Planering 6C/6D - Matematik Blueprint

What we will be doing:

We will be reviewing the 4 basic operations:

Addition
Subtraction
Multiplication
Division

as well as the variety of methods used to solve problems involving them.

We will then learn about the topic of Order of Operations and how to solve problems with more than one operation.

Once we have reviewed this material we will incorporate these skills with Decimals and Negative Numbers.

Core content

Rational numbers

Rational numbers and their properties.

Positioning system

The positioning system of numbers in decimal form. The binary number system and number systems used in some cultures through history, such as the Babylonian.

Calculations

Main methods of calculating using natural numbers and simple numbers in decimal form when calculating approximations, mental arithmetic, and calcu lations using written methods and calculators. Using the methods in different situations.

Plausibility

Plausibility assessments when estimating and making calculations in everyday situations.

Abilities

Knowledge requirements

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

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.

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 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.

Core concepts

Core questions

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w. 34

Week 34 - Lesson 1 - Introduction and Diagnostic Test (NP)

We will be introducing the course as well as performing a diagnostic assessment to see their knowledge of past material.

Week 34 - Lesson 2 - Addition and Subtraction (NP)

Addition and subtraction review and application

Week 34 - Lesson 3 - Multiplying and Dividing by 10/100/1000 (NP)

We will be going over placeholders and what happens to the digits in a number when multiplied and divided by 10/100/1000

Here is the slideshow from the lesson:

https://docs.google.com/presentation/d/1U-Hn8Y93Ak0MimpSqpznsF5b9SPdxW1--3GP1KGEArM/edit?usp=sharing

Week 34 - Lesson 4 - Review and Word Problems

We will review the content from the past week and apply our knowledge to word problems.

w. 35

Week 35 - Lesson 1 - Written Multiplication (NP)

Multiplying (written multiplication)

Learning intention: to remember the times tables and learning how to multiply bigger numbers

Success criteria: by the end of this lesson we will all be able to multiply two-digit by two-digit numbers

Click here for the steps (powerpoint)

Extension: KS3 Maths progress (Pi one); Unit 5.3; Page 115 - 117.

Week 35 - Lesson 2 - Division (NP)

Learning objective: being able to divide using the bus stop method

Steps (powerpoint)

Week 35 - Lesson 3 - AW

Learning Objective: being able to solve problems using division. Such as the bus stop method.

Example:

159 divided by 3

-3 does not go into 1, remainder of 1

-3 goes into 15, 5 times, no remainder

-3 goes into 9, 3 times, no remainder

the answer is 53.

Week 35 - Lesson 4 - Review and Word Problems

We will be reviewing the content from this work and apply our knowledge to word problems.

w. 36

Week 36 - Lesson 1 - Order of Operations (NP)

Teaching Point: To understand and practice solving equations using the order of operations with brackets.

Math Message:

How would you solve the following equation? Write down the steps you took to solve it and share your work with a partner. (3 x 7) + 3 =

Why is it important to follow an order in math?
What would happen if we did not solve what was in the brackets first?
Is it possible for people to get different answers?

Lesson:

We are going to review a type of recipe for solving math equations called the order of operations

The Steps:

PEMDAS:

Parentheses
Exponents
Multiplication
Division
Addition
Subtraction

Things to remember:

Begin with parentheses and work your way down the list of operations to solve the equaton. If the equation does not have an operation then continue down the list.

Ex: 9 x 2 + 4

§ There are no parentheses or exponents so then move on to multiplication

Multiplication and division can change in the order as well as addition and subtraction. Determine which one goes operations goes first by simply reading the equations from left to right, performing whichever comes first.

Ex: 3 x 4 ÷ 6 =

multiplication comes first, then division
= 12 ÷ 6
= 2

Practice:

Students can follow along with this site to practice and solve equations
Order of operations practice worksheet
Additional Practice

Week 36 - Lesson 2 - Order of Operations Cont. (NP)

Starter:

Insert brackets into the following equation to make the biggest answer possible: 50 / 2 - 3 x 4 + 6

Shows the importance of following the steps to PEMDAS and moving from left to right when solving an equation

Lesson:

Review steps: PEMDAS (Parentheses, Exponents, Multiplication, Division, Addition, Subtraction)
We will begin to work with equations with more operations, building on our knowledge from last class.
Worksheet to practice with more order of operations

If they can master the following questions:

