Ratios and unit rates
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 3⁄4 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.
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 1⁄2 mile in each ¼ hour, what is the (unit) rate at which the person is walking, expressed in miles per (1) hour?
- It takes 1⁄8 of a liter of water to fill 1⁄9 of the fish tank. How many liters of water are needed to fill the tank?
Addition, subtraction, multiplication, & division
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.
Convert rational numbers to decimals using long division.
What is 12/29 as a decimal?
What is 13 4/5 as a decimal?
Expressions & equations
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.
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.
Statistics & probability
Understand the concept of random sampling and representative sample size. Use random sampling to draw conclusions or inferences about a population from a representative 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.
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 -- 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.
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 - 10 or 20.
TODAY Parenting Guide resources were developed by NBC News Learn with the help of subject-matter experts and align with the Common Core State Standards.