From Start to End – Maximizing Instructional Time in the Intermediate Classroom

We are well into our school year and have now created a mathematical environment in our classroom.  When we walk in, we see walls covered with interesting puzzles, book shelves full of math story books, games available to sign out on weekends, and math tools in bins readily available when needed.  When we walk in, we hear pairs or triads discussing math problems, questions being asked and students articulating their mathematical thinking.

Now that we’ve created this environment, how do we use our math time to ensure we are utilizing this instructional time effectively?

TIMSSA video study from the TIMSS report had given some insight as to how time was spent within a mathematics class in the US, Japan and Germany (Fig 2).  Japanese lessons demonstrated a more active learning environment where students worked on problems, struggled with the problems and then articulated their thinking by sharing different representations of the solution.  Lessons from the US and Germany were more teacher-led by providing instructional steps, examples and opportunities to do seat work that were similar to the questions done in class.  So how do we structure our class to incorporate a more student-centered lesson?

Here in Ontario, many are familiar with the 3-Part lesson format.  TIPS4RM refers to the parts as:

  • Part 1 – Minds On
  • Part 2 – Action!
  • Part 3 – Consolidate Debrief

Part 1:  Minds On  “Activating Prior Knowledge”  ~ 5–10 min

The Minds On is the hook to activate prior knowledge that is needed for the task they will be doing in Part 2.  A math string is an example of a Minds On task.  For example, a question might be:


Given the following math string, how would you visualize these mathematical sentences?

CookieCrazeA Minds On can also be in a form of a problem.  In this problem, students were given the Cookie Craze problem.  Clickers were used to respond to the problem.  Discussions followed about how the mathematics was generally represented but further discussed later in Part 3: Consolidate Debrief.

Part 2:  Action!  “The Investigation” ~ 15-20 minutes

MangoesThe Action! is when students explore and investigate a new concept.  Students can work in pairs or triads to solve a problem.  Same-ability groupings allow every student to have a voice and be actively engaged in the process.  Often when students are partnered with another student of a different level, the stronger more assertive student tends to do the work.

ManipsA variety of manipulatives such as fraction rings and circles, are provided so students can choose tools that are appropriate to their learning style.  Chart paper and markers are used to record their thinking when solving the problem.

Part 3:  Consolidate Debrief  “Summarizing the Learning” ~ 20-30 minutes

soln1The purpose of the Consolidate Debrief is to connect the mathematical concepts to the actions they did in Part 2.  Students summarize their learning by sharing their strategies, comparing and contrasting solutions, identifying common misconceptions and raising other math questions that came out of the lesson.  This consolidation can be done through a math congress where students present and justify their work to their peers.


Questioning is a large and important part of the Consolidate Debrief.  In Classroom Instruction that Works: Research-Based Strategies for Increasing Student Achievement (ASCD, Alexandria, VA), Robert Marzano describes instructional strategies that are significant factors that increase student learning.    The following chart connects some of these strategies to actions that are done during the math congress.

Instructional Strategies During the congress…
Identifying similarities/differences Ask “What is similar about these solutions?  What is different?”
Summarizing Ask, “Can someone describe what you think this group did to solve the problem?” and “What did you do when you got stuck?”
Nonlinguistic representations Ask “How does the concrete representation connect to the algebraic expression?”
Cooperative Learning During the task, students work in same-ability pairs/triads to actively involve all learners.  These groups present together to justify their solutions.
Providing Feedback Teachers facilitate discussions providing feedback and encouraging students to also provide feedback to solutions they see.

Now that we have a structure for our lesson, how can we support each other in our schools to have consistency among all our classes? 

Administrator support is key to making this happen. Scheduled time is needed during the day for teachers to plan together and teach together.  Here are some suggestions that can help make this happen:

  • Pairs of teachers co-teach together.  This is inquiry based, reflective and collaborative. Teachers take on the role of lead co-teachers and teach one of their classes together or bring their classes together to teach the lesson. Co-teachers have “live-time” professional discussions about what they are observing, doing and make collaborative decisions to best meet the needs of the students. The teachers are learning from each other as their students are learning from them.
  • Collaborative Planning.  Teachers of a grade, division or subject meet and plan lessons that include trying out the task/activity/problem and anticipate what student responses might be. The group could consider a focus for their professional learning such as “questioning” or time on task for each portion of the 3 part lesson. The focus is on planning and instruction and moves the community of teachers in a school along their continuum of learning.
  • Professional Learning Communities. This professional learning community can take place right in the classroom.  Teachers could have colleagues (teachers, administrators, consultants, coaches) come to co-teach with them.  Other teachers can observe this co-teaching session  and still be involved in the debrief and planning for the next lesson.  The co-teaching model should be ongoing whether it be once or twice a week or once a month.  It’s a great model for students to learn from.

Happy planning!


  1. Fosnot, Catherine. Context for Learning: Investigating Fractions, Decimals and Percents. Portsmouth, NH:  Heinemann, 2007.
  2. Krulik, Stephen, Jesse A Runick.  Roads to Reasoning 8, Chicago, IL:  Wright Group/McGraw-Hill, 2002.
  3. Martinez, J., “Exploring, Inventing, and Discovering Mathematics:  A Pedagogical Response to the TIMSS”, Mathematics Teaching in the Middle School,  Vol 7, No. 2, (October 2001), pp 114 – 119.
  4. Marzano, R., Debra Pickering and Jane Pollock.  Classroom Instruction that Works:  Research-based Strategies for Increasing Student Achievement . Alexandria, VA: ASCD, 2001
  5. National Council of Teachers of  Mathematics  – Illuminations

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