Class Instructional Sequence

We will have a "two-book" organization for our class this year. This will mean that I will be teaching two separate lessons from two different texts each day.

Instruction follows a 5E lesson plan format: Engagement, Exploration, Explanation, Extension, and Evaluation. Lessons begin with an Engagement activity. This could be a prerequisite skill for a daily lesson, vocabulary review, or review of previously learned content to keep our skills sharp. The whole class will complete the Engagement as one group.

Then we move into Exploration. I will lead an activity that introduces the day's concept. Students will will be expected to explain their strategies and thinking as they worked to solve problems. Students will then complete a Quick Evaluation to determine extra help needs for the independent practice part of the Extension. The class will be assigned Extension activities based on their level of understanding. Finally, students will complete an Evaluation, and homework will be assigned.

Blocks shaded in green are times when students will be working with the teacher, and unshaded blocks represent independent or partner/group work times.

Centers

To allow students to work on developing their Math skills and practice previously learned materials, there are Math Centers for students to use: Computation, Algebra, Geometry, Thinking Skills, Parts of a Whole, and Problem Solving. Students are assigned to activities and track progress on a monitoring chart.

Newsletter

To keep parents informed about the math that we are studying, each unit will begin with a Unit Newsletter. It will explain the content we will cover in our unit of study, examples of the skills, applications, and suggestions for ways that students can practice. An electronic copy of the newsletters will be available on the Newsletter link at the top of the page.

Grading

Students' grades are based on three components: Classwork, Tests & Quizzes, and Basic Facts, Skills Maintenance, & Homework.

Not all classwork will be graded, although all work will be reviewed for accuracy and completeness. Each unit has a unit test, also called a Summative Assessment or Short Cycle Assessment.

Tests

The tests include selected response items (SR, more commonly known as multiple choice) and constructed response (CR, BCR, ECR) items. The selected response items will be scored by a scanning machine, and I will score the constructed response items according to a scoring key. Six of our assessments are 'secured' documents, so you will receive the summary document created for parents, but the actual tests cannot leave the classroom. To view your child's paper, please let me know when you wish to come for a visit.

BCRs and ECRs

(Translation: Brief Constructed Responses and Extended Constructed Responses)

The constructed response items have two parts. In Part A, students answer the problem that is posed. Space is provided for students to work the problem. This 'figuring' should be left on the paper...please help me to break the students of a bad habit among many of them: They should NOT erase this figuring; it can be counted for points toward the explanation, Part B.

In Part B the students write a brief explanation of the solution, including the steps to arrive at the solution and the math content that is used in the solution. Part B may ask students to explain how they determined their answer or why their answer is correct. BCRs that ask how may be explained in paragraph form or by providing a sequence of steps in the solution of the problem. BCRs that ask why may be explained in the same way, but the response must include a justification based on mathematical principles and connections. Both types of questions must close with a summary statement that includes the final answer.

A BCR is worth a total of 3 points: 1 point for a correct answer in Part A and 2 points for Part B. An ECR is worth a total of 4 points: 1 point for a correct answer to Part A and 3 points for the explanation in Part B. ECRs differ from BCRs in Part B; there will be an additional task required of students and students will recognize this from the format. The Part B task description will contain two bulleted items to address. The following shows a BCR and then two versions of an ECR based on the same problem.

BCR

Part A

Find the average for this set of quiz scores: 100, 90, 85, 95, 90

92

100 + 90 + 85 + 95 + 90 = 460

460 ÷ 5 = 92

Part B

Explain how you determined your answer.

Use what you know about finding averages in your response.

Use words, numbers, and/or symbols in your explanation.

Add the scores: 100 + 90 + 85 + 95 + 90 = 460

Divide by 5 to distribute: 460 ÷ 5 = 92

So, the average score is 92.

This example shows that the student understands how to find an average. It is demonstrated by the application of an appropriate strategy and operations, resulting in a correct answer.

ECRs

Extension to Constructed Response, Example 1

Part A

Find the average for this set of quiz scores: 100, 90, 85, 95, 90

92

100 + 90 + 85 + 95 + 90 = 460

460 ÷ 5 = 92

Part B

• Two more quizzes are taken. The scores are 80 and 90. Explain how the average might change.
• Explain how you determined your answer. Use what you know about finding averages in your response. Use words, numbers, and/or symbols in your explanation.

To find an average, the total of all scores should be divided equally among the total number of quizzes. The total is the sum of the quizzes and division is used to divide the total among the quizzes:

• Add the scores: 100 + 90 + 85 + 95 + 90 = 460
• Divide by 5 to distribute: 460 ÷ 5 = 92
• So, the average score is 92.

To find out whether the average will change, the average needs to be determined with all seven scores:

• Add the scores: 100 + 90 + 85 + 95 + 90 + 80 + 90 = 630 or 460 + 170 = 630
• 630 ÷ 7 = 90

So, the average will go down to 90 over the seven quizzes. I also know the average will be lower because each of the scores being added are less than the mean of the original set, so the new average would have to be lower.

Extended Constructed Response, Example 2

The examples differ in the tasks the students were directed to complete in Part B and whether the students needed to explain how or why in their response. Remember that why items require a demonstration of understanding of underlying math principles and connections.

Both BCR and ECR responses should be guided by the second statement in Part B that reads: 'Use what you know about ... in your response.' That statement is a clue to students about the math concepts that should be addressed in the response.

BCR Scoring

A rubric at http://www.mdk12.org/mspp/k_8/mathscoring_bcr.html shows more detail about the scoring explanations for a BCR (Brief Constructed Response) and the ECR (Extended Constructed Response and Extension to Constructed Response) is explained at http://www.mdk12.org/mspp/k_8/mathscoring_ecr.html . This is my abbreviated version of the scoring keys. When you look at a scored BCR or ECR, please keep in mind that the response is scored for the demonstrated understanding of the math. The student's intent or skills observed in class have no bearing on the score.