MBC Numeracy Pod


Our Numeracy Pod Goals

Goal 1: To build a supportive learning network within and across schools in MBC

Goal 2: To build teacher efficacy and understanding of an effective consolidation in mathematics using the 3-part lesson framework

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As part of our MBC Numeracy POD, the Primary teachers and Elementary Administrators engaged in a 2-day Lesson Study Experience. This experience allowed participants to dig deeper into lesson planning in an effort to develop a better understanding of the content in mathematics, the 5 practices and the flexibility behind the pedagogy of the 3-part lesson structure.

Why Lesson Study?

Lesson Study Goals

OVERALL: To collaboratively plan a math lesson using a 3-part structure and the 5 Practices being explored in our Numeracy Pod

Day 1:

  • To develop a good understanding of the mathematics content in order to plan a detailed lesson

  • To use the 5 practices to plan an detailed 3-part lesson

  • To determine the key components of a successful math lesson

Day 2:

  • To teach and observe the co-created lesson

  • To plan an effective consolidation within a 3-part lesson in math

  • To examine student learning in a math lesson

  • To determine the components of an effective math lesson


Grade 3 - Operational Sense

Overall Expectations #3:

Solve problems involving the addition and subtraction of single- and multi-digit whole

numbers, using a variety of strategies, and demonstrate an understanding of multiplication

and division.

Decomposing the Curriculum Expectation

Using the KNOW/DO strategy, we looked at what the students were expected to KNOW and what they were expected to DO with addition and subtraction in grade 3. We looked at what was explicitly stated, and also what was implicit. This gave use an idea of what we needed to focus on for our learning and lesson.
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Resources Used in Our Lesson Study

Using Addition and Subtraction in a Problem Solving Context

On page 9 and 10 in the Guides to Effective Instruction K-6 (Volume 5), is a list of the different types of addition and subtraction problems that can be used in the elementary grades.
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Summarizing the Computational Strategies for Addition and Subtraction

Using the information from the Guides to Effective Instruction and Math Curriculum document. Participants in the lesson study created anchor charts for the group to develop a common understanding of the computational strategies used in Primary.

The Importance of Exposing Students to a Variety of Strategies

On pg. 38 of the Guide to Effective Instruction K-6 (Volume 5), explains why students need to have access to a variety of strategies when adding multi-digit numbers.
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Using Relational Rods (Cuisinaire Rods) To Explore Addition Strategies

Try using the relational rods to explore number properties as well as various addition strategies. Watch the video below for ideas:
Teaching Addition with Cuisenaire Rods


STEP 1: What is the Learning Goal?

Using the KNOW/DO list and the host teacher's input, we determined our focus for the lesson. Students in the grade 3 class were exposed many addition strategies already and so we now wanted them to learn to select appropriate strategies when solving addition problems.

Student Learning Goals for the Lesson:

  1. We are learning to use a variety of strategies when adding
  2. We are learning to justify why we use a strategy when adding

STEP 2: What is the Problem Solving Task?

Because Valentine's day was approaching, the group decided that we should use a real-life problem that the students could related to using the theme of Valentine's day. The school had "heart cookies" available for students to purchase for Valentine's day. We decided to create a "joining problem" using 3-digit numbers that involved the purchase of the Valentine's cookies.
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The Problem

The Valentine’s Day heart cookies have been ordered. The Youth Faith Ambassadors had to order A LOT of cookies!!!!

  • The primary division ordered 333 cookies

  • The junior division ordered 239 cookies

  • The intermediate division ordered 67 cookies

How many heart cookies had to be ordered for the school?

Modified Problem (for students on a modified program):

The Valentine’s Day heart cookies have been ordered. The Youth Faith Ambassadors had to order A LOT of cookies!!!!

  • The primary division ordered 43 cookies

  • The junior division ordered 21 cookies

  • The intermediate division ordered 12 cookies

How many heart cookies had to be ordered for the school?

STEP 3: Anticipating Student Responses

The problem we used in class was changed after we anticipated student responses and completed the problem ourselves. We realized the numbers were too high and required students to regroup a few times. After many discussions, we decided on the numbers that were going to be used in the problem. The numbers in the problem had to lend itself to the computational strategies they were already exposed to.

Strategies we anticipated students would use most:

  1. Decompose and Regrouping - using base-ten blocks/drawings
  2. Skip Counting/ Counting On - using an open number line
  3. Standard Algorithm - using numbers only
  4. Making 10 or 100 - decompose and find groups of "friendly" numbers
  5. Doubles - finding doubles in the tens and ones

STEP 4: Selecting an Activation Task

We wanted the students to begin to think about the strategies they would select for different addition equations. We decided to use Number Strings to elicit addition strategy names and to begin to have students think about why they selected that strategy. One string was released at a time. Students were given time to think then share their ideas.

Activation Task

If we were to add these two numbers, what strategy would you use and why?

  1. 6 + 6

  2. 7 + 9

  3. 11 + 8

  4. 81 + 46

STEP 5: Thinking About Consolidation

Using the 5 Practices, we began to select key strategies that we going to monitor during the lesson. We ensured that we all had a common understanding of each addition strategy and the benefits of using each of the strategies.