9 + 2 x 5 - 11
(3 + 4) x (4 - 3)
14 x (15 - 7 + 4)
2 + 9 x 6
18 / (3 x 6 - 9) x 3
3 + 4 x 4 - 3

Then you can do harder questions, for example:

7. 16 / 8 + 2 x 5 - 21 / 7

8. (18 / 3 + 28 / 4 + 2 x 4) / 3

9. 2 + 15 / 3 - 2 x 3 + 10

10. 3 x (24 / 2 - 3 x 4 + 2 x 6)

Various Difficult Order of Operation Problems

Week 36 - Lesson 3 - Adding and Subtracting Decimals (NP)

Objective: to learn how to add and subtract decimals

Lesson:

What numbers would you add to the following numbers to make 10?

o 5,5

o 3,7

o 8,6

o 4,2

· What decimal can be added with each of these to make 1?

o 0,41

o 0,91

o 0,35

o 0,82

What method could you use to solve these questions?

1. 1,7 + 1,577 =

2. 31,745 – 1, 75 =

The column method is used for solving any addition or subtraction questions, placing the numbers in the same units above each other.

Example

In a science lesson, a pupil adds 0.45 kg of water and 0.72 kg of salt to a beaker that weighs 0.09 kg. He then pours out 0.6 kg of the mixture, followed by another 0.14 kg. What is the total mass of the beaker and mixture remaining?

Set out the calculation: 0,45 + 0,72 + 0,09 - 0, 6 - 0,14

First do all the additions together (remember to regroup if needed):

0.45

0.72

+ 0.09

1.26

Then do the subtractions one at a time (remember to borrow if needed):

1.26 0.66

- 0.6 - 0.14

0.66 0.52

So the final answer is 0.52 kg or 520 grams

Practice:

Textbook: Pg. 147-148

Week 36 - Lesson 4 - Rounding (NP)

Objective: to be able to round to the nearest 10, 100, 1000, tenths, hundredths, thousandths

Lesson:

Reviewing of place value and the importance of looking to the right of the digit you are rounding
Review rounding rules: 5 and above round up, 4 and below round down (rounding chart for further review)
Basic review practice worksheet
Complete questions in the textbook pg. 149-150 for more practice

Conclusion:

Round 5432,82 to the nearest thousand, hundred and tenth.

w. 37

Week 37- Lesson 1 - Multiplying Decimals

Lesson Objective: The students will be able to multiply whole numbers by decimals and multiply decimals by decimals.

Go over the multiplying principles and terms:

You can multiply numbers in any order (not like division)
When you multiply by 0, the product is 0.

The students will multiply using the column method and determine how to put the decimal in the correct place.

You can begin in the textbook with problems 4 and 5 on page 151-152. Problems 6 and 7 are real life examples using word problems.

Week 37 - Lesson 2 - Dividing Decimals

Objective: Students will be able to divide decimal numbers.

The first part of this lesson will focus on dividing decimal numbers. Set up the decimal problem normally. The decimal number should be either "inside the bus stop" or on top of the fraction. When you reach the decimal point in the dividend place a decimal point directly above in the answer (quotient). This will keep things organised. When solving as a fraction once you reach the decimal point, add a decimal point to the answer. Otherwise, the problems are solved exactly like a normal division problem.

Practice problems in the textbook: Pages 152-153 #8-11.

Use the "Level Up" book for examples. On page 144 and 145 in section 9.6, problem numbers 3, 5, 6 and 7 you can find examples.

Level Up problems

The second part of this lesson will be dividing by decimal numbers or decimals as the divisor. Multiply both the divisor and dividend by 10, 100 or 1000 until they are both whole numbers. Then solve as normal. These types of problems are in the "Level Up" book on page 145 in section 9.6, problem numbers 8 and 9.

Level Up problems

Week 37 - Lesson 3 - Adding and Subtracting Negative and Positive Numbers.

Objective: Students will be able to add and subtract negative and positive integers.

This lesson will serve as an introduction to integers. Students will compare, order, and describe real-life situations using positive and negative whole numbers. The concepts of opposites and vertical as well as horizontal number lines are addressed.

Students will use a number line to solve problems such as...

8 - 9
0 - 4
-3 - 5
-2 + 7

Example problems can be found in the textbooks on page 45-46

https://docs.google.com/document/d/1uji3SdInK-5YKttA2zn4ZLB3eQJ2bBdqiQMw3ZMp2kc/edit

This integer investigation can be used for further help and explanation.

http://teachersites.schoolworld.com/webpages/TAhrens/files/Adding%20and%20Subtracting%20Integers.pdf

More examples and practice.

