Benchmark Lessons
Key components of PBI are lessons known as benchmark lessons. Benchmark lessons are student-centered lessons designed to engage students and to encourage 'minds on' activities. They can be used to introduce a topic or to review a topic previously discussed, but they primarily cover topics that cannot be otherwise taught through an investigation. Concepts, principles and skills covered in a benchmark lesson are often thought of as what the students 'need to know'. Benchmark lessons can utilize various educational strategies. For example, the 5-E learning cycle, argumentative activities, student-led handouts, and placemat activities are just some of the techniques implemented in this unit to engage students, which are found below.
Benchmark Lesson 1 -Sweet Algebra
This lesson has been taken from a lesson designed by the Public Schools of North Carolina. It has been adapted so that it is an interactive and argumentative activity, which is relevant and student-centered. During the lesson, students should be placed in groups of 3 or 4 to stimulate argumentation and discussion. The teacher should monitor and encourage student thinking through the use of probing and eliciting questions, some of which are suggested in the attached lesson plan. Through the activity the students must write mathematical expressions based on given clues to help them solve for the number of candies in a brown paper bag, x, belonging to the teacher.
Students Will be Able To:
Standards Addressed:
Students Will be Able To:
- Translate words into algebraic expressions.
- Write and solve an equation to model a situation.
- Use the arithmetic from a problem to generalize an algebraic solution.
- Solve multi-step equations.
Standards Addressed:
- CCSS.Math.Content.7.EE.B.4 Use variables to represent quantities in a real-world or mathematical problem, and construct simple equations and inequalities to solve problems by reasoning about the quantities.
- CCSS.Math.Content.7.EE.B.4a Solve word problems leading to equations of the form px + q= r and p(x + q) = r, where p, q, and r are specific rational numbers. Solve equations of these forms fluently. Compare an algebraic solution to an arithmetic solution, identifying the sequence of the operations used in each approach. For example, the perimeter of a rectangle is 54 cm. Its length is 6 cm. What is its width?
Sweet Algebra (Teacher Materials) | |
File Size: | 373 kb |
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Sweet Algebra (Student Handout) | |
File Size: | 246 kb |
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As mentioned above, this lesson was taken from a collection of lessons developed by the Public Schools of North Carolina specifically geared toward meeting the 7th Grade Common Core Standards for Mathematics. To see the original lesson, follow the link below and refer to pages 22-27 .
Benchmark Lesson 2 - Snack Attack!
Benchmark lesson five should be implemented as a 5-E Lesson and contain the five key aspects of a 5-E lesson; Engagement, Exploration, Explanation, Elaboration, and Evaluation. To engage the students, the teacher should bring in a box of Oatmeal Creme Pies and ask the students questions pertaining to how large they think the box is and how many different ways they think the box can be stacked. The students then should be divided into groups in order to solve a real-world area, volume, and surface area problem provided on the handout below. After the students complete the exploration, the teacher should lead a discussion to summarize what the students found and highlight the key words and methods used. Following the explanation, the teacher should have the students complete a journal entry in which they answer the questions: What did you learn about ares, surface area, and volume today? What do you want to be better at, regarding these concepts? What is another instance in the real-world where you would have to calculate area, surface area, and/or volume? For this lesson, the elaboration and evaluation are combined through the completion of the journal entry.
Students Will be Able To:
Standards Addressed:
Students Will be Able To:
- Solve real-world area, surface area, and volume problems.
- Demonstrate fluency in calculating area, surface area, and volume.
- Use appropriate tools strategically.
Standards Addressed:
- CCSS.Math.Content.7.G.B.6 Solve real-world and mathematical problems involving area, volume and surface area of two- and three-dimensional objects composed of triangles, quadrilaterals, polygons, cubes, and right prisms.
Snack Attack! (Student Handout) | |
File Size: | 93 kb |
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Benchmark Lesson 3 - Finding Equivalent Ratios
This lesson is designed based on a 5-E Lesson design. It includes an Engagement, Exploration, Explanation, Elaboration, and Evaluation. Individual, small group, and whole group interactions engage the students and encourage collaboration. Furthermore, in this lesson the students will watch an engaging video regarding how animal-caretakers at the zoo determine the amount of food that is given to each animal. For this reason it is important that the teacher have access to the internet or that the teacher download the video prior to instruction. The handout for the Exploration and the quiz for the Evaluation can be found at the end of the 5-E Lesson Plan. Finally, the Elaboration is an interactive Jeopardy PowerPoint, which can be found below.
