Multi-Step Real-Life and Mathematical Problems Introduction

Learning Resource Type

Learning Activity

Subject Area

Mathematics

Grade(s)

7

Overview

In this learning activity, students will learn to solve multistep problems posed with positive and negative rational numbers in any form (whole numbers, fractions, and decimals), using tools strategically. The students will apply properties of operations to calculate numbers in any form; convert between forms as appropriate, and assess the reasonableness of answers using mental computation and estimation strategies.

 

This learning activity can be used as a stand-alone activity but is best used as a Before Activity, the During and After Activities can be found in the Tools or Recommendations section.

Phase

Before/Engage
Mathematics (2019) Grade(s): 7

MA19.7.8

Solve multi-step real-world and mathematical problems involving rational numbers (integers, signed fractions and decimals), converting between forms as needed. Assess the reasonableness of answers using mental computation and estimation strategies.

UP:MA19.7.8

Vocabulary

  • Rational numbers
  • Integers
  • Estimation

Knowledge

Students know:
  • techniques for converting between fractions, decimals, and percents.
  • Techniques for estimation, mental computations, and how to assess the reasonableness of their answers.

Skills

Students are able to:
  • convert between different forms of a rational number.
  • Add, subtract, multiply and divide rational numbers.-translate verbal forms of problems into algebraic symbols, expressions, and equations.
  • Use estimation and mental computation techniques to assess the reasonableness of their answers.

Understanding

Students understand that:
  • One form of a number may be more advantageous than another form, based on the problem context.
  • Using estimation strategies helps to determine the reasonableness of answers.
Mathematics (2019) Grade(s): 7

MA19.7.9

Use variables to represent quantities in real-world or mathematical problems and construct algebraic expressions, equations, and inequalities to solve problems by reasoning about the quantities.

UP:MA19.7.9

Vocabulary

  • Algebraic expressions
  • Equations
  • Inequalities
  • Greater than
  • Greater than or equal to
  • less than
  • less than or equal to

Knowledge

Students know:
  • p(x + q) = px + pq, where p and q are specific rational numbers.
  • When multiplying or dividing both sides of an inequality by a negative number, every term must change signs and the inequality symbol reversed.
  • In the graph of an inequality, the endpoint will be a closed circle indicating the number is included in the solution set (≤ or ≥) or an open circle indicating the number is not included in the solution set ( ).

Skills

Students are able to:
  • use variables to represent quantities in a real-world or mathematical problem.
  • Construct equations (px + q = r and p(x + q) = r) to solve problems by reasoning about the quantities.
  • Construct simple inequalities (px + q > r or px + q
  • Graph the solution set of an inequality.

Understanding

Students understand that:
  • Real-world problems can be represented through algebraic expressions, equations, and inequalities.
  • Why the inequality symbol reverses when multiplying or dividing both sides of an inequality by a negative number.
Mathematics (2019) Grade(s): 7

MA19.7.17

Solve problems involving scale drawings of geometric figures, including computation of actual lengths and areas from a scale drawing and reproduction of a scale drawing at a different scale.

UP:MA19.7.17

Vocabulary

  • Scale drawing
  • Reproduction
  • Scale factor

Knowledge

Students know:
  • how to calculate actual measures such as area and perimeter from a scale drawing.
  • Scale factor impacts the length of line segments, but it does not change the angle measurements.
  • There is a proportional relationship between the corresponding sides of similar figures.
  • A proportion can be set up using the appropriate corresponding side lengths of two similar figures.
  • If a side length is unknown, a proportion can be solved to determine the measure of it.

Skills

Students are able to:
  • find missing lengths on a scale drawing.
  • Use scale factors to compute actual lengths, perimeters, and areas in scale drawings.
  • Use a scale factor to reproduce a scale drawing at a different scale.

Understanding

Students understand that:
  • scale factor can enlarge or reduce the size of a figure.
  • Scale drawings are proportional relationships.
  • Applying a scale factor less than one will shrink a figure.
  • Applying a scale factors greater than one will enlarge a figure.

Learning Objectives

Students will be able to:

  • solve multi-step real-world and mathematical problems involving rational numbers (integers, signed fractions, and decimals), converting between forms as needed.
  • assess the reasonableness of answers using mental computation and estimation strategies.

Activity Details

This activity will be used at the beginning of solving multi-step real-world and mathematical problems involving rational numbers (integers, signed fractions, and decimals), converting between forms as needed lesson.

Engage (5 minutes, whole group)

  • The teacher will ask the students what comes to mind when they are asked to solve multi-step real-life and mathematical problems. The teacher will allow students to elaborate. (Answers will vary)

Lesson (20 minutes, whole group)

Conclusion (10 minutes, whole group)

The teacher will review the lesson content embedded in the Google Doc and answer any further questions the students may have concerning solving multi-step real-world and mathematical problems involving rational numbers (integers, signed fractions, and decimals), converting between forms as needed.

Assessment Strategies

The student responses during the class discussion will be used as a formative assessment.

Variation Tips

  • The teacher can make a copy of the Google Doc and change example problems as needed.
  • The teacher can assign the example problems and have the students work on the problems first before the whole group learns.
  • The teacher can have the students write their notes on plain notebook paper instead of in math journals.

Background / Preparation

https://docs.google.com/presentation/d/1GD-0g9gSsd3-bc7ACPpLPSFBwGsJSL8MXvhkbl-…

Approved Date

Owner (Author)

yvetteakridge
ALSDE LOGO

This site may contain links to other websites or content belonging to or originating from third parties or links to websites and features in banners or other advertising. Such external links are not investigated, monitored, or checked for accuracy, adequacy, validity, reliability, availability, or completeness by us. WE DO NOT WARRANT, ENDORSE, GUARANTEE, OR ASSUME RESPONSIBILITY FOR THE ACCURACY OR RELIABILITY OF ANY INFORMATION OFFERED BY THIRD-PARTY WEBSITES LINKED THROUGH THIS SITE.
Alabama Learning Exchange © 2002-2023 by Alabama State Department of Education is licensed under Attribution-NonCommercial-ShareAlike 4.0 International

Design by Adaptive Theme