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Fluency Expectations or Examples of Culminating StandardsStudents solve multistep problems posed with positive and negative rational numbers in any form (whole numbers, fractions, and decimals), using tools strategically. This work is the culmination of many progressions of learning in arithmetic, problem solving and mathematical practices.
Examples of Opportunities for In-Depth Focus
This is a major capstone standard for arithmetic and its applications.
Clusters should not be sorted from Major to Supporting and then taught in that order. To do so would strip the coherence of the mathematical ideas and miss the opportunity to enhance the major work of the grade with the supporting clusters.
- Assessment Limits :
Items should not use variables. Items should require two or more steps - Calculator :
Yes
- Context :
Required
- Test Item #: Sample Item 1
- Question:
Rolando is 13. In five years, his age will be
the age of his sister Marisa.How old will Marisa be in three years?
- Difficulty: N/A
- Type: EE: Equation Editor
- Test Item #: Sample Item 2
- Question: A set of pencils sells for $1.75 and costs $0.40 to make. Twenty percent of the profit
(the difference between the purchase price and the amount it costs to make) from
each set of pencils goes to a school.
If 500 sets are sold, what is the amount of money that will go to the school?
- Difficulty: N/A
- Type: EE: Equation Editor
- Test Item #: Sample Item 3
- Question: A bucket holds 243.5 ounces (oz) of water when full. The bucket loses 0.3 oz of water
per second.
In how many seconds will the bucket be 40% full?
- Difficulty: N/A
- Type: EE: Equation Editor
- Test Item #: Sample Item 4
- Question: A plane is flying at 31,348 feet. It needs to rise to 36,000 feet in two stages.
In stage 1, it rises 5% of its initial altitude of 31,348 feet.
In stage 2, it rises at a rate of 140.3 feet per minute.
How many minutes does it take for the plane to rise during stage 2?
- Difficulty: N/A
- Type: EE: Equation Editor
- Test Item #: Sample Item 5
- Question:
The dimensions of a rectangular pool are 24.5 feet by 13 feet. The depth of the water is 4 feet. Each cubic foot contains 7.48 gallons of water.
How many gallons of water, to the nearest tenth, are needed to fill the pool to 80% capacity?
- Difficulty: N/A
- Type: EE: Equation Editor
Related Courses
Related Access Points
Related Resources
Educational Games
Formative Assessments
Lesson Plans
Original Student Tutorial
Problem-Solving Tasks
Tutorials
Video/Audio/Animation
STEM Lessons - Model Eliciting Activity
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Model Eliciting Activities, MEAs, are open-ended, interdisciplinary problem-solving activities that are meant to reveal students’ thinking about the concepts embedded in realistic situations. Click here to learn more about MEAs and how they can transform your classroom.
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This MEA requires students to formulate a comparison-based solution to a problem involving finding the best decision on purchasing official vehicles for school district considering different aspects. Students are provided the context of the problem, a request letter from a client asking them to provide a recommendation, and data relevant to the situation. Students utilize the data to create a defensible model solution to present to the client.
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Model Eliciting Activities, MEAs, are open-ended, interdisciplinary problem-solving activities that are meant to reveal students’ thinking about the concepts embedded in realistic situations. Click here to learn more about MEAs and how they can transform your classroom.
Uncle Henry's Dilemma is a problem solving lesson to determine the global location for the reading of Uncle Henry's will. The students will interpret data sets which include temperature, rainfall, air pollution, travel cost, flight times and health issues to rank five global locations for Uncle Henry's relatives to travel to for the reading of his will. This is an engaging, fun-filled MEA lesson with twists and turns throughout. Students will learn how this procedure of selecting locations can be applied to everyday decisions by the government, a business, a family, or individuals.
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MFAS Formative Assessments
Students are asked to assess the reasonableness of an answer using mental computation and estimation strategies.
Students are asked to solve a multi-step problem involving rational numbers.
Students are asked to assess the reasonableness of answers using estimation strategies.
Original Student Tutorials Science - Grades K-8
Use models to solve balance problems on a space station in this interactive, math and science tutorial.
Student Resources
Original Student Tutorial
Use models to solve balance problems on a space station in this interactive, math and science tutorial.
Type: Original Student Tutorial
Educational Games
In this timed activity, students solve linear equations (one- and two-step) or quadratic equations of varying difficulty depending on the initial conditions they select. This activity allows students to practice solving equations while the activity records their score, so they can track their progress. This activity includes supplemental materials, including background information about the topics covered, a description of how to use the application, and exploration questions for use with the java applet.
Type: Educational Game
In this activity, two students play a simulated game of Connect Four, but in order to place a piece on the board, they must correctly solve an algebraic equation. This activity allows students to practice solving equations of varying difficulty: one-step, two-step, or quadratic equations and using the distributive property if desired. This activity includes supplemental materials, including background information about the topics covered, a description of how to use the application, and exploration questions for use with the Java applet.
Type: Educational Game
Problem-Solving Tasks
The purpose of this task is to give students an opportunity to solve a challenging multistep percentage problem that can be approached in several different ways. Students are asked to find the cost of a meal before tax and tip when given the total cost of the meal. The task can illustrate multiple standards depending on the prior knowledge of the students and the approach used to solve the problem.
Type: Problem-Solving Task
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Type: Problem-Solving Task
This problem asks the students to represent a sequence of operations using an expression and then to write and solve simple equations. The problem is posed as a game and allows the students to visualize mathematical operations. It would make sense to actually play a similar game in pairs first and then ask the students to record the operations to figure out each other's numbers.
Type: Problem-Solving Task
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Type: Problem-Solving Task
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Type: Problem-Solving Task
Tutorials
Many real world problems involve involve percentages. This lecture shows how algebra is used in solving problems of percent change and profit-and-loss.
Type: Tutorial
Video/Audio/Animation
This Khan Academy video tutorial introduces averages and algebra problems involving averages.
Type: Video/Audio/Animation
Parent Resources
Problem-Solving Tasks
The purpose of this task is to give students an opportunity to solve a challenging multistep percentage problem that can be approached in several different ways. Students are asked to find the cost of a meal before tax and tip when given the total cost of the meal. The task can illustrate multiple standards depending on the prior knowledge of the students and the approach used to solve the problem.
Type: Problem-Solving Task
This purpose of this task is to help students see two different ways to look at percentages both as a decrease and an increase of an original amount. In addition, students have to turn a verbal description of several operations into mathematical symbols. This requires converting simple percentages to decimals as well as identifying equivalent expressions without variables.
Type: Problem-Solving Task
This problem asks the students to represent a sequence of operations using an expression and then to write and solve simple equations. The problem is posed as a game and allows the students to visualize mathematical operations. It would make sense to actually play a similar game in pairs first and then ask the students to record the operations to figure out each other's numbers.
Type: Problem-Solving Task
Students are asked to determine the change in height in inches when given a constant rate of change in centimeters. The answer is rounded to the nearest half inch.
Type: Problem-Solving Task
The purpose of this task is to give students an opportunity to solve a multi-step ratio problem that can be approached in many ways. This can be done by making a table, which helps illustrate the pattern of taxi rates for different distances traveled and with a little persistence leads to a solution which uses arithmetic. It is also possible to calculate a unit rate (dollars per mile) and use this to find the distance directly without making a table.
Type: Problem-Solving Task
Video/Audio/Animation
This Khan Academy video tutorial introduces averages and algebra problems involving averages.
Type: Video/Audio/Animation
