SERP has prepared 12 lessons aligned with the Common Core State Standards for sixth and seventh grade mathematics.
RATIO AND PROPORTIONAL RELATIONSHIPS
Aligned to CCSS Sixth Grade Standard 6.RP - 1 and 3
In this problem, students are given a recipe for a mixture – making chocolate milk from chocolate syrup and milk. Given that recipe, students can use ratio reasoning when applying the recipe to different quantities. In later variations, not only do the ingredients vary, so does the quantity of the final mixture. With only 2 ingredients, the lesson offers students the opportunity to both examine the ratio of the ingredients and to analyze what occurs when this ratio changes.
Aligned to CCSS Seventh Grade Standard 7.RP - 1, 2a, 2b, 2c, 2d
The tasks in this lesson give students the opportunity to work with situations that represent three types of rate problems:
THE NUMBER SYSTEM
Aligned to CCSS Sixth Grade Standard 6.NS.1
Among the many topics in the sixth grade Number System strand is one of the least intuitive topics for both students and teachers: “Interpret and compute quotients of fractions, and solve word problems involving division of fractions by fractions, e.g., by using visual fraction models and equations to represent the problem.” Most teachers can use the “invert and multiply” procedure to divide fractions, and in many mathematics textbooks, fraction division is only taught algorithmically. This lesson plan explores fraction division in depth with the goal of building an understanding of why the standard algorithm, often called “invert and multiply,” works. The concluding activity is a Poster Problem presenting applied fraction division to illustrate the “why” and “how” of dividing fractions by fractions.
Aligned to CCSS Seventh Grade Standard 7.NS - 1 a, b, c, d
Unlike other poster problems, this problem is about mastering a mathematical model, the number line model for sums, rather than using the model to solve a “real life” problem. The model will provide a context for sparking a discussion in which your students will use language and reasoning skills highlighted in the CCSSM. In the launch, you can first set the stage by asking students to consider limitations of the familiar set model for sums and differences. Then, you can introduce the number line model with a short animation. Next, the students explore the model, first by hand, and then with a dynamic number line game. Finally, in the concluding discussion, you will use the model to elicit key ideas from your students.
Aligned to CCSS Seventh Grade Standard 7.NS 2a
The Number System standards in grades 6-8 build on the grades K-5 standards related to Number and Operations in Base Ten as well as the Fractions strand from grades 3-5. In the 6-8 Number System standards, students are expected to reason about and compute with rational numbers, which include integers (positive whole numbers, 0, and negative whole numbers) as well as decimals that terminate or repeat, and fractions.
This problem leads students through a sense-making activity that helps them think through why a negative times a negative is a positive.
EXPRESSIONS AND EQUATIONS
Aligned to CCSS Sixth Grade Standard 6.EE - 1, 2a, 2c
This problem is meant to connect the familiar issue of cell phone rates to numerical expressions with variables. Students learn to attach algebraic expressions to particular real-world situations. Also, students interpret expressions explaining the rate plans of three fictional cell phone companies and recommend the best plan for certain users. A bit of misleading advertising appears in this problem for fun!
Aligned to CCSS Sixth Grade Standard 6.EE - 2, 3, 4, 9
This problem helps to bridge the gap in student thinking from a pattern or story to a generalized arithmetic expression or formula. By the end of this problem, students will generate equations showing the number of toothpicks in a pattern that grows linearly. Since there are many ways to look at this problem, students may generate equations that look different but actually result in the same values. When this happens, we say that the equations are equivalent. A key part of this problem is highlighting the fact that equivalent expressions exist and that we can simplify expressions.
Aligned to CCSS Seventh Grade Standard 7.EE - 4a
When you download movies, games, or other items with a large amount of data to your phone, the download process may take a long time to finish. But how long, exactly? This problem uses cell phone download speeds as a context for setting up and solving linear equations. The mathematical goals are to solve equations for a specific value and to represent a delayed start time meaningfully.
Aligned to CCSS Sixth Grade Standard 6.G - 1, 2, 3, 4
This problem is intended to open students' imagination and to create a discussion on important topics of the 6th-grade geometry standards: polygon area, prism volume, and nets. This lesson plan begins with a discussion of geometrical nets, and connects two dimensions representations to three-dimensional objects. This lesson also focuses upon the calculation of surface area.
Aligned to CCSS Seventh Grade Standard 7.G 2
In this poster problem, students try to build triangles based on specific criteria. These could be side lengths, or angles, or a combination of both. Students get experience constructing triangles based on “conditions,” for example, when they know some angles and side lengths. They go on to generalize, and develop understanding about when you can determine a triangle from partial information and when you cannot.
STATISTICS AND PROBABILITY
Aligned to CCSS Sixth Grade Standard 6.SP 1–5, especially 1 and 4
In this poster problem, students will demonstrate their understanding of the central idea in the Grade 6 Standards in Statistics and Probability: Statistical questions anticipate variability. When you roll five dice and add, you can’t know exactly what you will get, but you can still predict a lot about the result. Students will also get practice with underlying concepts and tools: the collection of results forms a distribution; the distribution has a center and spread; and we can display distributions usefully in graphs, especially in box plots. Students use all of these together to make decisions and explain them coherently.
Aligned to CCSS Sixth Grade Standard 7.SP 5–8
In this problem, students get experience with both theoretical and empirical probability for compound events; that is, situations where something happens more than once, and you’re trying to find the probability of a particular combination of results.
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Project funding provided by The William and Flora Hewlett Foundation and S.D. Bechtel Jr. Foundation
Poster Problems by SERP is licensed under a Creative Commons Attribution-NonCommercial-ShareAlike 4.0 International License.