##
* *Reflection: Continuous Assessment
Quotients - Just the Basics - Section 3: Independent Practice

In this lesson, it’s important to look out for students struggling with the idea of splitting up a number into equal parts / groups. I am always surprised when I see a confused student, because I feel that our work with multiplication should have made the move to division almost second nature. For some of them, it is, but many of them still perceive it as a separate process. In the past, I attributed this to the curriculum we used.

Now that I am creating my own lessons and, I thought, trying to move fluidly back and forth between the concepts of multiplication and division, I was startled to see that a few students remained perplexed. In reflecting on my practice, I think that next year I should be explicit in using the word division right from the start, instead of demonstrating it in models and discussing how it’s related to multiplication. To assist these students, I retold several of their practice equations in story form. This helped students apply the strategy more comfortably. I don’t know why, but am wondering if this is a developmental roadblock that I just need to support them through until their brain is ready for this particular abstraction?

This is the first year that I’ve planned lessons with explicit attention to mathematical practices. In this lesson, the goal was to engage students in attending to precision. Attending to precision refers to a lot more than obtaining the correct answer to a mathematical calculations, but in thei particular lesson, I am focusing on that simple but essential task.

Often students will rush ahead when they think they understand something and they end up misapplying the rule or simply miscounting. There are a few examples of this in the student work sample document. There is no sound reason for children to make errors, particularly when the problems have such small dividends. This is an example of a lesson in which it’s okay and important to stress to students that precision with these basic facts is attainable if models are used strategically. If they do not rush, they can all succeed with these basic facts that are at the root of all higher mathematics.

*Continuous Assessment: Attending to Precision with Basic Facts*

# Quotients - Just the Basics

Lesson 4 of 6

## Objective: SWBAT use drawings to find the quantity unknown in division problems with dividends no larger than 30.

#### Introduction

*3 min*

Today students draw neat models of simple division problems, write the equations, and solve. While drawing out division problems is not a long term strategy, as least not on a 1 item per one drawing basis (as opposed to graphically resembling larger groups - such as a symbol for 10 or 100), it is an important strategy when children are first grappling with the idea.

All that is needed for today's lesson is scrap paper and a pencil, or a whiteboard and marker. I printed out the papers because having the models to look at later in a quiet moment helped me plan for the next day's instruction. (Misconceptions on paper are very visible).

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#### Guided Practice

*6 min*

Remind students to make certain they are starting with the correct number, and also remind them to move their groups to distinct locations. I show them several examples, either in these video clips showing 12 stones being divided into different equal groupings and 18 stones being divided into different equal groupings, or use manipulatives on a document camera, or call students to the carpet and work with real objects.

Examples to model:

18 divided by 3 = 6

20 divided by 4 = 5

12 divided by 3 = 4

15 divided by 5 = 3

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#### Independent Practice

*35 min*

My goal is that by the the conclusion of this lesson, students will be able to solve division problems with dividends no larger than 30 by drawing out an *equal groups model* on paper. In order for them to successful in using this strategy, it's important to closely monitor this independent or partner work.

While this is rather easy for some students, others struggle with it and fail to make the connection between multiplication and division. Some students may know how to parrot it, but underneath the words, the understanding is still developing. If a student is really struggling, I either sit with them as they draw it out, build the model on a white board with them, or go and get some of the manipulatives and then have them draw out their solution after they have built it with cubes.

#### Resources

*expand content*

#### Closure

*8 min*

To close, I place students with a partner or within a small group and ask them to take turns explaining to each other how they used the strategy of splitting up the dividend into equal groups (divisor) to determine the amount in each group (quotient).

Students are given a scenario for their work together. They are told to pretend that one of them is the teacher, and the other partner pretends they are a 2nd grade student who knows nothing at all about division.

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#### Homework

*2 min*

I explain to the students that this homework page has 3 levels. They can choose the one that best suits them. Version A has smaller numbers and it is recommended for students who are still really struggling with the concept. Version B is for children who were able to successfully work through the guided practice most of the time. Answers to questions, such this one where the student is asked to divide 30 as many different ways as possible, can be very informative and give me additional information about who is ready for something more complicated, which they will find on Version C of the homework.

*expand content*

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- UNIT 1: 1st Week: Getting to Know Each Other Through Graphs
- UNIT 2: Addition and Subtraction
- UNIT 3: Multiplication
- UNIT 4: Introduction to Basic Division
- UNIT 5: Division in Context
- UNIT 6: Time
- UNIT 7: Rounding
- UNIT 8: Place Value Practice
- UNIT 9: Fractions
- UNIT 10: Math and Me: Nutrition, Health and More
- UNIT 11: Geometry in Architecture
- UNIT 12: Time Cycle 2
- UNIT 13: Patterns in Math
- UNIT 14: Area and Perimeter
- UNIT 15: Solving Mult-Step Word Problems Using the Four Operations
- UNIT 16: Musical Fractions
- UNIT 17: Volcanoes (Data Collection, Graphs, Addition & Subtraction)

- LESSON 1: Exploring the Idea of Division
- LESSON 2: Drawing Equal Group Models
- LESSON 3: Thinking About Threes
- LESSON 4: Quotients - Just the Basics
- LESSON 5: Designs with Nines: Patterns in Multiplication and Division (Day 1)
- LESSON 6: Designs with Nines: Patterns in Multiplication and Division (Day 2)