Planering 6C/6D - Matematik Blueprint

What we will be doing:

In this unit we will be learning the basics of Algebra, such as...

Expressions

Solving for a variable

Multiplying with brackets and exponents

Solving single step equations

Solving multi step equations

Core content

Unknown numbers

Unknown numbers and their properties and also situations where there is a need to represent an unknown number by a symbol.

Algebraic expressions

Simple algebraic expressions and equations in situations that are relevant for pupils.

Solving equations

Methods of solving simple equations.

Number sequences

How patterns in number sequences and geometrical patterns can be constructed, described and expressed.

Mathematical problem solving

Strategies for mathematical problem-solving in everyday situations

Mathematical questions

Mathematical formulation of questions based on everyday situations.

Abilities

Knowledge requirements

Pupils can solve simple problems in familiar situations in a well functioning way by choosing and using strategies and methods with good adaptation to the type of problem.

Pupils describe their approach in a well functioning way, and apply well developed and well informed reasoning about the plausibility of results in relation to the problem situation, and can make proposals on alternative approaches.

Pupils have very good knowledge of mathematical concepts and show this by using them in new contexts in a well functioning way.

Pupils can also describe different concepts using mathematical forms of expression in a well functioning way.

In the descriptions, pupils can switch between different forms of expression and also apply well developed reasoning over how the concepts relate to .

Pupils can choose and apply appropriate and effective mathematical methods with good adaptation to the context to carry out simple calculations, and solve simple routine tasks in arithmetic, algebra, geometry, probability, statistics, and also relationships and change with very good results.

Pupils can account for and discuss their approaches in an appropriate and effective way and use diagrams, symbols, tables, graphs and other mathemati cal forms of expression with good adaptation to the context.

In their accounts and discussions, pupils can apply and follow mathematical reasoning by putting questions, putting forward and responding to mathematical arguments in a way which takes the reasoning forward and deepens or broadens them.

Core concepts

Core questions

w. 2

Week 2 Lesson 1: Intro to Algebra

Objectives: The students will begin to learn Algebra. For this lesson they will focus on using letters as numbers. Identify the unknowns in an equations.

*You can use algebra to write an expression that describes how one amount compares with another amount

This video can be used to explain why we use letters in Algebra https://www.khanacademy.org/math/algebra-home/alg-intro-to-algebra/alg-overview-of-algebra/v/why-all-the-letters-in-algebra

The main focus on this lesson is to get the class used to using letters to represent variables and to write word problems as expressions.

Ask for different ways that we can write a variable. Explain to students that e shouldn’t be used and do not use x to show multiplication.

2 ¤ x This expression can be simplified to 2x

Now teach the students to find the missing number:

____ - 2 = 4

The answer is 6, because 6 − 2 = 4.

Well, in Algebra we don't use blank boxes, we use a letter (usually an x or y, but any letter is fine). So we write:

x - 2 = 4

It is really that simple. The letter (in this case an x) just means "we don't know this yet", and is often called the unknown or the variable.

And when we solve it we write:

x = 6

Example Algebra Word Problems: https://www.ixl.com/math/grade-6/write-variable-expressions-word-problems

Example Problems writing an expression: http://www.math-aids.com/cgi/pdf_viewer_2.cgi?script_name=pre-algebra_translate.pl&easy=1&language=0&memo=&answer=1&x=111&y=43

Examples in textbook:

Worksheet https://www.superteacherworksheets.com/algebra/basic-algebra2.pdf

Harder Examples: http://www.math-aids.com/cgi/pdf_viewer_12.cgi?script_name=pre-algebra_translate.pl&medium=1&language=0&memo=&answer=1&x=104&y=35

Week 2 Lesson 2: Simplifying Expressions

Objectives: The main focus on this lesson is to have students combine like terms (terms that have the same letter) and expanding brackets.

Video:https://www.khanacademy.org/math/algebra/introduction-to-algebra/alg1-manipulating-expressions/v/combining-like-terms

Start by asking what they think x + x equals. See how the class answers this question. If no one brings it up ask the class how you can quickly add the same number repeatedly. Hopefully this will make students think about multiplication.

You may have to remind students how to add negative numbers again.
Show the problem 2(a + 4). Ask the class what they think this expression means. Talk about and explain that it is 2 sets of a + 4 or 2
a + 2 4 or 2a + 8.

Examples:

v + 5v + v - v

Explain that in this expression there are 4 like terms so we can actually add/subtract them.

6 – 7b + 1 + b

Explain that in the expression above there are 2 pairs of like terms.

