Welcome to my Learning Station! Please review the content provided and provide your feedback!
I chose to profile the TIPS4M: Continuum & Connections “Solving Equations & Using Variables as Place Holders.” booklet for this learning station.
Key Student Learnings for this Topic
Scaffolding
of:
a) Increasingly
complex Computational Skills
b) Increasingly
moving from trial & error, to graphing, to algebraic (linear &
quadratic) expressions
c) Working
with integers, decimals & whole numbers
d) Developing skills
with formulas, substituting, solving & developing formulas
e) Estimating
results, identifying trends and drawing conclusions from data
f) Distinguishing
between linear and non-linear relationships & generating equations, linking
& describing how these equations apply to geometric relationships, quadratic
formulas & rates of change
g) Drawing
graphs by hand from data & representing linear & quadratic relations
Key Points
for Enrichment - Use models that are relevant, appropriate, powerful and well-crafted - the following video explains the use of good models:
Click the title caption to watch.
Learning Task
Note: Task
& Solutions obtained from TIPS4M:
Continuum & Connections “Solving Equations & Using Variables as
Place Holders.”, p. 27-32.
Please
solve this task:
Once you have completed your solutions, review
the possible solutions to this problem, by grade:
Solution A:
Solution B:
Solution C:
Solution D:
Solution E:
Reflect on the skills and knowledge the students would need to
correctly solve the questions, in each grade.
Please answer the following questions:
1) What are
some possible errors students could make at each grade level?
2) Why do you
think the students could make those errors?
3) What
misconceptions could be underlying here?
4) What could
you as an educator do to address these misconceptions?
Continue to the next section to compare your ideas and review Resources
and Connections.
Key Student Challenges/Misconceptions for this
Topic
a) Not
following through on reading the entire problem and understanding the question
b) Lack of understanding
in how to isolate a variable in an equation
c) Confusion
with distributive properties & integer operations across the equal sign (when
to add, subtract, multiply or divide)
d) Confusion
about the variable’s job as a placeholder
e) Confusion
in distribution of values when one side has a fraction
f) Difficulty
in working with operations involving fractions
g) Sign (+/-)
errors in computations
h) Poor understanding
that equations balance
i) Inability
to work with variables other than x
j) Poor
understanding of equations as a model of the situation – leading to inability to
generate equations for specific problems
The
following are Resources on student misconceptions in this theme :
e) https://danpearcymaths.wordpress.com/2011/11/19/solving-linear-equations-algebraically-november-8th/
Which misconceptions did you identify? Did any of these surprise you? Why?
Please post your ideas in the comment section!
To help in designing rich math tasks, please feel free to review the following resources:
Professional
Resources to Support this Theme
Mr.
Barton’s Math Blog – A website created by a maths teacher that provides
examples of rich, inquiry-based math lessons, and targets student achievement
and common student misconceptions
The
Learning Exchange – An online math education resource built in consultation with Ontario’s Ministry of
Education’s Student Achievement Division where the resources are developed by
educators: excellent source of videos and research-based ideas for mathematics
learning & development.
CPALMS – An online
resource with math lesson ideas, reflection on student misconceptions and how
to address them and worksheet downloads and resources for teachers.
Mr.
Buckton 4 Maths – An excellent resource created by a UK teacher,
Tim Buckton, for teaching linear equations from scratch. There are
levelled/graded worksheets, loop cards, discussion activities, flipchart
activities (requires Active Studio to be installed) and amazing interactive
Excel resources.
NRICH
Mathematics – A website with many resources for teaching rich math lessons.
Tap Into Teen Minds – a Website developed by Kyle Peace, a math
teacher, in partnership with, and funded by the Ontario Ministry of Education to create a paperless learning environment by
introducing a class set of iPads. The
purpose of the project was to increase engagement and student perception of
learning mathematics, to iprove student achievement in mathematics, and to use non-cost
prohibitive technology to solve real-world problems using math.
Andrew
Busch – Rich Math Tasks – A great website resource for rich math tasks in
intermediate level maths.
YouCubed – A website
developed by Stanford University offering links to brain research, pedagogical
insights and specific tasks that can form the foundation for a rich
mathematical task in the class.
How This
Theme Connects to Other Grades & Strands
Big Ideas
Connections across the grades from grade 7 through
to grade 10:
• representing linear growing patterns
(where the terms are whole numbers) using concrete materials, graphs, algebraic
expressions and equations;
• modeling real-life linear
relationships graphically and algebraically, and solving simple algebraic equations
using a variety of strategies, including inspection, guess and check and using a
“balance” model.
• solving problems involving
proportional reasoning;
• simplifying numerical and polynomial
expressions in one variable, and solving simple first-degree equations.
• manipulating and solving algebraic
equations, as needed to solve problems;
• graphing a line and writing the
equation of a line from given information;
• solving systems of two linear
equations, and solving related problems that arise from realistic situations.
Connections across Strands: In Grade 7:
Number
Sense & Numeration: Students
learn computational, estimation, integer and mathematical operations strategies.
Measurement: Students develop skills with equations in measurement,
learn to substitute in for values, and learn to develop formulas.
Data Management
& Probability: Students
learn to draw conclusions from data & identify trends.
Connections across Strands: In Grade 8:
Number
Sense & Numeration: Students
learn exponential notation and how to solve problems with integer operations.
Measurement: Students develop formulas and solve problems
using those formulas.
Geometry
& Spatial Sense: Students
use equations to determine geometric relationships and determine algebraic
relationships to geometric properties.
Data Management
& Probability: Students compare
theoretical & experimental probability, interpret & draw conclusions
from data & identify trends.
Connections across Strands: In Grade 9:
Number Sense & Numeration: Students
learn exponential notation and how to solve problems with integer operations.
Measurement & Geometry: Students solve
problems involving geometric & algebraic relationships involving the Pythagorean
Theorem, and use equations to determine geometric relationships, and
in solving problems.
Analytic
Geometry: Students distinguish
between linear and non-linear relationships, write equations of lines, graph
lines by hand, & explain geometric relationships, identify and explain any restrictions on the variables in a linear relation
and determine the point of intersection.
Linear Relationships: Students
represent linear realtions, determine the equation of a line, & describe
the effects of changing conditions on a linear graph.
Connections across Strands: In Grade 10:
Number Sense & Numeration: Students solve
problems using similar triangles, trigonometric rations and geometric
properties.
Modeling Linear Relations: Students write
equations, graph lines by hand, determine the equation of a line and point of
intersection on a graph, and solve systems of equations.
Quadratic Relations: Students
determine quadratic relations through experiment and graphically represent
quadratic relations.
THANK YOU FOR PARTICIPATING!
I LOOK FORWARD TO YOUR COMMENTS AND INPUT! 😁
