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Summative Assessment Examples

Here is the homework check rubric. The students are given this piece of paper and they will attach it to their homework to hand in when completed. As you can see the students have a checkbox to check off when they have complete and attached the assigned homework. As well as the students get to see the rubric so they know what we are expecting with their homework and can complete it accordingly.

Here is an example of the quiz that my students wrote. As you can see each question is explained (I also went over them before they started the quiz) and it shows how many marks each question is out of. I explained to the students before they wrote the exam what they were getting marked for (one mark for their work and one mark for their answer).

Here is the example of how I am organizing my students’ marks on the formative assessment that I perform with them. I got this template from my co-op, these marks will be entered online as well. My hand is covering the students’ names and each column represents a different activity performed. The first column is the quiz, I have the column labeled “Quiz 4.4&4.5, March 21, /28” , the second column is the homework check which is lebeled “Homework check, March 24, /5”. The students’ grade will be lined up accordingly.

Formative Assessment Examples “How are we up to here?” “Are you guys okay with this?” Get students to put Thumbs up (understand) Thumbs down (don’t understand)

Sideway thumb (so-so) on the concept they are learning Circulating throughout the classroom while the students are working on their

assignment Students’ questions they ask me will allow me to see whether I need to spend more

time on a concept Helping the students on their assigned questions Depending on how well the students grasp the concept will decide whether I need to

spend time reviewing a bit the next day or if I can move on

Here are my lessons that I have performed thus far. Including the handout sheet in which we complete together as a class

Foundations of Mathematics and Pre-Calculus 10 Lesson Plan 1 – Day 1Name: Hillary Strain Date: March 17, 2014Subject: Mathematics Grade: FP 10Lesson Length: 1 hour

Outcomes:

FP10.2

Demonstrate understanding of irrational numbers in both radical (including mixed radical) and exponent forms through:

◦ representing◦ identifying◦ simplifying◦ ordering◦ relating to rational numbers◦ applying exponent laws.

Indicators:j. Analyze patterns to generalize why

and when is an even integer.

k. Extend and apply the exponent laws to powers with rational exponents (limited to expressions with rational and variable bases and integral and rational exponents):

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Equipment/materials:

pencil “blue sheet” (table of

perfect squares, cubes, etc)

Advanced preparation:

Worksheet of pattern recognition of fractional exponents and radicals

Students’ notes Assigned homework questions

Introduction Activity (15): Introduction activity to get to know students

o We’re going to have a class party and each student has to bring something. You have to bring something that starts with the first letter of your name.

My name is Miss. Strain and I will bring Silly String

Set (15): Have students complete worksheet in groups of two (who they are sitting beside) Once students completed the worksheet, we will discuss as a class the questions that

are given on the handout. Remind students to keep this process in my while we go throughout the lesson

Development (20): Review exponent law when multiplying

o Ask students if they remember what it iso a^n + a^m = a^m+n

Ask students if order matters. Introduce to students that the multiplication exponent law will still be applicable even

if the exponents are fractions.o (Student notes handout has the examples)

Now conduct a discussion about if there could be another way of writing theseo Get students to refer back to the activity they did earlier

Specifically refer to the second/third question we discussed. Complete the same questions from above but multiplying radicals Point out that you get the same answer Ask the students:

o What do you believe the denominator of the fraction in the exponent represents?

The INDEX of a Radical!o Ask students if they believe we can conclude that if we are given a number

raised to a power, which is a fraction, that the denominator in the fraction is the index of your radical.

Write out the law of powers with rational exponentso (Student notes handout has the examples)

Do some examples with the students.. “Evaluate the following without using the calculator”

o (Student notes handout has the examples) Do some examples with the students.. “Write each power as a radical”

o (Student notes handout has the examples) Do some examples with the students.. “Write each radical as a power”

o (Student notes handout has the examples)Closure (10) :

Have students complete the given questions out of the textbook If the students do not complete this in class they will have to finish it at home

4.4 - Fractional Exponents and Radicals Day 1

FP10.2 Demonstrate understanding of irrational numbers in both radical (including mixed radical) and exponent forms through: relating to rational numbers & applying exponent laws.