(+6, +1)

(-7b, +b)

Let’s don’t forget that the sign in front of the variable is attached with the variable!

Work In Class:

KS3 Book

Page 65

Q. 4 - 8

Worksheet: http://www.math-aids.com/cgi/pdf_viewer_2.cgi?script_name=pre-algebra_simplifing.pl&two_add_sub=1&three_add_sub=1&four_add_sub=1&three_multi=1&four_multi=1&n_range=0&language=0&memo=&answer=1&x=112&y=16

Extra Practice: http://www.homeschoolmath.net/worksheets/table-simplify-expressions.php?col=2&row=7&like=1&level1=1&mincoeff=-10&maxcoeff=10&minconst=-10&maxconst=10&decimals=0&workspace=3&font=Arial&FontSize=14pt&pad=10&border=on&ptitle=&PDF_worksheet=1

Week 2 Lesson 3: Solving Expressions

Objective: This lesson will have students solving expressions. They will be given a value for 1 or more of the variables in the expression.

Review writing expressions from words.

Be able to write expressions from the following phrases:

A number + 5 = (n + 5)

14 minus a number = (14 - n)

a number multiplied 9 times = (9n)

a number divide by 6 = (n/6)

a number multiplied by 4 minus 2 (4n - 2)

This time give them a value for n (ex. n = 12). What would each of these problems equal?

Work In Class:

KS3 Books

Page 69; Q. 3 & 4

Page 70; Q. 5 - 9

Worksheet: http://www.math-aids.com/cgi/pdf_viewer_2.cgi?script_name=pre-algebra_eval_one.pl&two_add_sub=1&two_divid=1&n_type=0&language=0&memo=&answer=1&x=159&y=29

Week 3 Lesson 1: Multiplying and Dividing Variables

Lesson:

This lesson will focus on reviewing last week's content (constructing expressions, simplifying expressions, expanding brackets) and introducing multiplying and dividing variables.

MULTIPLYING VARIABLES

Ex 1: Multiplying different variables:

b x h = bh
the variables are written beside each other which tells us they are being multiplied together

Ex 2: Multiplying the same variables:

b x b = b2 (b squared)
you simply add the exponential values together
when a variable doesn't have an exponent that means it is to the power of 1
b3 x b5 = b8 (because 3 + 5 = 8)

Video explanation

DIVIDING VARIABLES

Ex 1: 25b / 5 = 5b

All you need to do is divide the coefficient (the number in front of the variable b) by 5.

Ex: b5 / b3 = b2

We are only going to focus on dividing terms with the same variables
You just need to take the exponential value of the first term and divide it by the exponential value of the second term (5 - 3 = 2, so the answer is b2)

Work In Class:

Textbook: Page 74 (Q. 5 - 20). Page: 81, 82, 83, 84, 85
Distribute Property with Multiplying Variables

w. 3

Week 3 Lesson 2: Solving Equations (One-step)

Lesson:

Equations contain an equal sign. The focus of this lesson is to isolate the variable on one side of the equation.
The can be done by using the ‘change side, change sign’ rule.
We inverse (opposite) operations to cancel out the terms on the side with the variable. Whatever you do to one side, you must also do to the other side.

Ex 1:

a + 2 = 10
a = 10 - 2
a = 8

Work in Class:

One Question each time (Khan Academy)
Adding and Subtracting: Worksheet
Multiplying and Dividing: Worksheet

Support:

Show this video to students (Khan Academy)

Extension:

Worksheet

Week 3 Lesson 3 - Solving Equations (Two-Step)

Lesson:

This lesson will be a continuation of the last lesson but will progress to two-step equations.

Example: 2a + 5 = 13

Subtracting 5 fro both sides: 2a = 13 - 5
Divide both sides by 2: 2a = 8

Answer: a = 4

Work in Class:

Worksheets

Extension:

Worksheet
2 step worksheet (mixed operations)

Week 3 Lesson 4 - Review

We will be reviewing all the content that was covered this week

Week 4: Lesson 1- Substituting Expressions

Lesson Objective: Students will be solving expressions. They will be given a value for 1 or more of the variables in the expression and follow the steps to solve.

Review writing expressions from words.

Be able to write expressions from the following phrases:

A number + 5 (n + 5)

14 minus a number (14 - n)

a number multiplied 9 times (9n)

a number divide by 6 (n/6)

a number multiplied by 4 minus 2 (4n - 2)

This time give them a value for n (ex. n = 12). What would each of these problems equal?

