Comparing Speeds and Prices

5 min

Teacher Prep
Setup
Display one problem at a time. 1 minute of quiet think time per problem, followed by a whole-class discussion.

Narrative

This Warm-up activates ideas about rates and constant speed before students solve problems about them later in the lesson. Students are presented with a situation with some numerical values and prompted to develop mathematical questions that can be asked about the situation. The routine allows students to make sense of a context before feeling pressure to produce answers, and it develops students’ awareness of the language used in mathematics problems.

This activity uses the Co-Craft Questions math language routine to advance reading and writing as students make sense of a context and practice generating mathematical questions.

Launch

Tell students to close their books or devices (or to keep them closed). Arrange students in groups of 2. Remind students of the context of running on a treadmill, which they had encountered in an earlier unit. Use Co-Craft Questions to orient students to the context and to elicit possible mathematical questions.

Give students 1–2 minutes to write a list of mathematical questions that could be asked about the situation before comparing questions with a partner.

Action and Expression: Internalize Executive Functions. To support working memory, provide students with access to sticky notes or mini whiteboards.
Supports accessibility for: Memory, Organization

Student Task

Some students did treadmill workouts.

  • Tyler ran 4,200 meters in 30 minutes.
  • Kiran ran 6,300 meters in 12\frac{1}{2} hour.
  • Mai ran 6.3 kilometers in 45 minutes.

Sample Response

Sample responses:

  • Were the students running at the same rate?
  • Were the students running at a constant speed?
  • What was each student’s speed?
  • Who ran the fastest?
  • How far would Tyler and Kiran run in 45 minutes?
  • How far did Mai run in the first 30 minutes?
Activity Synthesis (Teacher Notes)

Invite several partners to share one question with the class, and record responses. Ask the class to make comparisons among the shared questions and their own. Ask, “What do these questions have in common? How are they different?” Listen for and amplify language related to the learning goal, such as “constant speed,” “at the same rate,” and “‾\underline{\hspace{.5in}} meters per hour (or minute).”

Tell students that they will now look more closely at Tyler's, Kiran's, and Mai’s workouts and compare them.

Standards
Building On
  • 5.NF.3·Interpret a fraction as division of the numerator by the denominator (a/b = a ÷ b). Solve word problems involving division of whole numbers leading to answers in the form of fractions or mixed numbers, e.g., by using visual fraction models or equations to represent the problem. <em>For example, interpret 3/4 as the result of dividing 3 by 4, noting that 3/4 multiplied by 4 equals 3, and that when 3 wholes are shared equally among 4 people each person has a share of size 3/4. If 9 people want to share a 50-pound sack of rice equally by weight, how many pounds of rice should each person get? Between what two whole numbers does your answer lie?</em>
  • 5.NF.B.3·Interpret a fraction as division of the numerator by the denominator <span class="math">\((a/b = a \div b)\)</span>. Solve word problems involving division of whole numbers leading to answers in the form of fractions or mixed numbers, e.g., by using visual fraction models or equations to represent the problem. <span>For example, interpret <span class="math">\(3/4\)</span> as the result of dividing <span class="math">\(3\)</span> by <span class="math">\(4\)</span>, noting that <span class="math">\(3/4\)</span> multiplied by <span class="math">\(4\)</span> equals <span class="math">\(3\)</span>, and that when <span class="math">\(3\)</span> wholes are shared equally among <span class="math">\(4\)</span> people each person has a share of size <span class="math">\(3/4\)</span>. If <span class="math">\(9\)</span> people want to share a <span class="math">\(50\)</span>-pound sack of rice equally by weight, how many pounds of rice should each person get? Between what two whole numbers does your answer lie?</span>

15 min

15 min