ACOS Objective 3

Solve problems involving rational numbers.
  • Describing the method used
  • Determining the reasonableness of results
  • Using percents to solve problems, including problems involving discounts, taxes, commissions, and simple interest

ARMT Possible Points = 8 (MC)
  • The four basic operations (addition, subtraction, multiplication, division) will be required.
  • Word problems/real-life situations may be required.
  • Money values may be used.
  • Mixed numbers may be used.
  • Solving problems involving addition and subtraction with common and uncommon denominators may be required.
  • Changing mixed numbers to improper fractions may be required.
  • Solving problems involving percents may be required.
  • One of the options may be NH, which means "Not Here."

Sample problems from Item Specs


Objective 7.3.1: Demonstrate computational fluency with addition, subtraction, multiplication, and division of decimals and fractions.
Objective 7.3.2: Solve problems involving decimals, percents, fractions, and proportions.

Additional content to be taught

  • Describing the method used
  • Determining the reasonableness of results
  • Using percents to solve problems, including problems involving discounts, taxes, commissions, and simple interest

Issues to consider

  • Yes, they are supposed to learn how to compute with rational numbers in 6th grade, but 7th graders are tested over them as well.
  • How do you review fractions?
  • Do students truly need to demonstrate computational fluency with decimals without a calculator in 7th grade?
  • Percents are so practical. How do you take advantage of the chance to teach a "real-life" skill that most students have already used?


A Well-Planned Diet
You are what you eat! So are you ice cream or broccoli? You're on a mission to find out! Along the way, you'll collect and analyze data about what you eat over a period of five days. You'll take into account serving sizes, Calories, and fat grams. You'll also take on the roll of a nutritionist, researching the Food Pyramid and creating a healthy meal plan. So bring a hearty appetite and your math tool kit. This adventure will tantalize your taste buds!

Nutritional Challenge 1:
First, keep a record of all the food that you eat for five straight days, keeping a record of the amount you eat as well as the different characteristics of the foods.
Nutritional Challenge 2:
Second, research the Food Pyramid and create the healthiest meal from a selection of food choices.
Nutritional Challenge 3:
Third, create a presentation that includes your nutritional analysis of what you currently eat and of what you feel is a well-balanced meal.

Math Content: convert decimals to fractions, mean, median, mode, simplest form, percents

Technology Skills: searching, presentation (web page, poster, article)

Interdisciplinary: Health (calories, fat intake, Food Pyramid, healthy eating), Language (writing paragraphs)


Sixth Grade wiki page on rational numbers

Place Value Lessons

Abacus in Various Number Systems
History of the Abacus and an applet of an abacus.

Base Ten Blocks Applet
This page is specifically for teachers and describes a complete lesson plan on how to teach base 10 place value as well as basic arithmetic operations using this online version of the base 10 blocks manipulatives. This can also be used for exploring other bases.

Fraction Shapes
This a great lesson by Cynthia Lanius that uses Pattern Blocks to explore the relationships between the part and the whole of fractions. Activities can be printed out and completed using actual Pattern Blocks or solved online with a pattern block applet.

Integer Bars (Cuisenaire Rods)
Hands-on to learn almost every math concept -- number sense, basic math skills (addition, subtraction, multiplication, and division), fractions, algebra, and more...

Fraction Bars
This lesson will allow students to learn, through the hands-on use of virtual fraction bars, the following concepts: a good understanding of fractions, equivalent fractions, ordering and comparing fractions, basic addition and subtraction of fractions, and fraction size notation.

Cool Problems

Mystery Number
A number gives you the follwing clues as to its identity.
1. I am a two-digit number.
2. I am not prime.
3. My two digits are not the same.
4. I am not a multiple of 2, 3, or 5.
What is the number?
Answer: The Daily Spark Critical Thinking, p. 39.


Shake ‘n Go Fractions
This lesson is designed for cooperative groups. Students will use a computer tutorial to practice computing equivalent fractions and then will apply what they have learned to adjust a recipe for a tasty snack.

Counting the Rice
Through this hand-on and role play activity the students will discover the concept of place value. Using different bases, this activity can be used through middle school.

Name That Portion
AMSTI 5th grade unit on Fractions, Decimals, and Percents. Contains lots of great games.