j. Analyze patterns to generalize why and when is an even integer.

j. Extend and apply the exponent laws to powers with rational exponents (limited to expressions with rational and variable bases and integral and rational exponents)

Exponent Law When Multiplying : am · an = am+n

Example #1 Evaluate the following without using a calculator

a) 31/2 · 31/2 (Check to see if the bases are common)

=31/2+1/2 (With common bases you can add the exponents)

=32/2 (Ensure denominators are the same, add them)

=31

=3

b) 41/3· 41/3· 41/3

c) 51/2· 51/2

d) 61/3· 61/3· 61/3

Law of Powers With Rational Exponents:

e) 0.491/2 - write this power as a radical

f) - write this radical as a power

g) -161/4 - write this power as a radical

h) - write this radical as a power

i) - write this radical as a power Assignment Pg 227 #3acde, 5, 6

Foundations of Mathematics and Pre-Calculus 10 Lesson Plan 1 – Day 2Name: Hillary Strain Date: March 18, 2014Subject: Mathematics Grade: FP 10Lesson Length: 1 hour

Outcomes: Indicators:

FP10.2


◦ representing◦ identifying◦ simplifying◦ ordering◦ relating to rational

numbers◦ applying exponent laws.


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m. Express powers with rational exponents as radicals and vice versa.


pencil



Set: Have different types of decimals written out on the chalk board Ask the students if they know any other way that they can represent the value of these

decimalso Have students write on board the other way they could write the decimal

Hopefully students will write in fractions Make sure students understand how the decimal got put into fraction form

o The place the number is in the decimals (10ths, 100ths)o You will put that number over the fraction

Announce writing a fraction in their decimal form and that they have the same meaning/answer

Development: Introduce to students that there can be powers that have exponents that are in decimal

form. Introduce example of 1000.5

o Tell the students we want to try and evaluate this power as a whole without using out calculators.

o Tell the students think back to the activity we just did before, Ask them if there is any other way they can represent 0.5 = 5/10 = 1/2

o Rewrite the example above as 10012

o Get the students to refer back to what they learnt yesterday. Using the Law we learnt yesterday, how can we rewrite this so we can

evaluate our power?o Students will write 2√100 and figure out the answer is 10

Do one more example with decimal Before moving on make sure students know that whenever they see a power as a

decimal, re-write it as a fraction and then apply the Powers with Rational Exponents with numerator 1 Law.

o Before getting started do a brief refresher of Exponent law when multiplying power of a power

o (am )n=amno Tell students to keep this in mind for later

o Recall from yesterday when we were dealing with fractional exponentso Point out to students that yesterday we worked with fractions that the numerator

was always 1.o Introduce to students that today we will be working on fractional exponents that have a

numerator that isn’t 1.o Write the example 8

23 on the board

o Ask the students how they think they could write this Power as a Radicalo Write the Powers with Rational Exponents law on the boardo Explain to students the two methods of solving this Power which will give you the same

answero CASE ONE – Denominator First!

o In this case we are going to focus on our denominator getting applied to our base first.

o Our first step is to break down the fraction into two different parts.o Since we know from yesterday that the denominator of a fraction turns into the

index of our radical we can apply this law when using case one. How can we write cubed root as a fraction

o So then we’ll be left with 1/3 x 2o Now we have to deal with the numerator.

We approached the question focusing on the denominator first. Now we must apply the numerator

The numerator stays as a power but it gets applied to our whole expression

o CASE TWO – Numerator First! o In this case we are going to focus on our numerator getting applied to our base

first.o Our first step is to break down the fraction into two different parts.

o If we apply our numerator to our base first, what is left in our original exponent?o Whatever we are left with as our exponent, we must apply that to our whole

expressiono What does 1/3 mean?

We can write it our in radical formo Point out to students that the second step we take to solving this is actually the exponent

law when multiplying powerso Point out to students that you end up with the same answer so they can use whatever one

they feel the most confortableo Go through more examples of powers with fractions and exponents without numerator

1.

Closure: Have students complete the given questions out of the textbook If the students do not complete this in class they will have to finish it at home

4.4 - Fractional Exponents and Radicals Day 2



>

m. Express powers with rational exponents as radicals and vice versa.

