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An extension would be to include Quadratic expressions of the form (2x-1)(x+3) 

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An extension would be to include Quadratic expressions of the form (2x-1)(x+3) 

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"Why" is a strong questioning technique and it allows students to think aloud

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"Why" is a strong questioning technique and it allows students to think aloud

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Perhaps the reason for not requiring students to use Desmos in the middle section was so that the students focus more on the various equations and see what remains the same and what changes so that they can sketch the graph. Later on Desmos is used to help them check for understanding. Desmos is useful here so that students can do self-marking.

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Ask students to explain the graph transitions with reference to x- and y-values (properties of functions), and as a concept map to illustrate the graphical properties.

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Allow opportunities for the students to do pair work, this helps in promoting reasoning and discussion.

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intentional variation thru' a series of questions(with invariance) allows for pattern-recognition. 

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intentional variation thru' a series of questions(with invariance) allows for pattern-recognition. 

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after varying examples, generalized form.
generalized form is typically daunting for students. with VT, it is much more easily arrived at.

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I like the 'What if' questions to help students to move away from their comfort zone and think of other scenarios 

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I like the 'What if' questions to help students to move away from their comfort zone and think of other scenarios 

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1) The overview structure of the task is designed based on the 'predict-explain-check-reflect' structure, which ties the sequencing of questions very logically.

2) Asking the 'why's' and guiding students to describe their sketches to compare and contrast is also a path towards promoting metacognitions.

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What promotes metacognition?
(1) Begin with the basic form y=x^2 and slowly vary (with small number) in the vertex form
(2) Use of Desmos to lighten the metacognition load in sketching
(3) Repeat question to identify the type of turning point, its coordinates and line of symmetry
(4) Generalization after 4 examples

What qn were asked to developed metacognition?
(1) At Generalization: "Why?" "Explain why" (Reason), "What if"
(2) Translation from use of Desmos to without Desmos; apply "Predict explain check and reflect"

Desmos as a tool for checking after prediction

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Asking students to first make observations of  some important features of specific examples and make conjecture of the general form.
Asking What and Why help them to reflect on what they learn and provide reasons to substantiate what they believe.

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The reflection questions at the end of the worksheet that ask students to describe their thinking process make students' thinking visible. Students are also required to think through the questions they did and make some generalization to consolidate their thinking.

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"Explain" allows students to make their thinking visible

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"Explain" allows students to make their thinking visible

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Students are made to be aware how changing certain aspects of the function will result in a change in the turning points while still remaining minimum points. Steers them to understand the relation between certain features with certain changes in the function. Desmos helps to lighten the cognitive load.

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Students are made to be aware how changing certain aspects of the function will result in a change in the turning points while still remaining minimum points. Steers them to understand the relation between certain features with certain changes in the function. Desmos helps to lighten the cognitive load.

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This worksheet provides a smooth transition from learning functions of the form y = (x-h)(x-m) to the form y = (x-h)^2, and to the form y = (x - h)^2 - k.
Students will zoom in to focus on the effect of the slight variation on the graph and its properties

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Asking students to 'explain why' gets students to think about how they derived their answers and to list out their thinking process on paper

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"Why" questions are included in the task. The "why" questions get students to reflect how the graphical features observed are related to the algebraic function. Hence, enhancing their understanding of the relationship between the two forms.