Looking to engage your students? Teaching through problem-solving and using this 3 part lesson provides an ideal opportunity for your students to develop mathematical skills, tools, and strategies. Working cooperatively through hypothetical real-world problems and sharing their ideas, further strengthens communication skills.

My students say that the mean is a fitting name for the average because it is more difficult to calculate than any other measure of central tendency. This activity provides your students with additional practice calculating the mean in a meaningful context. Your students will be invited to explore how the mean or average is affected by the addition of an extreme value (outlier). The cooperative group work is differentiated through the inclusion of 2 parallel tasks that vary in difficulty. The first task involves determining how much the mean has changed because of an added value. The second task is about determining which central tendency (mean, median, or mode) has changed the most because of the added value.

2020 ONTARIO MATH CURRICULUM EXPECTATIONS:

Grade 5:

D1.5

determine the mean and the median and identify the mode(s), if any, for various data sets involving whole numbers and decimal numbers, and explain what each of these measures indicates about the data

Grade 6:

D1.5

determine the range as a measure of spread and the measures of central tendency for various data sets, and use this information to compare two or more data sets

Grade 7:

D1.5

determine the impact of adding or removing data from a data set on a measure of central tendency, and describe how these changes alter the shape and distribution of the data

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WHAT'S INCLUDED IN YOUR FREEBIE

• Tips Sheet: This detailed guide will provide you with a breakdown of each part of the lesson. This includes how much time is allocated, what the students and teacher role is, and a list of guiding questions that the teacher could ask students in order to clarify their thinking.

• Problem Solving Checklist: An optional problem-solving checklist has been included for your students to use to self-assess their work.

• Getting Started: Your students will be led through a quick activity to activate prior knowledge or review concepts. There is also a note about how to calculate the mean that your students can use as a reference.

• Working On It: This is a rich problem-solving task in which your students can work together to solve.

• Reflect and Connect: This is a list of things the teacher needs to highlight while students present and share their solutions to the Working On It task. It includes a list of guiding questions to ask while students present. It also includes a list of problem-solving and number talk strategies that could be identified in the presenting group's work. This sheet also demonstrates how to effectively display student work in the classroom so that strategies can easily be referenced during other problem-solving opportunities.

• Exit Ticket: This problem-solving task is similar to the one students worked cooperatively on during the Working On It part of the lesson. Each student will complete one independently and apply the strategies they have learned. This work is used for assessment purposes and allows the teacher to identify common misconceptions or areas of need. It is also a great opportunity for the teacher to provide individualized descriptive feedback that is directly related to the criteria on the problem-solving checklist.

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BENEFITS

1. Increases engagement: Students are more involved in problems that are relatable and relevant.
2. Making connections: Helps students to connect concepts and skills to everyday contexts.
3. Clearly outlined learning goals: The learning goal of the lesson is posted at the top of each page.
4. Less anxiety: Provides students with the chance to process their thoughts and check their ideas with a partner or small group.
5. Builds student confidence: Before students complete an independent problem-solving task, they have the opportunity to engage in discussions, ask questions, and observe their peers model effective strategies.
6. Variety of groupings: This allows the teacher to create guided math groups based on individual needs.
7. Variety of solutions: Students develop an awareness and appreciation of multiple ways to solve problems.
8. Differentiated: Parallel tasks and multiple pathways to solving problems help reach more learners.
9. Communication skills developed: Students are engaged in deep meaningful discussions and make use of appropriate math vocabulary or terms.

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OTHER MATH PROJECTS BY BLUE SKY SCHOLASTICS:

• Measures of Central Tendency (Mean, Median, Mode, and Range) Bundle
• Comparing Mean, Median, Mode 3-Part Problem-Solving Lesson
• Median 3 Part Lesson Problem Solving Activities
• Mode and Range 3 Part Lesson & Puzzle and Riddle Worksheets
• Changing the Mean with Extreme Values
• Double Bar Graphs - Bundle - Grade 5 New Ontario Curriculum
• Building Graphing Skills
• Scatterplot Graphs Bundle- Create, Interpret, Draw Conclusions, Identify Trends
• Creating and Analyzing Scatterplot graphs 3 part Lesson
• Scatter Plot Graphs 3 Part Lesson - Read, Interpret, Draw Conclusions
• Double Bar Graphs Problem Solving Activities (Read, interpret, draw conclusions)

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