Expressions and Equations

Students are expected to solve multi-step equations fluently. But do they understand the connection between expressions and equations? Or the foundation and purpose behind the order of operations? The following prompt could be used as an informal assessment to answer these questions.

Expressions and Equations

Students create a numerical expression with a specified value. Ask students to stand up, hand up, pair up to trade expressions and check for accuracy. Students replace the integer "-2" with the variable x, set the algebraic expression equal to their specified value, and solve for x. Again ask students to stand up, hand up, pair up to trade equations to check for accuracy. Ask students to Mix-N-Match to pair with someone using the same goal number. Students set their algebraic expressions equal to each other and solve for x. Note: To avoid the possibility of quadratic equations, be sure students do not place "-2" in the denominator of their numerical expression.

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

Probability

The Common Core Standards prompt students to investigate chance processes and develop, use, and evaluate probability models in Grade 7. This Pondering Probability post and Sample Assessment post give a quick overview of the content. The most commonly used probability models include a coin or dice toss, spinners, drawing marbles or cards, and the random number generator (or another random number generator). Decide Now! is my favorite app for creating spinners...we use it for deciding our after-church restaurant each week.

Decide Now! App

There are lots of options for teaching probability...organizing a series of stations that include different probability-based games would be a fun way to introduce this unit. And probability allows integration of other concepts such as integer operations, area of geometric figures, and so much more! Notice the attached resources begin with the Twister Lab Activity and continue using the same problem to work from likelihood all the way to probability models of compound events.

7.SP.C.5-8 Resources

These activities highlight Common Core State Standards 7.SP.C.5, 7.SP.C.6, 7.SP.C.7, and 7.SP.C.8 included in MATH-7 and Accelerated MATH-7.

Circumference of a Circle

Image Credit: John Reid and Arpad Horvath

Constructing Triangles

There are different levels of precision involved in creating the model of a geometric figure. Sketch implies freehand without tools. Draw produces a rough sketch with the aid of a straightedge. Construct requires the use of measurement tools such as a ruler, compass, or protractor. The main focus in Grade 7 lies with the construction of triangles and determining the number of possible triangles that can be formed given a set of three attributes. This objective investigates the possible combinations of attributes (SSS, SAS, ASA, AAS, SSA, and AAA) and determining when the conditions form a unique triangle, more than one triangle, or no triangle.

7.G.A.2 Resources

This activity set highlights Common Core State Standard 7.G.A.2 included in MATH-7 and Accelerated MATH-8.

Benchmark Grade 7

State testing is just around the corner! And all thoughts assessment can be found in the 'Tis the Season post. This Grade 7 activity set could be used with the Find Someone Who structure to conduct a general review of sample questions organized by Arkansas Frameworks strand. Each question is an adapted released item from Grade 7 Benchmark exams over the past four years. If you choose to use these in your classroom, remember to remind students to only pair with others who are not their teammates. This will allow students to return to their teams and wrap-up by using the RoundRobin structure to share solutions and discuss any questions that may arise.

Grade 7 Benchmark Resources

This structure requires students to coach each other as needed. Coach: Tip, Tip, Teach, Try again! Let me encourage you to use a coaching chart with these activities to strengthen the math vocabulary that is used during coaching. Perhaps let your students work with a classmate or two and then freeze the class to discuss a list of coaching tips. Review things they may say and things they may do while working collaboratively. For example, on the measurement coaching chart you could list "Did you measure from zero?" or "Add ALL sides to find the perimeter of a polygon." under the say column. And then list these examples under the do column: "Show pinky for an estimate of centimeter." or "Make eye contact." or "Nod your head."

You may choose to accompany each Find Someone Who activity with a coordinating sample open response question. There is a bank of prompts already on file or you could update with newer released items. Details are not included in this post because everything I know about setting kids up for success with open response questions was learned from Rhonda Kobylinski. Without a doubt, she is your resident expert.

Happy testing to YOU!

Scale Drawings

The Grade 7 standard that involves scale drawings is an application of  proportional reasoning while it also sets the stage for similarity addressed in Grade 8 (CCSS 8.G.A.4). The following lesson contains a team project that requires students to generate scale drawings of a bedroom and selected furnishings in their assigned floor plan. Students collaborate as a team to determine an appropriate scale that can be easily used by all members and produce drawings appropriate for display on their team poster. And they have tons of creative fun in the midst of the critical thinking required for task completion. Resources are included for scaffolding as needed.

7.G.A.1 Resources

This activity set highlights Common Core State Standard 7.G.A.1 included in MATH-7.

Cross Sections

When introducing cross sections, it may be difficult for students to visualize the polygon that is formed by slicing a solid. Consider this interactive investigation for slicing a cube as a launch for the concept of cross sections from Annenburg Learner.

Source: Learner.org 

Then allow students to investigate cross sections of multiple solids through a Play-Doh Cross Sections Lab Activity. Materials needed include play-doh, paper plates, dental floss, plastic knife, and ruler. In teams of four, each student constructs two of the solids listed on the record sheet. When the team finishes building models with the specified cross sections, use the All Write RoundRobin structure to share discoveries and complete the record sheet. Follow-up with the to check for understanding.

7.G.A.3 Resources

This activity set highlights Common Core State Standard 7.G.A.3 included in MATH-7.

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?