Example #1 Evaluate the following without using a calculator

a) 1000.5 (since 5 is in the tenth decimal place, write it as a fraction)

1005 /10 (simplify)

1001 /2 (applying the law of powers with rational exponents)

√100

10

b) 810.25

c) 320.2

Exponent Law when Multiplying Power of a power: (an )m=an+m

Law of Powers with Rational Exponents with numerator other than 1: When m and n are natural numbers, and x is a rational number, then:

xmn=(x 1

n )m= ( n√x )m∧xmn=(xm )

1n=

n√xm

a) 82/3

= 81/3·2 = 82·1/3

= (81/3)2 OR =(82)1/3 = (3√8)2 = 3√82

= (2)2 = 3√64= 4 = 4

b)163/4 c) Write 293/5 in two ways.

Solve the following:d) 274/3 e)82/3

f) (-32)0.4 g) Write 270.8 in two ways

f) Write (3/4)2/3 in two ways

Write the following as powers:g) (3√4.5)2 h) 35√274

i)3√(4 /3)2 j) √ (−15 )3

Assignment #4, 8, 9, 10abde, 11abe, 12acf, and 16.

Foundations of Mathematics and Pre-Calculus 10 Lesson Plan 4.5Name: Hillary Strain Date: March 19, 2014Subject: Mathematics Grade: FP 10Lesson Length: 1 hour

Outcomes:

FP10.2


◦ representing◦ identifying◦ simplifying◦ ordering◦ relating to rational numbers

Indicators:


>

◦ applying exponent laws.i. Analyze patterns to generalize why .


pencil



Set: Have different numbers written on the board

o 4, 2/3, 7, ½, Ask the students what can I multiply these number by to get ONE as an answer Explain to the students that this is called the reciprocal

o “If two numbers multiplied together and the answer is one, they are reciprocals of each other”

So what would the reciprocal of 2 be? Would it be 2?o 2 X 2 = 4o that doesn’t equal to 1o How can we make it equal to 1o Multiply by ½

Development: Point out the exponent law when multiplying powers on their notes Write a power on the board 52

Ask the students what can we do to this power to make it so the overall answer is ONEo Give students the hint: What exponent gives us the answer one?o Give students hint to use the exponent law when multiplying powerso 52 X 5−2=52±2=50=1o So here we can conclude that 52 and 5−2 are reciprocals

Review Powers with Negative exponents Lawo Stop after the first sentence and refer back to the example we just did

Didn’t we just come up with this conclusion?o Continue reading…o Refer back to our example of 5−2

o So using the law we just found out, how can we write this negative exponent? 5−2=1/52

15−2 =52

Do examples Be sure to announce that if there is a negative applied to the base that sign DOES

NOT change… only the sign of the exponent changes! Review the fractional base law/tip with the students Do examples Announce to students that there will be an open book quiz tomorrow about all that

we’ve learnt thus far (4.4 and 4.5)o Given the class period to complete it.o Can use text book, notes and ask me questions

Closure: Have students complete the given questions out of the textbook Students can also complete any of the assignments they didn’t finish that I previously

assigned. If the students do not complete this in class they will have to finish it at home

4.5 - Negative Exponents and Reciprocals


i. Analyze patterns to generalize why .

Exponent Law when multiplying powers: an⋅am=an+m

What does a0 = ?

Powers with Negative Exponents Law: When x is any non-zero number and n is a rational number, x−n is the reciprocal ofxn

That is: x−n=1xn

and 1x−n

=xn , x≠0

Example #1 Evaluate each power

a) 6−2 b) 9−12

= 162

= 136

c)(−7)−4 d) 27−23

Fraction Bases with Negative Exponent: When you have a fraction raised to negative exponent, you will FLIP the fraction (numerator becomes the

denominator, vise versa) and the exponent will become positive: ( ab )−n

= ( ba )n

Example #1 Evaluate each power

a) ( 59 )

−3

b) (−43 )

−3

= ( 95 )

−3

= ( 95 )

3

= 729125

c)(−35 )

−4 d)( 9

16 )−32

Assignment Pg 233 #3,6,7,8acde,13aef

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