(based on a $500 initial balance)
(based on a $500 initial balance)
0
0
0
1
5
5
2
10
10.05
3
15
15.15
4
20
20.30
5
25
25.51
10
50
52.31
Note that this does not necessarily imply that "hours spent on homework" = 2 or that "hours spent in school" = 7. During a week, 10 hours may have been spent on homework while 35 hours were spent in school. The proportion is still true because $\frac{10}{35}=\frac{2}{7}$.
Cramer, K. & Post, T. (1993, February). Making connections: A case for proportionality. In Arithmetic Teacher, 60(6), 342-346.
Answer: a DOK: Level 3 Source: Minnesota Grade 7 Mathematics MCA - III Item Sampler Item, 2011, Benchmark 7.1.2.4
Answer: c DOK: Level 3 Source: Massachusetts Comprehensive Assessment System Release of Spring 2009 Test Items
Assume you borrow $900 at 7% annual compound interest for four years.
Answers: Part A: $900 + $252 = $1179.72; Part B: $279.72 DOK: Level 2 Source: Test Prep: Modified from MCA III Test Preparation Grade 7, Houghton Mifflin Harcourt Publishing Company, Attn: Contracts, Copyrights, and Licensing, 9400 South Park Center Loop, Orlando, FL 32819.
Tim is mixing 1 L of juice concentrate with 5L of water to make juice for his 10 guests. After he pours the mix into 10 different cups, he realizes that the juice is not sweet enough, so he adds 0.1 L of syrup into each of the cups. What is the final amount of juice in each cup? A. 0.5 L B. 0.7 L C. 1.7 L D. 2.0 L Answer: b DOK: Level 2 Source: Test Prep: MCA III Test Preparation Grade 7, Houghton Mifflin Harcourt Publishing Company, Attn: Contracts, Copyrights, and Licensing, 9400 South Park Center Loop, Orlando, FL 32819.
Answer: b DOK: Level 2 Source: Minnesota Grade 7 Mathematics MCA - III Item Sampler Item, 2011, Benchmark 7.1.2.5
Answer: b DOK: Level 2 Source: Minnesota Grade 7 Mathematics Modified MCA - III Item Sampler Item, 2011, Benchmark 7.1.2.5
Answer: d DOK: Level 2 Source: Massachusetts Comprehensive Assessment System Release of Spring 2010 Test Items
Answer: b DOK: Level 2 Source: Massachusetts Comprehensive Assessment System Release of Spring 2010 Test Items
Administrative/peer classroom observation.
(descriptive list) | (descriptive list) |
finding the percent sign on a calculator. | providing several different types of calculators to show the differences in the place value each calculator displays. |
rounding to correct place value. | making tables of values to help introduce the concept of proportionality in these situations. |
converting percents to decimals, decimals to percents, and decimals to fractions, etc. | using real-world contexts that the students are familiar with: recipes, scores in games, numbers of girls/boys in a class, etc. |
making tables of values to find patterns. | making sure students are not just memorizing an algorithm for solving proportions when solving these types of problems. |
finding a percent of a number using multiple methods. | exposing students to the difference between simple and compound interest. |
scaling values up and down correctly. |
|
using the context of the problem to make sense of it and perhaps drawing diagrams of the problem situation. |
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using real-world examples to solve problems. |
|
relating proportions to everyday situations. |
|
7.1.2a applying & making sense of rational numbers.
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Adding and subtracting rational numbers to solve problems, lesson plan.
Students will compute and solve problems using rational numbers. They will:
60–90 minutes
The possible inclusion of commercial websites below is not an implied endorsement of their products, which are not free, and are not required for this lesson plan.
IXL’s Grade 7 Add and Subtract Rational Numbers will give students additional practice with addition and subtraction of rational numbers.
IXL’s Grade 8 Add and Subtract Rational Numbers: Word Problems will give students additional practice with solving word problems that involve rational numbers.
: | Students will learn to compute with rational numbers and use these skills to solve real-world problems. |
: | Hook students into the lesson by asking them to model a problem involving the addition of two rational numbers using a number line. |
: | The focus of the lesson is on computing sums and differences of rational numbers. Once students are adept at computing with rational numbers, the lesson will proceed to problem solving with rational numbers. After you walk students through several example problems, students will participate in the final class activity, which culminates in a class PowerPoint file. |
: | Opportunities for discussion occur with each computation and real-world example, leading students to rethink and revise their understanding throughout the lesson. The PowerPoint activity gives students an opportunity to review their understanding, prior to completing the exit ticket. |
: | Evaluate students’ level of understanding and comprehension by giving students the exit ticket. |
: | Using suggestions in the Extension section, the lesson can be modified to meet the needs of students. The Small-Group Practice worksheet offers more practice for students. The Expansion Worksheet includes more difficult numeric expressions and additional word problems for students who are ready for a challenge. |
: | The lesson is scaffolded so that students first model an addition problem with manipulatives before attempting to compute a few sums and differences. Next, students discuss the computation process for all examples. The second part of the lesson involves problem solving with rational numbers. Students provide the solution process with the teacher serving as a facilitator. This lesson is meant as a refresher for adding and subtracting rational numbers and as an introduction to problem solving with rational numbers. The next lesson in the unit will present multiplication and division with rational numbers and problem solving using these operations on rational numbers. |
As students come into class, have them evaluate the following expressions using a number line.
