1. unit about analitic geometry
PLANNING A LESSON
unit about analitic geometry
PLANNING A LESSON An example of a CLIL math lesson plan for Y. L. This is a lesson of a unit about analytic geometry or graphic resolution of systems of equations in two variables Content Introduction to graphing linear equations in two variables. Teaching aims: to understand that equation explain the relationship between coordinate pairs, to understand the differences between linear and nonlinear equations, to be able to draw linear graphs from an equation or table of value.
ConcetTa BORTONE, Patrizia sgrò, Tangredi Lucio

2. ConcetTa BORTONE, Patrizia sgrò, Tangredi Lucio
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Learning outcomes
Know:
The expression of the linear equation in two variables
The names of division into four subcategories: horizontal lines, vertical line, lines with positive and negative gradient .
Be able to:
Classify and decide which equations are linear and which are nonlinear
Make predictions about their gradient
To draw linear graph from an equation
Be aware:
That the linear dependence of two variables is in economics, physics and other sciences
Assessment
Can the learners…
Identify and name proprieties of linear equations and their graphical representation?
Be able to sort equations into two and then four different groups?
Make predictions about their graph and their gradient?
Plot many coordinate pairs?
Be aware:
Cooperate in a group?
ConcetTa BORTONE, Patrizia sgrò, Tangredi Lucio

3. ConcetTa BORTONE, Patrizia sgrò, Tangredi Lucio
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Communication
Vocabulary
Revisited: equation, linear, graph, point
New: straight line equation, curves or nonlinear graphs, coordinate pairs, x-axis, y-axis, origin point, vertical and horizontal lines
Structures:
(I think) It’s … (I believe) …
Functions:
Describing graphs and line types
“will” prediction
Examples of communication
Pointing to and naming line types
Sharing ideas about linear or nonlinear equation
Stating which lines are vertical or horizontal or with positive or negative gradient
ConcetTa BORTONE, Patrizia sgrò, Tangredi Lucio

4. ConcetTa BORTONE, Patrizia sgrò, Tangredi Lucio
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Cognition
Identifying linear equation and relative properties
Classifying different lines
Predicting and reasoning
Examples of cognition
Sorting equations into two different groups (linear and nonlinear) using a special table
Classifying (range of properties)
Citizenship
Be aware of the use in other disciplines, such as physics
Examples of citizenship
Law of motion at constant speed
ConcetTa BORTONE, Patrizia sgrò, Tangredi Lucio

5. ConcetTa BORTONE, Patrizia sgrò, Tangredi Lucio
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Approach Linear graphs can have one letter: y=3, x=-2, s=0 Linear graphs have no more than two letters: x-y=1, y=3x-7; s=2t-1 Nonlinear graphs always have more than one letter In linear graph there are no powers of x other 1: x1. We don’t see x2 or 1/x
ConcetTa BORTONE, Patrizia sgrò, Tangredi Lucio

6. ConcetTa BORTONE, Patrizia sgrò, Tangredi Lucio
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Procedure
Whole class Activate prior knowledge about proprieties lines and new nouns.
Groups Sort equation types into two different group
Sort equations according to properties of their gradient Predict which equation graph with a horizontal, vertical or not Check predictions using graph
Feed-back ideas. Were there any surprises?
Individually Learning record observations on worksheets
Whole class Compare different graphics med by individual pupils
Differentiation Additional vocabulary cards and gap-fill sentences
ConcetTa BORTONE, Patrizia sgrò, Tangredi Lucio

7. ConcetTa BORTONE, Patrizia sgrò, Tangredi Lucio
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Classify and differentiate Given the following equations y=2-3x, x2-3y2=8, t=4, z=-1, t=1/p, ….. produce a classifying sheet
Linear
Nonlinear
Don’t know
ConcetTa BORTONE, Patrizia sgrò, Tangredi Lucio

8. ConcetTa BORTONE, Patrizia sgrò, Tangredi Lucio
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And
Linear
Nonlinear
Horizontal lines
Vertical lines
Positive gradient
Negative gradient
ConcetTa BORTONE, Patrizia sgrò, Tangredi Lucio

9. ConcetTa BORTONE, Patrizia sgrò, Tangredi Lucio
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Completing the table of values of equation y=2x x 1 -3 …
... y 2 -6
We need to plot the points (0,0), (1,2), …..
ConcetTa BORTONE, Patrizia sgrò, Tangredi Lucio

10. Different linear graph
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Different linear graph
Horizontal line
Vertical line
ConcetTa BORTONE, Patrizia sgrò, Tangredi Lucio

11. Different linear graph
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Different linear graph
Positive gradient
Positive and different gradients
ConcetTa BORTONE, Patrizia sgrò, Tangredi Lucio

12. ConcetTa BORTONE, Patrizia sgrò, Tangredi Lucio
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To consolidate learning of new maths vocabulary we can propose a crossword puzzle
Across
1. The name of the pair of variables that describes the point 3. The name of line parallel to the y-axis
5. The name of line parallel to the x-axis
Down
2. The name of the point O(0,0)
4. The name of a straight curves
6. The plural of axis
ConcetTa BORTONE, Patrizia sgrò, Tangredi Lucio

13. PLANNING A LESSON Answer Across Down
1. The name of the pair of variables that describes the point 3. The name of line parallel to the y-axis
5. The name of line parallel to the x-axis
Down
2. The name of the point O(0,0)
4. The name of a straight curves
6. The plural of axis
thanks for your attention
ConcetTa BORTONE, Patrizia sgrò, Tangredi Lucio CLIL 2013/14 LICEO RUMMO BENEVENTO