Standards-based assessment and Instruction

# Math 3-5

## Hot Dogs for a Picnic

Mrs. Richards is planning a picnic for many of her relatives. Everyone coming to the picnic wants to eat hot dogs. Mrs. Richards knows that hot dogs at the local store are sold 10 in a package. The hot dog rolls are sold 8 in a package.

What is the least number of packages of hot dog and hot dog rolls Mrs. Richards can buy to have exactly the same amount of hot dogs and rolls?

Mrs. Richards discovers that 30 relatives are coming to the picnic and every one wants to eat 2 hot dogs! What is the least number of packages of hot dogs and hot dog rolls that Mrs. Richards will have to buy to feed all her relatives?

#### More Accessible Version:

Mrs. Richards is planning a picnic for many of her relatives. Everyone coming to the picnic wants to eat hot dogs. Mrs. Richards knows that hot dogs at the local store are sold 10 in a package. The hot dog rolls are sold 8 in a package.

What is the least number of packages of hot dog and hot dog rolls Mrs. Richards can buy to have exactly the same amount of hot dogs and rolls?

#### More Challenging Version:

Mrs. Richards is planning a picnic for many of her relatives. Everyone coming to the picnic wants to eat hot dogs. Mrs. Richards knows that hot dogs at the local store are sold 10 in a package. The hot dog rolls are sold 8 in a package.

What are three ways Mrs. Richards can buy packages of hot dog and hot dog rolls so she has exactly the same amount of hot dogs and rolls?

Mrs. Richards discovers that 30 relatives are coming to the picnic and every one wants to eat 2 hot dogs! What is the least number of packages of hot dogs and hot dog rolls that Mrs. Richards will have to buy to feed all her relatives?

### NCTM Content Standards and Evidence

#### Number and Operations Standard for Grades 3-5:

Instructional programs from Pre Kindergarten through grade 12 should enable students to...

• Understand numbers, ways of representing numbers, relationships among numbers and
number systems.
• NCTM Evidence: Describe classes of numbers according to characteristics of their factors.
• Exemplars Task-Specific Evidence: This task requires students to find the least common multiple of eight and 10.
• Compute fluently and make reasonable estimate.
• NCTM Evidence: Develop fluency in adding, subtracting, multiplying and dividing whole numbers.
• Exemplars Task-Specific Evidence: This task requires students to add the number of rolls and hot dogs till they reach a target sum.

### Time/Context/Qualifiers/Tip(s) From Piloting Teacher

This is a short- to medium-length task. This is a good task to use as an assessment after lessons on common multiples.

This task can be used before or after holidays or celebrations at school.

### Common Strategies Used to Solve This Task

Many students kept a running total of the number of hot dogs and rolls and checked for their target sums.

### Possible Solutions

#### Original Version:

The Least Common Multiple of 8 and 10 is 40.

4 packages of hot dogs x 10 = 40 hot dogs
5 packages of rolls x 8 = 40 rolls
6 packages of hot dogs x 10 = 60 hot dogs
8 packages of rolls x 8 = 64 rolls

#### More Accessible Version:

The Least Common Multiple of 8 and 10 is 40.

#### More Challenging Version:

The Least Common Multiple of 8 and 10 is 40.

4 packages of hot dogs x 10 = 40 hot dogs
5 packages of rolls x 8 = 40 rolls

Other common multiples of 8 and 10 are 80, 120, etc.

8 packages of hot dogs x 10 = 80 hot dogs
10 packages of rolls x 8 = 80 rolls
12 packages of hot dogs x 10 = 120 hot dogs
15 packages of rolls x 8 = 120 rolls
6 packages of hot dogs x 10 = 60 hot dogs
8 packages of rolls x 8 = 64 rolls

General Notes: This is a good task to see if students recognize that they are working with multiples and factors.

Click on a level for student example.
Novice The Novice will not be able to successfully engage in a strategy that will give a correct number of packages of hot dogs and rolls. There will be no mathematical language and if there is a drawing or representation, it will not represent the mathematics of the task.
Apprentice The Apprentice will have a strategy that will work but may make an error in computation. They may be able to solve part of the task but not all of the task. The representation may not be labeled and there is one mathematical language term. An Apprentice may find a correct solution to all of the parts of the task but an observation or connection will not be made.
Practitioner The Practitioner will have the correct number of packages of hot dogs and rolls for each part of the solution. All the supporting work needed to communicate their strategy and mathematical reasoning will be present. At least two mathematical terms will be used and a connection or observation about the task or solution will be made. An accurate and appropriatemathematical representation will be constructed.
Expert 1 Expert 2 The Expert will achieve a correct solution. Evidence will be used to justify and support decisions made and conclusions reached, for example by solving the task in more than one way to verify the solution. A sense of audience and purpose is communicated by using precise mathematical language to consolidate mathematical thinking and to communicate ideas. Mathematical connections or observations are made and mathematical representation will be used to extend thinking and clarify or interpret the solution.

Our teacher-friendly tasks are designed to support both the Common Core and Citywide instructional expectations. GO Math! alignments are also available.
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## Here's What People Are Saying

If you walk into a Tacoma classroom during math instruction, you will see kids huddled around an Exemplars task, cooperatively selecting their problem-solving strategy. Rich conversations will follow, in which students will not only defend their solutions, but also get a chance to study alternative strategies unveiled by other groups assigned to solve that very same problem ...

Gaye Lantz

Curriculum Coordinator

Tacoma School District

Exemplars | 271 Poker Hill Road | Underhill, Vermont 05489 | ph: 800-450-4050 | fax: 802-899-4825 | infoREMOVETHISBEFORESENDING@exemplars.com