Reasonable Solutions

Students often get so excited to finish solving a problem that they fail to consider the reasonableness of their solution. How can students be trained to reflect BEFORE jumping into the solving process? One possibility is requiring students to define variables in writing and make note of any restrictions.

• Can the solution be negative?
• Positive?
• Zero?
• Fraction?

Reasonable Solutions Discussion Activity

Use the Takeoff-Touchdown activity to add movement to a whole class discussion on reasonable solutions. Prompt discussion by asking students to explain their reasoning to their shoulder partner. Pose a follow-up question to RoundRobin in their teams. And then consider using a problem set strictly for the purpose of defining variables and making note of potential restrictions...no solving!

This discussion activity highlights Common Core State Standard 7.EE.B.3 included in MATH-7.

Properties of Inequalities

The battle of process teaching vs. concept teaching rages on...especially when a school has used several snow days and feels the pressure of cutting corners to cover essential content by mandated deadlines. Unfortunately, that's exactly the result that should be expected when corners are cut...COVERAGE...as opposed to building conceptual understanding that will act as a foundation for future learning. There are no magical answers when it comes to rearranging best laid plans, but concept teaching is always better for the long-term benefit of the student.

Properties of Inequalities Concept Builder

This "Properties of Inequalities" discovery activity serves as an excellent example of when it would be easier and quicker to teach process rather than develop conceptual understanding. This activity requires a record sheet and integer dice. Students generate original inequalities and perform a variety of operations to create transformed inequalities. Students analyze the results as to whether the transformed inequality has a same or different inequality symbol. Next students prepare short summaries on Post-It notes to sort as a whole class and generalize conclusions based on the results in each category.Try this one. Leave a comment to provide feedback...the good, the bad, and the ugly!

This activity highlights Common Core State Standard 7.EE.B.4b included in MATH-7.

The Distributive Property

How do you teach the distributive property? When planning lessons, be sure you are maintaining perspective. Ask: What have your students already experienced with the content? This is particularly critical when students have gaps and require support to bridge that gap. You will need to have the perspective of how the related content has developed over the years/courses so that you can replicate that progression for struggling students via individualized learning. Ask: What leaps will your students make in upcoming courses that stem from what you do with the content now? It is important to identify future learning so that you can ensure adequate depth in your course. Let's review the progression of the distributive property...

3.OA.B.5

In Grade 3, students use the distributive property as a strategy for multiplying. This is the concept builder for the distributive property. If students were unsuccessful when working strictly with numbers, then their efforts in applications with variables will be a stretch at best. Or worse yet...what if students memorized multiplication facts and never made sense of the concept through the distributive property?!?

6.EE.B.5

In Grade 6, students use the distributive property to produce equivalent expressions. Notice the example includes using the distributive property to toggle between factored form (the result from division) and expanded form (the result from multiplication).

7.EE.A.1

In Grade 7, students continue with the same concepts learned in Grade 6 with an extension to using rational numbers. Should 7th graders be solving equations that require using the distributive property? Continue reading.

8.EE.C.7b

In Grade 8 (and Accelerated MATH-7), students will use the distributive property to solve linear equations with rational coefficients. Notice the standard says "whose solutions REQUIRE expanding expressions using the distributive property..." in order to solve the linear equation.

Differentiate the necessity of the distributive property.

Perhaps MATH-7 students should be asked to solve equations that are similar to the equation in the left column above; however, this begs the question "How do we hope students solve that type of equation?". We also hope MATH-8 students recognize the need for the distributive property before they start the process of solving equations that are similar to the equation in the right column above.

This discussion highlights the Common Core State Standards 7.EE.A.1 and 8.EE.C.7b included in MATH-7, MATH-8 and Accelerated MATH-7.

Building Vocabulary

I remember my days of teaching trigonometry with fond memories. The students always carried a perspective that refreshed my soul. One day in the depths of summarizing characteristics of trig functions a discussion about vocabulary erupted. A student claimed he should receive a foreign language credit for math because it was a whole new language!

Aligned to CCSS for Grade 7

Vocabulary is essential to deep understanding of math concepts and the ability to communicate that understanding. Math teachers integrate the teaching of vocabulary throughout their lessons. In a recent Genius Hour, we reflected on that integration and discussed methods that would support strategic efforts. From word walls to Frayer models to graphic organizers to activities via Kagan structures to fun games...we investigated 12 strategies that align with the research described on this Vocabulary Development post. We used a recent unit on Percent (7.RP.A.3) to model the strategies and an Excel spreadsheet that included vocabulary from the MATH-7 course as a possible starting point.

Which strategy would most improve vocabulary development in your classroom? How would you like to organize your efforts?