Equality
PLC Full Presentation
Goals
Connecting to the TQS, Division Goals and QLE
Teaching Quality Standard
Today we will be…
Engaging in professional learning and critical reflection to improve teaching and learning.
Teaching Quality Standard
Today we will be…
Applying a current and comprehensive repertoire of effective planning, instruction, and assessment practices to meet the learning needs of every student.
Teaching Quality Standard
Today we will be…
Sustaining inclusive learning environments where diversity is embraced and every student is welcomed, caref for, respected and safe.
Teaching Quality Standard
Today we will be…
Developing... knowledge about First Nations, Métis and Inuit for the benefit of all students.
Division Goal: Academic Excellence
Focusing on Mathematics
QLE
As we progress through this learning session, consider the following questions as they pertain to each of the four quadrants:
Ongoing Reflection Opportunity
When you see this icon, you can use this handout to reflect.
Before we begin...
Please write down a simple addition, subtraction, multiplication (if applicable) or division (if applicable) question you typically ask students to solve.
Include a __ or a ? for the part you are asking them to find.
We’ll come back to this later.
One Process for Concept Attainment
If all students earned Excelling or Proficient, they have the concept.
If any students didn’t, you can use a process similar to the following…
Equality Example 1 of 3
Equality Example 2 of 3
Equality Example 3 of 3
5
Non-Example of Equality
Create a definition for Equality
Example
Example
Example
Non-Example
Examples / Non-Examples Sort
Give students examples and non-examples to sort.
(We are not doing this today)
More Examples
Examples of Equality
Examples of Equality
Examples of Equality
Refine your definition of Equality
Example of Equality
Refine your definition of Equality
What are the critical attributes of Equality?
Create your own examples and non-examples
Identify Key Vocabulary
Identify Key Vocabulary
Kdg: quantity, same, not same, more, less, relationship
Grade 1: quantity, equal, equal sign, relationship
Grade 2: quantity, equal, equal sign, not equal, not equal sign, relationship
Grade 3: equation, expressions, symbols, values, unknown values, one-step equation, relationship
Grade 4: generalize, equations, unknown values, symbols, unknowns, relationship
Identify Key Vocabulary
Grade 5: equation, variable, single-variable, unknown, one-step equations, solutions, relationship
Grade 6: equation, letter variable, unknown number, preservation of equality, relationship
Grade 7: equivalent, preservation of equality, equations, relationship, expression, linear equations, one-step linear equations
Grade 8: two-variable linear relations, linear equations, congruence, relationship
Reflection
The MIPI+ Question #1
The Equality Question
Write a number on the line that makes the following equation true.
8+4 = __ + 5
Convince me that the number makes the equation true.
Criteria for Questions
The Equality Question
Write a number on the line that makes the following equation true.
8+4 = __ + 5
Convince me that the number makes the equation true.
Criteria for Questions
Do not prompt students to replace the __ with a variable!
This turns it into a procedural question rather than a conceptual question that focuses on equality.
Research
The Equality Research Question Grades 1-6
Make the following statement true: 8+4 = __ + 5
How did you figure that out?
Criteria for Questions
| Gr 1 | Gr 1/2 | Gr 2 | Gr 3 | Gr 4 | Gr 5 | Gr 6 |
7 | 0% | 6% | 6% | 10% | 7% | 7% | 0% |
12 | 79% | 54% | 55% | 60% | 9% | 48% | 84% |
12& 17 | 0% | 0% | 14% | 5% | 30% | 0% | 2% |
17 | 7% | 20% | 10% | 20% | 44% | 45% | 14% |
Other | 14% | 20% | 15% | 5% | 10% | 0% | 0% |
Responses student provided
The Equality Research Question Grades 7-8
Grades 7 - 8 were given a slightly different question in the research project.
| Gr 7 | Gr 8 |
Operational Understanding | 36% | 52% |
Relational Understanding | 43% | 31% |
Other Understanding | 20% | 17% |
No Response/ Don’t know | 1% | 0% |
Responses student provided
The Equality Research Question Combined Results
| Gr 1 | Gr 1/2 | Gr 2 | Gr 3 | Gr 4 | Gr 5 | Gr 6 | Gr 7 | Gr 8 |
Operational | 86% | 74% | 79% | 85% | 83% | 93% | 100% | 36% | 52% |
Relational | 0% | 6% | 6% | 10% | 7% | 7% | 0% | 43% | 31% |
Other | 14% | 20% | 15% | 5% | 10% | 0% | 0% | 20% | 17% |
No Response | | | | | | | | 1% | |
What is the misconception?
