If she has a cell phone, familiarize him with the details of the cell phone bill and how much the charge is per text or per minute of usage, so that she can learn to keep track of how much she is spending.

##### Long Division

Convert rational numbers to decimals using long division. ##### Generating Simple Equations

Use letters to represent numbers in real-world math problems and generate simple equations to solve them. Graph the solution set when there are multiple answers.

Tess, Nico, and Sal are collecting money for a trip to Stonehenge. Tess has collected T dollars, Nico has collected N dollars, and Sal has collected S dollars. If Tess has collected twice as much as Nico and Sal combined, the relation can be expressed as T = 2(N + S).

##### Solving for X

Determine the value of the variable in an equation, and a multi-step equation.

• Solve for x: 5x + 6 = 46
• Solve for b: 7 + 4b = 35
• Solve for c: 2(c + 7) = 26 + 10
##### Writing Equivalent Expressions

Using diagrams as tools, understand and generate equivalent mathematical expressions.

A length of a rectangle is five times as long as its width. To find the perimeter, you could write the expression as: 5w + 5w + w + w. Write the expression in two other ways. ##### Understanding Scale

Use understanding of ratio and proportion to understand scale: the ratio of the length in a drawing (or model) of an object to the length of the actual object. In the example problem figures, scale of the top figure to the bottom figure is 1:2 (“one to two”). Change scale and compute actual lengths and areas of geometric figures.

What is the area of the figure on the left? What is the area of the figure on the right? If a third triangle was drawn with a sclae of 1:3 to the trangle on the left, what is the area of the new triangle? Explain your reasoning. ##### Samples

Understand the concept of random sampling and representative sample size. Use random sampling to draw conclusions or inferences about a population from a representable sample.

The reporter interviewed the four newest teachers in the city’s school district. Is this sample likely to be representative?

Tip: Discuss The News
As you watch the news together keep track of how often statistics are cited. Discuss the details of any polls that are mentioned. Talk about how these concepts are being used and the points they are being used to support or refute.

##### Understanding Probability

Understand probability as a mathematical representation of the likelihood that something, like an event or a result, will happen. Larger numbers represent greater likelihood.

Calculate The Odds
If your school is holding a raffle, discuss the details with your child. Have him find out how many tickets will be sold and how many prizes will be awarded. Then have him determine your probability of winning if you buy a ticket -- or 10 or 20.

Encourage Math Appreciation Through Sports
Sports provide an engaging way of exploring a host of mathematical concepts. Any hard-core baseball fan knows that the game can’t truly be appreciated without an understanding of some essential statistics, like a player’s batting average and runs batted in. Football is also full of statistics, such as the percentage of passes a quarterback completed. If your child is passionate about a sport, encourage her to explore it through math.

##### Calculating Probability

Calculate probability by dividing the number of chances that the event or result will happen by the number of possible outcomes – for example, if there are 10 oranges, 5 peaches, and 15 apples in a bag, the probability of randomly selecting a peach is 5 out of 30 (5/30 or 1/6). Calculate probabilities of simple and compound events.

What is the probability of rolling a six with one die? (simple event)

What is the probability of rolling double sixes using two dice (compound event)

A letter is to be selected from the 26 letters in the English alphabet. What is the probability of choosing a consonant? Explain your reasoning.

Tip: Math in Practice: Raffle Odds

If your school is holding a raffle, discuss the details with your child. Have him find out how many tickets will be sold and how many prizes will be awarded. Then have him determine your probability of winning if you buy a ticket -- or 10 or 20.