Students will measure the circumference and diameter of round things in the classroom and discover the ratio pi. They will see that the ratio of a circle's circumference to its diameter can be used to solve for the circumference when the diameter is known.Key ConceptsStudents have seen circles before, but have not analyzed the relationships between parts of a circle. The ratio of the circumference to the diameter is pi, about 3.14 or about 227. Students see that all of the objects they measure have this ratio (or close, depending on accuracy) and that the ratio is true for all circles. Students also see that the ratio can be used to solve for the circumference of a circle if the diameter (or radius) is known.GoalsMeasure round things looking for similarities.Find the ratio of the circumference to the diameter of those round things.Find a formula to find the circumference of a circle.SWD: Make sure students understand these domain-specific terms:It may be helpful to preteach these terms to students with special needs. If possible, reinforce the definitions of these terms with visual supports (diagrams).ELL: As new vocabulary is introduced, be sure to repeat it several times and to allow students to repeat after you as needed. Write the new words as they are introduced and allow enough time for ELLs to check their dictionaries or briefly consult with another student who shares the same primary language if they wish.ratiocircumferencecirclediameterscatter plot

Students will continue to explore surface area, looking at more complex solids made up of cubes. Students will look at the 2-D views of these solids to see all of the surfaces and to find a shorter method to calculate the surface area.Key ConceptsThe 2-D views of 3-D figures (front top and side) show all of the surfaces of the figure (the area of the three views is doubled or the back, bottom, and other side) and so can be used to calculate surface area. The only exception is when surfaces are hidden or blocked and must be accounted for.GoalsExplore the relationship between 2-D views of figures and their surface area.Find the surface area of different solids.

Students find the area of regular polygons, recalling what they already know about the area of geometric shapes and generalizing a formula for any regular polygon.Key ConceptsStudents will recall what they already know about the area of geometric shapes and apply that to find the area of regular polygons. Any regular polygon can be divided into congruent isosceles triangles. If the length from the center to the midpoint of a side (the apothem) is known, the area of the triangles and the area of the polygon can be found. Students will see the similarities between the area of a polygon and derive the formula for the area of a circle.GoalsReview area of triangles, rectangles, and parallelograms.Find the area of regular polygons.Generalize an area formula for any regular polygon.ELL: This lesson offers students a rich opportunity to learn academic vocabulary. Display the new terms in writing somewhere visible in the classroom so that you can refer to them. Allow ELLs to use their bilingual dictionaries to help with understanding the terms. When possible, have ELLs discuss the terms in their language of choice with other ELLs who share the same primary language.

Lesson OverviewStudent groups make their presentations, provide feedback on other students’ presentations, and get evaluated on their listening skills.Key ConceptsIn this culminating event, students present their project plan and solution to the class. The presentation allows students to explain their problem-solving plan, communicate their reasoning, and construct a viable argument about a mathematical problem.Students also listen to other project presentations and provide feedback to the presenters. Listeners have the opportunity to critique the mathematical reasoning of others.GoalsPresent project to the class.Give feedback on other project presentations.Exhibit good listening skills.Reflect on the problem-solving process.

Students will explore scale and use it to find measurements in scale drawings.Key ConceptsScale drawings are drawn proportionally so that there is a ratio between a given length on the drawing and the actual length. This ratio is used to set up a proportion to find other measurements.GoalsUnderstand that scale drawings are proportional.Use scale to find actual measurements.ELL: Define these terms in the context of the discussion:scalescale drawingscaled to fitproportionalAllow ELLs to use the dictionary if they wish.

Students will critique their work from the Self Check in the previous lesson and redo the task after receiving feedback. Students will then take a quiz to review the goals of the unit.Key ConceptsStudents understand how to find the surface area (using nets) and volume of rectangular prisms. They have extended that knowledge to all right prisms and were able to generalize rules for both measurements. Students also found the surface area (and volume) of figures made up of cubes by looking at the 2-D views.GoalsCritique and revise student work.Apply skills learned in the unit.Understand 3-D measurements:Surface area and volume of right prismsArea and circumference of circlesSurface area and volume of figures composed of cubesSWD: Consider the prerequisite skills for this Putting it Together lesson. Students with disabilities may need direct instruction and/or guided practice with the skills needed to complete the tasks in this lesson. It may be helpful to pull individual students or a small group for direct instruction or guided practice with the skills they have learned thus far in this unit. While students have had multiple exposures to the domain-specific terms, students with disabilities will benefit from repetition and review of these terms. As students move through the lesson, check to ensure they understand the meaning of included domain-specific vocabulary. Use every opportunity to review and reinforce the meaning of domain-specific terms to promote comprehension and recall.

