Multi-Step Real-Life and Mathematical Problems Lesson

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 During Activity, the Before and After Activities can be found in the Notes or Recommendations section.

Phase

During/Explore/Explain
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.
  • assess the reasonableness of answers using mental computation and estimation strategies.

Activity Details

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

I Do:

  • The teacher will demonstrate how to solve multi-step real-world and mathematical problems involving rational numbers (integers, signed fractions, and decimals), converting between forms as needed using the following examples:
  1. If a woman making $25 an hour gets a 10% raise, how much will her salary increase per hour, and what is her new salary?
  2. If you want to place a towel bar 9 3/4 inches long in the center of a door that is 27 1/2 inches wide, how far from the edge will you need to place the bar?

Answer #1: She will make an additional 1/10 of her salary an hour, or $2.50, for a new salary of $27.50.

Answer #2: you will need to place the bar about 9 inches from each edge; this estimate can be used to check the exact computation.

  • Students will observe, take notes, use their math journals or paper, and ask questions.
  • The teacher will have the students turn and talk about any misconceptions they may have at this point in the lesson.

We Do:

    • The teacher will say, "We will now collaborate and discuss various ways of solving multi-step real-world and mathematical problems involving rational numbers (integers, signed fractions, and decimals), converting between forms as needed using Shrinking, Discounted Books, Gotham City Taxis, and Anna in D.C. Tasks from Illustrative Mathematics." (These 3 tasks are embedded at the bottom of the Multi-Step Real-Life and Mathematical Problems Lesson).
    • The teacher will issue whiteboards, pens, and erasers to the class. 
    • The teacher will ask students to work on the “We Do” problems on their whiteboards holding them up as they find each answer for the teacher to check. (This will be used as a formative assessment to see if students understand the lesson.)
    • Important: The teacher will need to verbally discuss any problems and have students explain their thinking to ensure solidification of understanding.

You Do:

Assessment Strategies

The student responses during the class discussion and Multi-Step Real-Life and Mathematical Problems Practice sheet will be used as a formative assessment.

Variation Tips

  • For students who struggle with this activity, the teacher should provide a work buddy.
  • For students who excel at this activity, the teacher could assign the example problems individually.
  • The teacher can have the students write their answers on plain notebook paper or tablets instead of whiteboards.
  • The teacher can choose not to use the Multi-Step Real-Life and Mathematical Problems Practice sheet as a means of formative assessment.

Background / Preparation

https://tasks.illustrativemathematics.org/content-standards/7/EE/B/3

Approved Date

Owner (Author)

yvetteakridge
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