Students Will be Able To:
Students Will be Able To:
- Calculate equivalent ratios using a common factor to scale a given ratio up or down.
- Use unit rates effectively to make unit conversions.
Finding Equivalent Ratios (5-E Lesson Plan) | |
File Size: | 544 kb |
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Finding Equivalent Ratios (PowerPoint) | |
File Size: | 305 kb |
File Type: | pptx |
Benchmark Lesson 4 - Real-World Proportions
This lesson is designed to engage students through the use of multiple place mat activities. The handout below should be distributed to the students or put up on a SMART Board. It consists of four different, real-world proportion problems. The teacher should give the students the opportunity to work through the problems in groups of 3 or 4 students. Each group should be given one whiteboard. On the whiteboard, the students should respond to the questions using the place mat method. Then, as a group, they will compare and discuss their answers to those of their peers. They will choose their group response and write it in the center of the whiteboard. Each student should be able to explain the reasoning behind their group’s final response. After the students go through the problems, they will be given the opportunity to create their own proportion problems for their peers to solve.
Students Will be Able To:
Standards Addressed:
Students Will be Able To:
- Demonstrate understanding of proportional relationships by calculating interest rates, fees, and percent increase and decrease.
- Add, subtract, multiply, and divide with fluency and accuracy when calculating values.
Standards Addressed:
- CCSS.Math.Content.7.RP.A.3 Use proportional relationships to solve multistep ratio and percent problems. Examples: simple interest, tax, markups and markdowns, gratuities and commissions, fees, percent increase and decrease, percent error.
- CCSS.Math.Content.7.NS.A.3 Solve real-world and mathematical problems involving the four operations with rational numbers.
- CCSS.Math.Content.7.EE.B.3 Solve multi-step real-life and mathematical problems posed with positive and negative rational numbers in any form (whole numbers, fractions, and decimals), using tools strategically. Apply properties of operations to calculate with numbers in any form; convert between forms as appropriate; and assess the reasonableness of answers using mental computation and estimation strategies. For example: If a woman making $25 an hour gets a 10% raise, she will make an additional 1/10 of her salary an hour, or $2.50, for a new salary of $27.50. If you want to place a towel bar 9 3/4 inches long in the center of a door that is 27 1/2 inches wide, you will need to place the bar about 9 inches from each edge; this estimate can be used as a check on the exact computation.
Real World Proportions (Teacher Handout) | |
File Size: | 163 kb |
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Real World Proportions (Student Handout) | |
File Size: | 119 kb |
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Benchmark Lesson 5 - Sailing and Scaling
In this lesson, the students are engaged in an activity in which they design and draw their own sail boat on a larger scale and later transfer that design to a smaller scale. Following this activity, the students respond to conceptually rich questions which stimulate student cognition. Like in the above lessons, the teacher should walk around and monitor student understanding and engagement through the use of probing and eliciting questions. The teacher can choose to put the students into pairs for this last portion, or allow them to work individually, but eventually the students should be paired up to explain and defend their reasoning with their peers.
The questions asked of the students are essential to all lessons. These questions can either stimulate student inquiry or instigate rote, systematic responses. In this lesson, the teacher should monitor the students' activities and ask probing and eliciting questions as the students work through the problems to encourage higher order thinking and metacognition.
Students Will be Able to:
Standards Addressed:
The questions asked of the students are essential to all lessons. These questions can either stimulate student inquiry or instigate rote, systematic responses. In this lesson, the teacher should monitor the students' activities and ask probing and eliciting questions as the students work through the problems to encourage higher order thinking and metacognition.
Students Will be Able to:
- Calculate the dimensions of a geometric shapes using scaling.
- Reproduce a drawing using scaling.
- Draw geometric shapes given certain conditions.
Standards Addressed:
- CCSS.Math.Content.7.G.A.1 Solve problems involving scale drawings of geometric figures, including computing actual lengths and areas from a scale drawing and reproducing a scale drawing at a different scale.
- CCSS.Math.Content.7.G.A.2 Draw (freehand, with ruler and protractor, and with technology) geometric shapes with given conditions. Focus on constructing triangles from three measures of angles or sides, noticing when the conditions determine a unique triangle, more than one triangle, or no triangle.
Sailing & Scaling (Student Handout) | |
File Size: | 189 kb |
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