Walk around the classroom as students are working through the example problems. Briefly discuss the answers and make sure students are comfortable modeling addition and subtraction of rational numbers on a number line before moving on.
“In Lesson 1 of this unit, we learned how to model addition and subtraction of rational numbers on a number line. Today, we are going to focus on performing these computations without the use of a number line. We will then use these skills to solve some real-life problems.”
Computations: Adding and Subtracting Rational Numbers
Before presenting some real-world problems, give students the opportunity to practice adding and subtracting rational numbers without the help of a number line. If necessary, go over the following examples together as a class.
the other is not. Often, when computing with fractions, it is best to write all numbers in fraction form.”
common denominator. The lowest common denominator in this case would be 5.”
numerators as indicated. The denominator will stay as is.”
it is, but we may want to rewrite the fraction as a mixed number to get a better idea of the value.”
Example 2: − 4.64 + 9.85
you suspect our final answer here will be positive or negative?” (Positive, the absolute value of 9.85 is larger than the absolute value of −4.64.)
Distribute the Lesson 2 Computations Worksheet ( M-7-5-2_Computations and KEY.docx ). Instruct students to complete the worksheet individually. Walk around the room as students work to be sure they are on task and performing the computations accurately. Following the worksheet, provide time for students to discuss any problems they encountered, questions they have, or revelations they discovered. First, ask students to describe the computation process used to find each sum or difference. Then confirm their understanding by restating the correct process.
Problem Solving with Rational Numbers
Now it is time for students to apply their understanding of computation to solving real-world problems. Discuss the following examples together as a class.
Distribute Lesson 2 Word-Problem Examples ( M-7-5-2_Word Problem Examples and KEY.docx ). Have students discuss the solution process for each example problem in a manner similar to the process demonstrated above. Confirm the correct ideas students express. Then say: “Look through the problems you just received. Think of how the example word problems can be solved. Do you need to add or subtract the rational numbers? How will you go about doing this for fractions with unlike denominators, or for mixed numbers?”
Activity 1: Write-Pair-Share
Ask the whole class to think of some real-world contexts that involve the addition or subtraction of rational numbers. Students should make a list of at least five real-world contexts and provide one word problem. Ask students to share their ideas with a partner. Give students about 5 minutes to share contexts and word problems. During this time, each partner may ask questions of the other partner. Then, the whole class can reconvene. One member from each partner group will share the list of real-world contexts and word problems with the class. The teacher may wish to post the real-world contexts and word problems in a file on the class Web page or use them as a classroom display. These student examples would then serve as a reference tool.
Have students complete Lesson 2 Exit Ticket ( M-7-5-2_Exit Ticket and KEY.docx ) at the close of the lesson to evaluate students’ level of understanding.
Use the suggestions in the Routine section to review lesson concepts throughout the school year. Use the small-group suggestions for any students who might benefit from additional instruction. Use the Expansion section to challenge students who are ready to move beyond the requirements of the standard.
Insert template, information.
IMAGES
COMMENTS
Dividing Rational Numbers Practice and Problem Solving: A/B Find each quotient. 1. 1 2 y 3 2. 6 y 3 4 §·¨¸ ©¹ 3. 5 6 y 10 BBBBBBBBBBBBBBBBB BBBBBBBBBBBBBBBBB BBBBBBBBBBBBBBBBB 4. 5.25 15 5. 24 y 3.2 6. 0.125 y 0.5 BBBBBBBBBBBBBBBBB BBBBBBBBBBBBBBBBB BBBBBBBBBBBBBBBBB 7. 13 714 y 8. 3 2 9 8 9. 11 13 23 y
A rational number is a number that can be written as the quotient of two integers. Rational numbers include positive and negative fractions and decimals, and also integers since an integer can be written as a fraction with 1 as the denominator: 26 5 2 6. ··1. When you multiply positive and negative fractions, you multiply the numerator by the ...
To find the number of pizzas required for 36 students, we have to multiply 36 by 1/4. 36 ⋅ 1/4 = 9. So, the teacher needs 9 pizzas. Problem 3 : Mason made 3/4 of a pound of trail mix. If he puts 3/8 of a pound into each bag, how many bags can Mason fill? Solution : To find the number of bags, we have to divide 3/4 by 3/8.
