Solving math problems can intimidate sixth-graders but it shouldn't. Using a few simple formulas and a bit of logic can help students quickly calculate answers to seemingly intractable problems. Explain to students that you can find the rate (or speed) that someone is traveling if you know the distance and time that she traveled. Conversely, if you know the speed (rate) that a person is traveling as well as the distance, you can calculate the time he traveled. You simply use the basic formula: rate times the time equals distance, or **r * t = d **(where "*" is the symbol for multiplication.)

The free, printable worksheets below involve problems such as these, as well as other important problems, such as determining the largest common factor, calculating percentages, and more. The answers for each worksheet are provided in the next slide right after each worksheet. Have students work the problems, fill in their answers in the provided blank spaces, then explain how they would arrive at the solutions for questions where they are having difficulty. The worksheets provide a great and simple way to do quick formative assessments for an entire math class.

## Worksheet No 1

**Print PDF**: Worksheet No 1

On this PDF, your students will solve problems such as: "Your brother traveled 117 miles in 2.25 hours to come home for school break. What’s the average speed that he was traveling?" and "You have 15 yards of ribbon for your gift boxes. Each box gets the same amount of ribbon. How much ribbon will each of your 20 gift boxes get?"

## Worksheet No. 1 Solutions

**Print Solutions PDF**: Worksheet No. 1 Solutions

To solve the first equation on the worksheet, use the basic formula: rate times the time = distance, or **r * t = d**. In this case, r = the unknown variable, t = 2.25 hours, and d = 117 miles. Isolate the variable by dividing "r" from each side of the equation to yield the revised formula, **r = t ÷ d**. Plug in the numbers to get: **r = 117 ÷ 2.25, **yielding** r = 52 mph**.

For the second problem, you don't even need to use a formula—just basic math and some common sense. The problem involves simple division: 15 yards of ribbon divided by 20 boxes, can be shortened as **15 ÷ 20 = 0.75. **So each box gets 0.75 yards of ribbon.

## Worksheet No. 2

**Print PDF**: Worksheet No. 2

On worksheet No. 2, students solve problems that involve a little bit of logic and a knowledge of factors, such as: "I’m thinking of two numbers, 12 and another number. 12 and my other number have a greatest common factor of 6 and their least common multiple is 36. What’s the other number I’m thinking of?"

Other problems require only a basic knowledge of percentages, as well as how to convert percentages to decimals, such as: "Jasmine has 50 marbles in a bag. 20% of the marbles are blue. How many marbles are blue?"

## Worksheet No. 2 Solution

**Print PDF Solutions**:** **Worksheet No. 2 Solution

For the first problem on this worksheet, you need to know that the **factors of 12 are 1, 2, 3, 4, 6, and 12**; and the **multiples of 12 are 12, 24, 36**. (You stop at 36 because the problem says that this number is the least common multiple.) Let's pick 6 as a possible greatest common multiple because it's the largest factor of 12 other than 12. The **multiples of 6 are 6, 12, 18, 24, 30, and 36**. Six can go into 36 six times (6 x 6), 12 can go into 36 three times (12 x 3), and 18 can go into 36 twice (18 x 2), but 24 cannot. Therefore the answer is 18, as **18 is the largest common multiple that can go into 36**.

For the second answer, the solution is simpler: First, convert 20% to a decimal to get 0.20. Then, multiply the number of marbles (50) by 0.20. You would set up the problem as follows: **0.20 x 50 marbles = 10 blue marbles**.