Worksheet: http://www.mathworksheets4kids.com/algebra/evaluating-expressions/single-variable-medium2.pdf

Harder Worksheet: http://www.mathworksheets4kids.com/algebra/evaluating-expressions/single-variable-hard3.pdf

Work In Class:

KS3 Books

Page 69; Q. 3 & 4

Page 70; Q. 5 - 9

w. 4

Week 4: Lesson 2: Substituting Formulae

Lesson Objective: Students will be substituting into formulas and solving for the amount of variables.

Examples:

Work out the value of P. If n = 6

P = 3n

P=3(6)

P= 18

Find the value of y when x = 9

y = 5x – 3

y = 5(9) - 3

* Remember to follow order of operations

y = 45 -3

y = 42

Examples: http://www.mathsgenie.co.uk/resources/32_substitution.pdf

Week 4: Lesson 3- Word Problem Practice

Lesson Objective: Have students practice learned algebra skills in the form of real life word problems

Solving one step problems: http://www.math-aids.com/cgi/pdf_viewer_12.cgi?script_name=algebra1_equations_one_word.pl&fnums=0&xinfo=2&language=0&memo=&answer=1&x=111&y=28

Solving two step problems: http://www.math-aids.com/cgi/pdf_viewer_12.cgi?script_name=algebra1_equations_two_word.pl&fnums=0&language=0&memo=&answer=1&x=110&y=27

Mixed word problems: http://www.dadsworksheets.com/worksheets/pre-algebra-word-problems/mixed-pre-algebra-word-problems-hard-v3.html

Week 4: Review

Lesson Objective: Review topics related to what the students have learned in the algebra unit so far.

This can be used as a basic algebra review: https://www.superteacherworksheets.com/algebra/basic-algebra8_TTZZF.pdf?up=1466611200

writing expressions: https://cdn.kutasoftware.com/Worksheets/Alg1/Variable%20and%20Verbal%20Expressions.pdf

combining like terms: https://cdn.kutasoftware.com/Worksheets/Alg1/Combining%20Like%20Terms.pdf

distributive property: https://cdn.kutasoftware.com/Worksheets/Alg1/Distributive%20Property.pdf

Two Step equations: https://cdn.kutasoftware.com/Worksheets/Alg1/Two-Step%20Equations.pdf

Substituting values into expressions: http://blackville.nbed.nb.ca/sites/blackville.nbed.nb.ca/files/noteattach//y2016/Oct/sub_the_x_value_into_expression.pdf

Week 5: Lesson 1: Statistical Averages

Objective (Teaching Point):

Find the mode and range of a small set of discrete data
Find the modal class for a small set of grouped discrete data
Calculate the mean and median for a small set of discrete data
Calculate the mean from a simple frequency table

Lesson:

We will be working on a new unit starting today.

First define the following words: mean, median, mode and range.

Mean:

The mean is the average of the numbers: a calculated "central" value of a set of numbers.

To calculate: Just add up all the numbers, then divide by how many numbers there are.

Ex: what is the mean of 2, 7 and 9?

Add the numbers: 2 + 7 + 9 = 18

Divide by how many numbers (i.e. we added 3 numbers): 18 ÷ 3 = 6

So the Mean is 6

Median:

The middle number (in a sorted list of numbers).

To find the Median, place the numbers you are given in value order and find the middle number.

Example: find the Median of {13, 23, 11, 16, 15, 10, 26}.

Put them in order: {10, 11, 13, 15, 16, 23, 26}

The middle number is 15, so the median is 15.

(If there are two middle numbers, you average them.)

Mode:

The number which appears most often in a set of numbers.

Example: in {6, 3, 9, 6, 6, 5, 9, 3} the Mode is 6 (it occurs most often).

Range:

The difference between the lowest and highest values.

In {4, 6, 9, 3, 7} the lowest value is 3, and the highest is 9, so the range is 9 − 3 = 6.

Make sure that every student copies these in their notebooks. The Swedish translations are the following:

Mean - Medelvärde
Median - Median
Mode - Typvärde
Range - Värdemängd

A good strategy is to list the numbers from the least to the latest. That will make sure that don’t skip any and make finding the range, mode and median easier. Cross them off as you use them.

Work In Class:

Page 11 (Range & Median)

Q. 1 - 11

Page 14 - 16

Q. 1 - 14

Use this website for more work.

Support:

Watch these videos

Extension:

There are addition problems here.
For more difficult sets of numbers use this worksheet.
challenge problems

Conclusion:

Review the following terms and how to find them:

Mean
Median
Mode
Range