How would you explain the misconception in one or two sentences?
Operational Understanding
Students who place 12 on the line believe that the equal sign means “the answer comes next”.
Other Understanding
Students who write 17 on the line are ignoring the equals sign, completing all of the operations and then writing the answer on the line.
They may even be changing the equals sign into an addition symbol to represent their thinking.
Digging into Your Students’ Responses
Understanding the Levels
This line separates what is acceptable understanding and what is not acceptable understanding. This rubric does NOT equate to our 5 point scale which has 3 levels of acceptable understanding.
Acceptable
NOT Acceptable
Understanding the Levels
Find someone who is a similar height to you who is not at your school or at your table.
Understanding the Levels
Find someone with a similar hair colour as you who is not at your school or at your table.
The Equality Rubric
Sort your students’ work into the 5 levels.
Exemplar Check: Watch for “helpful” explanations.
The Equality Rubric
You might find it helpful to write down students’ names on the rubric.
Fold the paper over so you see the levels in the left column.
Write student’s names in the appropriate level.
Middle School 5 Point Scale
How might you correlate future learning assessments with our 5 Point Scale?
Elementary 5 Point Scale
How might you correlate future learning assessments with our 5 Point Scale?
Why is this a misconception?
Comparing Your Example Questions
What is the relationship between each of your questions?
How might this unintentionally create misconceptions?
How many of you wrote
# + # = ?
# - # = ?
# x # = ?
# ÷ # = ?
How many questions in our resources use this format?
How do we deal with this misconception?
What does the equals sign mean?
“The equal sign represents an equivalence relation between two quantities - what’s on the left side equals the right side.”
Wording
I used to say “the left side of the equals sign is the same as the right side”
HOWEVER
although 4 + 4 = 7 + 1
Context changes everything!
Example
You and a friend are buying a box of chocolates. Each of you puts in $4.00. How should you share the box?
Example
You and a friend are buying a box of chocolates. You put in $1.00. Your friend puts in $7.00. How should you share the box?
Wording
The left side of the equals sign has the same VALUE as the right side.
How might you describe / state the following?
30% + 60% = 25% + 65%
$1.25 + $0.25 = $0.75 + $0.75
Two 2 lb bags of flour = 4 lb of flour
How might you describe / state the following?
30% + 60% = 25% + 65%: ex. Same total percent as
$1.25 + $0.25 = $0.75 + $0.75 ex. Same total dollar amount as
Two 2 lb bags of flour = 4 lb of flour ex. Same amount of flour as
High Leverage Strategies
What are high leverage strategies?
Mathematics Framework
All strategies shared in P LC’s can be found at http://mathframework.com
Because this book is written and translated by an Indigenous author and translator, and because it contains Cree language, an element of Indigenous culture, this work has received the Authentic Indigenous text label and a text content label of Cree. The story itself and the images within the book are not specifically Indigenous or Cree, however.
This book is in IMC!
Activity Idea for younger students: Have them write their own story showing how numbers can be decomposed.
Mini Assessment
Create an equation using a minimum of the following:
3 4 6 = +
You must use the 3 as a 3, 4 as a 4, 6 as a 6, exactly one equal sign, and at least one addition symbol. You may use additional operations.
Compare to your seat partner’s.
How are they the same? Similar? Different?
How does changing the order, change the meaning of the equation?
Reflection
What might this look like at the grade level you teach?
How might I adjust this for students at varying levels?
Where is this going?
Place Value:
Students' understanding of equality has a huge impact on place value.
How many different ways are there to represent the number 23 using base ten blocks?
Your mission
Choose one high leverage strategy shared today that you will try in your classroom.
Try it.
Report back next time. How did it go? What worked? Didn’t work?
High leverage strategies will then be added to the
Math Framework
What might this look like in your classroom?
Where is Equality in Your Curriculum?
Review your curriculum to find the outcomes
Why is it important for all grades to focus on Equality?
Experts in the Room
What high leverage strategies are you already using to build an understanding of equality in your classroom?
Think-Pair-Share
Ongoing Reflection Opportunity