Lesson Planning and Monitoring Template

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STEP 6: Preparing for the Lesson

Selecting Roles

Teacher (1)

Co-teacher (1)

Student Observers (3)

Classroom Observer (1)

The host teacher determine the students that were to be observed. Each observer was given only one student to monitor. The goal for the observers to look only at their assigned student and take observational notes about that student throughout the entire lesson. Notes are shared with the classroom teacher to provide further insight into the selected students in the class.

STEP 7: Teaching and Observing Part 1 & 2 of the Lesson

We all went into the grade 3 class to participate in the co-created lesson in our assigned roles. Here are the anchor charts created from the Activation and the Problem Solving Task. The Learning Goals were also presented and unpacked with the students.
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STEP 8: Debriefing & Planning the Consolidation

We were excited to debrief about the lesson as students were highly engaged and used many strategies to solve the problem.

One student used a strategy that we didn't anticipate: compensation strategy (see 9, think 10). For the most part, students did not focus on the 2nd Learning Goal and did not justify why they used a strategy. The host teacher prompted some justifications orally but we agreed as a "lesson study team" that we would focus on the 2nd learning goal in the consolidation.

Using the 5 Practices, we selected the strategies to highlight with students and the order in which the strategies would be presented. Then, we looked at the student work to support our selections.

The "Exit Ticket" was then created with numbers that would encourage the use of the highlighted strategies from consolidation.

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STEP 9: Teaching and Observing the Consolidation Part of the Lesson

3 Computational strategies were highlighted with student work and the host teacher shared the new learning after each strategy was presented.

New Learning Shared With Students:

  1. Look for numbers in the problem that already make 10 or 100 first
  2. Use bigger jumps if possible when skip counting on an open number line. This may help you make less errors and is quicker.
  3. New Strategy: See 9-Think 10 (Compensation) -- when numbers in the problem end in 9, you can think of it as 10 then take away 1 at the end.
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STEP 10: Analyzing Exit Tickets & Provding Feedback

As a lesson study team, we looked at the exit tickets together, discussed and determined descriptive feedback for each student. Based on our feedback, the host teacher developed ideas of what lessons needed to follow in the upcoming week. We noticed that the consolidation had an impact on several students and that the majority of the students still need more practice with selecting appropriate computational strategy (using the information from the problem).

STEP 11: Reflecting on the Entire Lesson

As a Lesson Study Team, we discussed the following reflection questions. Below is a list of highlights gathered from the voice of the team:

1) What worked?

  • students were engaged
  • all students had an entry point (modified task given to the 2 students)
  • students were able to experience success showing different addition strategies
  • students worked well together
  • activation elicited the computation strategies students could use in the during task of the lesson
  • exit ticket clearly revealed next step for each student

2) What would we change if we did it again?

  • consolidate to only 2 strategies (for time management and to keep students focused)
  • be more cognizant of annotating student thinking on the board or chart paper so all students can see (instead of writing on the student work - which was small at times)
  • prompt more students to justify why they selected a strategy in the "During" part of the lesson so more reasons could be shared during consolidation.

3) What might this lesson look like in your class? Why?

4) What could you do to make the lesson successful in your math class?

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Here is a summary of some key learning statements taking from Exit Tickets:

  • Having the Learning Goal written on chart/board and the student exit tickets is beneficial and students ARE capable of referring to them
  • There is a benefit to naming the strategies that students use and making an anchor chart for students and teacher to refer to
  • Different strategies work for different students
  • Anticipating and Selecting (along with the other 5 Practices) can improve and focus the consolidation for students (reveal strategies) and teachers
  • Students need to explore why addition strategies work and why some strategies are more useful at times
  • Our goal as teachers is to move student thinking forward. We need to know where each student is and try to move them forward in their thinking little by little
  • Exit tickets help you plan the follow-up lessons
  • The standard algorithm for addition (with regrouping) is not natural for students so we must explore other strategies
  • Open number lines are a great tool for students to use when adding
  • Students sharing their mathematical thinking with the class is the foundation for teachers to be more explicit with math instruction
  • It's important to set the conditions for students to become problem solvers in math
  • Having the conditions for learning in place is a major part of a successful math lesson

What Are We Still Wondering About:

  • Assessment??? - What does a level 1, 2, 3 and 4 look like with regards to each category in the achievement chart?
  • In a 3-part math lesson, how do you pull out a variety of strategies when students are so focused on one?
  • How can you effectively integrate Number Sense & Numeration into the other strands in order to help students make connections?
  • How can we teach estimation effectively?
  • How can I encourage students to self-assess more often?

Facilitated By: Natasha Moore

If you are a part of the MBC Numeracy Pod and would like more information about this Primary Lesson Study, please don't hesitate to contact me. If you would like a copy of the lesson or any items used in this Lesson Study, you can email me and I will send it to you. I sincerely thank the wonderful Primary teachers and the administrator that collaborated in this two-day Primary Lesson Study. It was an amazing learning experience!