# MBC Numeracy Pod

### PRIMARY LESSON STUDY #1

## 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

## 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.

## 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*

## DAY #1: UNDERSTANDING THE CONTENT AND PLANNING THE LESSON

## Grade 3 - Operational Sense

**Overall Expectations #3:**

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

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

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**and division.**

## Decomposing the Curriculum Expectation

__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.

## Resources Used in Our Lesson Study

## Reading About Operational SenseWe read through pp. 17-32 in the Guide. This gave use an overview of operational sense. http://eworkshop.on.ca/edu/resources/guides/Guide_Math_K_3_NSN.pdf | ## Digging Deeper into Addition and SubtractionWe read about the types of addition and subtraction problems that could be used when teaching math. We also looked at the different computational strategies used most frequently by the Primary students. (pp. 9 - 10, pp. 13, pp. 20 - 27) http://eworkshop.on.ca/edu/resources/guides/Guide_Math_K_6_Volume_5.pdf | ## Understanding AlgorithmsMarian Small's book explores computational strategies in depth. Please refer to Chapter 8 - Computation with Whole Numbers (pp. 159-170). Look specifically at page 171 for misconceptions and common errors students have with addition and subtraction. |

## Reading About Operational Sense

We read through pp. 17-32 in the Guide. This gave use an overview of operational sense.

http://eworkshop.on.ca/edu/resources/guides/Guide_Math_K_3_NSN.pdf

## Digging Deeper into Addition and Subtraction

We read about the types of addition and subtraction problems that could be used when teaching math. We also looked at the different computational strategies used most frequently by the Primary students. (pp. 9 - 10, pp. 13, pp. 20 - 27)

http://eworkshop.on.ca/edu/resources/guides/Guide_Math_K_6_Volume_5.pdf

## Using Addition and Subtraction in a Problem Solving Context

## Summarizing the Computational Strategies for Addition and Subtraction

## More Addition Strategies Making 10, Skip Counting by 2s, 5s, 10s & Using the Commutative Property | ## Subtraction Strategies Exploring inverse facts and Adding Up to Subtract |

## The Importance of Exposing Students to a Variety of Strategies

*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.

## USING TOOLS WITH THE COMPUTATIONAL STRATEGIES

## Counters- best used for single-digit addition - builds one-to-one correspondence - encourages counting | ## Ten-Frames- best used for single- or small two- digit number addition - precursor to base ten - develops beginning idea of regrouping - helps students see units of five, ten (and two) | ## Base-Ten Blocks- best used for single- and multi- digit addition - used for addition with and without regrouping - helps to develop place value understanding - helps students to see units of 1, 10, 100 and 1000 |

## Counters

- best used for single-digit addition

- builds one-to-one correspondence

- encourages counting

## Ten-Frames

- best used for single- or small two- digit number addition

- precursor to base ten

- develops beginning idea of regrouping

- helps students see units of five, ten (and two)

## Place Value Chart- best used with base-ten blocks - used to for multi-digit addition - helps to visualize the standard algorithm - helps to develop place value understanding | ## Number Lines & Hundreds Charts- best used for single-digit or small two-digit addition - helps students with counting up or counting on - encourages counting (skip counting) | ## Open Number Lines- best used for single- or multi- digit addition - helps to develop counting-on strategy - encourages skip counting - helps students make their thinking visible - helps to develop mental math |

## Place Value Chart

- best used with base-ten blocks

- used to for multi-digit addition

- helps to visualize the standard algorithm

- helps to develop place value understanding

## Number Lines & Hundreds Charts

- best used for single-digit or small two-digit addition

- helps students with counting up or counting on

- encourages counting (skip counting)

## Using Relational Rods (Cuisinaire Rods) To Explore Addition Strategies

## PLANNING THE LESSON

## STEP 1: What is the Learning Goal?

*select appropriate strategies*when solving addition problems.

**Student Learning Goals for the Lesson:**

**We are learning to use a variety of strategies when adding****We are learning to justify why we use a strategy when adding**

## STEP 2: What is the Problem Solving Task?

__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

**Strategies we anticipated students would use most:**

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

## STEP 4: Selecting an Activation Task

*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?**

**6 + 6****7 + 9****11 + 8****81 + 46**

## STEP 5: Thinking About Consolidation

## Lesson Planning and Monitoring Template

## DAY #2: TEACHING, OBSERVING, FINE-TUNING AND DEBRIEFING THE LESSON

## 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

## 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.

## 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:__

- Look for numbers in the problem that already make 10 or 100 first
- Use bigger jumps if possible when skip counting on an open number line. This may help you make less errors and is quicker.
- 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.

## STEP 10: Analyzing Exit Tickets & Provding Feedback

## 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?**

**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?