Choose and complete a graphic organizer to help you study the concept. 1. dividing integers. 2. writing fractions or mixed numbers as decimals. 3. writing decimals as fractions or mixed numbers. 4. multiplying rational numbers. 5. dividing rational numbers. "I finished my Information Frame about rainforests.
Improve your math knowledge with free questions in "Multiply and divide rational numbers: word problems" and thousands of other math skills.
Hexingo - Operations with rational numbers. Online practice for grades 7-8. Practice adding, subtracting, and multiplying a mixture of fractions and decimals (some are negative) in this fun game! To win, you need to get four correct answers in a row on the hexagon-tiled board. You can choose to include or not include three different operations ...
Rational Numbers - Dividing Rational Numbers ... Problem-solving skills (explore, plan, solve, verify.) 3. PA.3.3 ... VII. Independent Practice: Dividing Rational Numbers Worksheet A. Class work: #2 - 44 Even B. Homework: #1 - 45 odds C. Due in two days. Allow for the day in between the date assigned and the date due for
1. Divide the absolute values of the two rational numbers. 2. If the two numbers (dividend and divisor) have the same sign, their quotient is positive. 3. If the two numbers (dividend and divisor) have opposite signs, their quotient is negative. Exercise 3 (20 minutes)
Practice. Have students practice dividing rational numbers including fractions, integers, and decimals using the color by code activity included in the resource. Walk around the classroom to answer any student questions and provide assistance as needed. Fast finishers can work on the maze activity for extra practice.
Sam remembers that to divide rational numbers, he can actually turn this problem into a multiplication problem by flipping the second rational number. So 7/8 becomes 8/7 and the division symbol ...
IXL's Grade 8 Multiply and Divide Rational Numbers: Word Problems offers students additional practice with solving word problems involving rational numbers. Formative Assessment. View. The modeling activity can be used to assess students' conceptual understanding of multiplication and division of rational numbers.
Practice the questions given in the worksheet on word problems on rational numbers. The questions are related to various types of word problems on four fundamental operations on rational numbers. 1. From a rope 11 m long, two pieces of lengths 13/5 m and 33/10 m are cut off. What is the length of the remaining rope?
Answers to Add, Subtract, Multiply, Divide Rational Numbers (ID: 1) 1) −4 2) 6 3) 6 4) 1 5) −252 6) −90 7) 336 8) 36 9) 5 4 ... 7th Grade Summer Practice 1) Write an equation then solve. a. Find the width of a rectangle if its length is 5 more than the width and its perimeter is 90 cm.
Dividing Rational Expressions The rule for dividing rational expressions is the same as the rule for dividing fractions: multiply the fi rst by the reciprocal of the second, and write the result in simplifi ed form. Rational expressions are closed under nonzero division. KEY IDEA Dividing Rational Expressions Let a, b, c, and d be expressions ...
2.2 Use a Problem Solving Strategy; 2.3 Solve a Formula for a Specific Variable; ... The domain of a rational function is all real numbers except for those values that would cause division by zero. ... To divide rational functions, we divide the resulting rational expressions on the right side of the equation using the same techniques we used ...
est form.MULTIPLYING RATIONAL EXPRESSIONSExample 1. Multiply, 15 14. 49 45. First, reduce by dividing out the common factors from numerator and denominator (15 and 7 ) 2 . 7 3. her and the denominators together2 21Our AnswerWhen multiplying rational expressions, we first divide. e numerators and denominators by any common factors. T.
They solve problems with rational numbers in the context of a negative flow rate from a tank and negative charges on an electricity bill or a bank account. The problems in this section are designed so that it is natural to solve them by filling in tables or making numerical calculations. In the next lesson, students will move towards solving ...
To multiply two fractions, multiply the numerators and multiply the denominators. IXL's SmartScore is a dynamic measure of progress towards mastery, rather than a percentage grade. It tracks your skill level as you tackle progressively more difficult questions. Consistently answer questions correctly to reach excellence (90), or conquer the ...
1 2. Well, a rational number is a fraction, so we can use: Adding Fractions, Subtracting Fractions, Multiplying Fractions and. Dividing Fractions. Here we will see those operations in a more general Algebra style. You might also like to read Fractions in Algebra. Let us start with multiplication, as that is the easiest.
Standard 7.1.2. Calculate with positive and negative rational numbers, and rational numbers with whole number exponents, to solve real-world and mathematical problems. Grade: 7. Subject: Math. Strand: Number & Operation. Benchmark: 7.1.2.4 Solve Problems with Rational Numbers Including Positive Integer Exponents.
Cite this lesson. The steps of multiplying or dividing rational polynomial expressions are to factor, flip (when dividing), slash or cancel, and multiply. Put these steps for multiplying and ...
The next lesson in the unit will present multiplication and division with rational numbers and problem solving using these operations on rational numbers. ... give students the opportunity to practice adding and subtracting rational numbers without the help of a number line. If necessary, go over the following examples together as a class ...