4. The definite integral has a unique value.
Integrals
What is definite integral?
What do
we
have?
5. The definite integral has a unique value.
A definite integral is denoted by , where a is called the lower
limit of the integral and b is called the upper limit of the integral.
Integrals
What is definite integral?
What do
we
have?
6. The definite integral is introduced either as the limit of a sum or if it has
an anti derivative F in the interval [a, b], then its value is the difference
between the values of F at the end points, i.e., F(b) – F(a).
Integrals
What is definite integral?
What do
we
have?
7. To define definite integrals
To interpret fundamental theorems of definite integrals
To apply concepts learned so far
Learning Outcomes
How confident do you feel?
8. To define definite integrals
To interpret fundamental theorems of definite integrals
To apply concepts learned so far
Learning Outcomes
How confident do you feel?
11. Integrals
What is an area function?
What do
we
have?
We have defined ( ) b a f x as the area of the region
bounded by the curve y = f(x),
12. Integrals
What is an area function?
What do
we
have?
We have defined ( ) b a f x as the area of the region
bounded by the curve y = f(x), the ordinates x = a and
x = b and x-axis.
13. Integrals
What is an area function?
What do
we
have?
Let x be a given point in [a, b]. Then ( ) x a f x d
represents the area of the shaded region.
14. Integrals
What is an area function?
What do
we
have?
In other words, the area of this shaded region is a
function of x.
15. Integrals
What is an area function?
What do
we
have?
We denote this function of x by A(x) as Area function
and is given by:
16. Theorem 1:
Let f be a continuous function on the closed interval [a, b] and let A(x) be the
area function. Then A′(x) = f(x), for all x ∈ [a, b].
Integrals
Let's look at a few theorems!
What do
we
have?
17. Theorem 2:
Let f be continuous function defined on the closed interval [a, b] and F be an
anti derivative of f. Then
Integrals
Let's look at a few theorems!
What do
we
have?
18. To define definite integrals
To interpret fundamental theorems of definite integrals
To apply concepts learned so far
Learning Outcomes
How confident do you feel?
19. To define definite integrals
To interpret fundamental theorems of definite integrals
To apply concepts learned so far
Learning Outcomes
How confident do you feel?
25. To define definite integrals
To interpret fundamental theorems of definite integrals
To apply concepts learned so far
Learning Outcomes
How confident do you feel?
26. To define definite integrals
To interpret fundamental theorems of definite integrals
To apply concepts learned so far
Learning Outcomes
How confident do you feel?
An overview of the content of the lesson
Must be in the form of a question where appropriate
Students should be able to answer the question at the end - either fully, partly or in a way that demonstrates they understand what gaps in their knowledge they need to address
Verbs such as to understand / to know / to gain confidence / to learn
Ask students to give the question a go and point out that, at the end of the lesson, they should be able to answer fully
Measurable outcomes that students can demonstrate and self-assess against
Must be written using Bloom’s taxonomy verbs
Verbs based on students ability and pitch of lesson
It must be clear that students understand the outcomes before moving on
Make an activity of this slide:
Ask students to read this aloud
Ask them to paraphrase
Ask that they explain what they mean
Ask what they already know related to these outcomes
There may be as few as 2 outcomes, or max 4
The next slides should be focused on achieving first outcome
Make reference to the outcome in the teaching
Fill this with thinking skills activities, peer assessment, higher-order questioning, engaging activities and challenge
The next slides should be focused on achieving first outcome
Make reference to the outcome in the teaching
Fill this with thinking skills activities, peer assessment, higher-order questioning, engaging activities and challenge
The next slides should be focused on achieving first outcome
Make reference to the outcome in the teaching
Fill this with thinking skills activities, peer assessment, higher-order questioning, engaging activities and challenge
The next slides should be focused on achieving first outcome
Make reference to the outcome in the teaching
Fill this with thinking skills activities, peer assessment, higher-order questioning, engaging activities and challenge
Revisit the first outcome and use the polling function to allow students to privately self-assess
You may feel that the students do not need privacy to self-assess and in this instance, the chat box may be used
Polling must be used until you can fully assess their confidence to use the chat box and express honesty
If students self-assess as a 4/5, ensure that you are fully confident in their assessment
Ask questions
Ask for examples
Students to ask each other questions
If a few students self-assesses as a 3, but others as a 4/5, discretely ask the higher ones to give examples and to explain their achievement/understanding
If all students are a 3 or below, do not move on. Move to a blank page at the end of the presentation and use as a whiteboard to further explain
If students are ½, go back to the beginning
Always ask students what the gaps are and help them to identify these in order to promote metacognition
1. The outcome changes colour when achieved to the same colour as the objective to demonstrate the connection, progress and what happens next
The next slides should be focused on achieving first outcome
Make reference to the outcome in the teaching
Fill this with thinking skills activities, peer assessment, higher-order questioning, engaging activities and challenge
The next slides should be focused on achieving first outcome
Make reference to the outcome in the teaching
Fill this with thinking skills activities, peer assessment, higher-order questioning, engaging activities and challenge
The next slides should be focused on achieving first outcome
Make reference to the outcome in the teaching
Fill this with thinking skills activities, peer assessment, higher-order questioning, engaging activities and challenge
The next slides should be focused on achieving first outcome
Make reference to the outcome in the teaching
Fill this with thinking skills activities, peer assessment, higher-order questioning, engaging activities and challenge
The next slides should be focused on achieving first outcome
Make reference to the outcome in the teaching
Fill this with thinking skills activities, peer assessment, higher-order questioning, engaging activities and challenge
The next slides should be focused on achieving first outcome
Make reference to the outcome in the teaching
Fill this with thinking skills activities, peer assessment, higher-order questioning, engaging activities and challenge
The next slides should be focused on achieving first outcome
Make reference to the outcome in the teaching
Fill this with thinking skills activities, peer assessment, higher-order questioning, engaging activities and challenge
The next slides should be focused on achieving first outcome
Make reference to the outcome in the teaching
Fill this with thinking skills activities, peer assessment, higher-order questioning, engaging activities and challenge
The next slides should be focused on achieving first outcome
Make reference to the outcome in the teaching
Fill this with thinking skills activities, peer assessment, higher-order questioning, engaging activities and challenge
As previously.
As previously.
The next slides should be focused on achieving first outcome
Make reference to the outcome in the teaching
Fill this with thinking skills activities, peer assessment, higher-order questioning, engaging activities and challenge
The next slides should be focused on achieving first outcome
Make reference to the outcome in the teaching
Fill this with thinking skills activities, peer assessment, higher-order questioning, engaging activities and challenge
The next slides should be focused on achieving first outcome
Make reference to the outcome in the teaching
Fill this with thinking skills activities, peer assessment, higher-order questioning, engaging activities and challenge
The next slides should be focused on achieving first outcome
Make reference to the outcome in the teaching
Fill this with thinking skills activities, peer assessment, higher-order questioning, engaging activities and challenge
The next slides should be focused on achieving first outcome
Make reference to the outcome in the teaching
Fill this with thinking skills activities, peer assessment, higher-order questioning, engaging activities and challenge
As previously.
As previously.
An overview of the content of the lesson
Must be in the form of a question where appropriate
Students should be able to answer the question at the end - either fully, partly or in a way that demonstrates they understand what gaps in their knowledge they need to address
Verbs such as to understand / to know / to gain confidence / to learn
Ask students to give the question a go and point out that, at the end of the lesson, they should be able to answer fully