Students critique their work from the Self Check and redo the task after receiving feedback. Students then take a quiz to review the goals of the unit.Key ConceptsStudents understand how to find the area of figures such as rectangles and triangles. They have applied that knowledge to finding the area of composite figures and regular polygons. The area of regular polygons was extended to understand the area of a circle. Students also applied ratio and proportion to interpret scale drawings and redraw them at a different scale.GoalsCritique and revise student work.Apply skills learned in the unit.Understand two-dimensional measurements:Area of composite figures, including regular polygons.Area and circumference of circles.Interpret scale drawings and redraw them at a different scale.SWD: Make sure all students have the prerequisite skills for the activities in this lesson.Students should understand these domain-specific terms:composite figuresregular polygonsareacircumferencescale drawingstwo dimensionalIt may be helpful to preteach these terms to students with disabilities.ELL: As academic vocabulary is reviewed, be sure to repeat it and allow students to repeat after you as needed. Consider writing the words as they are being reviewed. Allow enough time for ELLs to check their dictionaries if they wish.

Students will extend their knowledge of surface area and nets of rectangular prisms to generalize a formula for the surface area of any prism.Key ConceptsStudents know how to find the surface area of a rectangular prism using a net and adding the areas for pairs of congruent faces. Students have not seen that the lateral surface forms one long rectangle whose length is the perimeter of the base and whose width is the height of the prism.Using this idea, the surface area of any right prism can be found using the formula:SA = 2B + (perimeter of the base)hGoalsFind a general formula for surface area of prisms.Find the surface area of different prisms.SWD: Generalization of skills can be particularly challenging for some students with disabilities. Students may need direct instruction on the connection between what they already understand and a general formula.Some students with disabilities may have difficulty recalling formulas when it comes time to apply them. Once students discover the formula SA = 2B + (perimeter of the base)h, consider posting the formula in the classroom and encouraging students to add the formula(s) to the resources they have available when completing classwork and homework.

Students will join the buildings together to form a city with streets and sidewalks running between the buildings. Student groups will make their presentations, provide feedback to other students’ presentations, and get evaluated on their listening skills.Key ConceptsIn this culminating event, students  present their project plan and solution to the class. The presentation allows students to explain their problem-solving plan, communicate their reasoning, and construct a viable argument about a mathematical problem.Students also listen to other project presentations and provide feedback to the presenters. Listeners have the opportunity to critique the mathematical reasoning of others.GoalsPresent projects and demonstrate understanding of the unit concepts.Clarify any misconceptions or difficult areas from the Final Assessment.Give feedback on other project presentations.Exhibit good listening skills.Review the concepts from the unit.

Lesson OverviewStudents will work on the final portion of their project which includes creating the nets for the sides, making a slice in one of their buildings, and putting their buildings together. Once their two model buildings are complete, they will find the surface area and volume for their models and the full-size buildings their models represent.Key ConceptsThe second part of the project is essentially a review of the second half of the unit, while still using scale drawings. Students will find the surface area of a prism as well as the surface area of a truncated prism. The second prism will require estimating and problem solving to figure out the net and find the surface area. Students will also be drawing the figure using scale to find actual surface area.GoalsRedraw a scale drawing at a different scale.Find measurements using a scale drawing.Find the surface area of a prism.SWD: Students with disabilities may have a more challenging time identifying areas of improvement to target in their projects. It may be helpful to model explicitly for students (using an example project or student sample) how to review a project using the rubric to assess and plan for revisions based on that assessment.Students with fine motor difficulties may require grid paper with a larger scale. Whenever motor tasks are required, consider adaptive tools or supplementary materials that may benefit students with disabilities.Students with disabilities may struggle to recall prerequisite skills as they move through the project. It may be necessary to check in with students to review and reinforce estimation skills.

Students will begin to think about probability by considering how likely it is that their house will be struck by lightning. They will consider the relative likelihood of familiar events (e.g., outdoor temperature, test scores) on the continuum between impossible and certain. Students will discuss where on the continuum "likely," "unlikely," and "equally likely as unlikely" areGoals and Learning ObjectivesThink about the concept of likelihood.Understand that probability is a measure of likelihood.Informally estimate the likelihood of certain events.Begin to think about why one event is more likely than another.SWD: Students with disabilities may need additional support seeing the relationships among problems and strategies. Throughout this unit, keep anchor charts available and visible to assist them in making connections and working toward mastery. Provide explicit think alouds comparing strategies and making connections. In addition, ask probing questions to get students to articulate how a peer solved the problem or how one strategy or visual representation is connected or related to another.