ALEX Learning Activity

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.

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.

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:

• The teacher will hand out the Multi-Step Real-Life and Mathematical Problems Practice sheets.
• The teacher will monitor students as they complete the worksheet.
• The teacher will remind the students the worksheet will be graded for accuracy.

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

• The teacher will need copies of the Multi-Step Real-Life and Mathematical Problems Practice sheets. in advance.
• The teacher will provide each student with a copy of the worksheet, a whiteboard, a dry erase pen, and an eraser for the “We Do” section.
• The students will need math journals if used for notes or paper if math journals are not used.
• The teacher will need Internet access and the required equipment to display the Multi-Step Real-Life and Mathematical Problems Lesson.

• 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.

This activity can stand alone or be used as a Before/Engage activity for the following learning activities:

Multi-Step Real-Life and Mathematical Problems Introduction (Before Activity)

Multi-Step Real-Life and Mathematical Practice Problems (After Activity)