Week 37 - Lesson 4 - Adding and Subtracting Negative and Positive Numbers Continued.

Objective: Students will be able to add and subtract negative and positive integers.

In this lesson we will review how to add/subtract positive and negative integers and start to include more details such as when we add or subtract positive and negative numbers with double sign.

Adding and subtracting with a double sign means...

+ - = -
- + = -
+ + = +

- - = +

Have the students copy this in their notebooks and ask if they notice any patterns.

When you have two of the same signs they make a positive

When you have two different signs they make a negative.

Examples:

3 + ( - 5)

- 4 - ( - 6 )

9 - ( + 4 )

12 - ( - 7)

10 - ( -3 + 8)

https://docs.google.com/presentation/d/11paZrY8f1I6nDo3MmPe_V-ffYgZ5BF6bgmgyS_InFnY/edit#slide=id.p10

More examples and practice can be found on this document.

w. 38

Week 38 - Lesson 1 - Multiplying and Dividing Negative Numbers

Learning Intention:

To understand how to multiply and divide negative numbers

Lesson:

When multiplying and dividing negative numbers look at the signs before both numbers. If they are different signs then the answer will be a negative number. If the signs are the same then the answer will be a positive number.

Rules:

1. (+ -)= -

2. (- +) = -

3. (- -) = +

4. (+ +) = +

Examples:

1) -6 x 2 = -12

one number is negative (-6) and the other is positive (2) so the answer is a negative number (-12)

2) -2 x -5 = 10

both numbers are negative so the answer is a positive number

3) 21 / -3 = -7

one number is positive (21) and the other is negative (-3) so the answer is a negative (-7)

4) -8 / -2 = 4

both numbers are negative so the answer is a positive number

Practice

Worksheet: Click here

Week 38 - Lesson 2 - Order of Operations with Negatives

Lesson Intention:

To be able to solve order of operations questions with negatives numbers

Lesson:

We will review order of operations:

Brackets or Parentheses
Exponents
Dividing
Multiplication
Addition and Subtraction

Then we will proceed to incorporate negative numbers:

Ex/

(-2 + 4 x 8) x -2

= (-2 + 32) x -2

= 30 x -2

= -60

Starter:

1. 7- (-2) =

2. -3 + (-5) =

3. 9 x -8 =

4. -56 / 7 =

5. 55 - (-18) =

6. -34 +17 =

7. -18 x 9 =

8. 275 / -5 =

Week 38 - Lesson 3 - Order of Operations with Negative Numbers and Decimals

Lesson Intention:

To be able to solve order of operations questions with negatives numbers

Lesson:

We will review order of operations:

Brackets or Parentheses

Exponents

Dividing

Multiplication

Addition and Subtraction

Then we will proceed to incorporate negative numbers:

Ex/

(-2 + 4 x 8) x -2

= (-2 + 32) x -2

= 30 x -2

= -60

Week 38 - Lesson 4 - Review

This lesson will be used to review previous material.

w. 39

Week 39 Lesson 1: Square Numbers and Simple Roots

Learning Objective: Students will learn how to square numbers and how to find the square root of numbers.

Square Number - the product of a number multiplied by itself, e.g. 1, 4, 9, 16.
Square Roots - a number which produces a specified quantity when multiplied by itself.

These can be related to exponents since we have talk about them in PEMDAS

Project a 10 x 10 multiplication table on the whiteboard. Circle the row of squares. Ask the class what do the circled numbers have in common.

Be sure to include how to find a number’s square root on the calculator. Press the "square root key" then type in the number and finally press "enter"

Practice worksheet...

https://drive.google.com/drive/folders/0BxLGn7H4O_2-YlA1RC0yNW9LN3M

Additional Practice...

file:///home/chronos/u-d9f8b07bcb74e5eadfb8e45ae3646bb58c1e1a92/Downloads/Square%20Numbers%20_%20Square%20Roots%20by%20fionajones88%20-%20UK%20Teaching%20Resources%20-%20TES%20(1).mhtml

Week 39 Lesson 2: ORIENTEERING

The students will not be in class due to Orienteering day.

Week 39 Lesson 3: Checkpoint

The students will complete a checkpoint exam to prepare before the test during week 40.

Skills that will be focused on during the checkpoint will be...

-Adding and Subtracting

-Multiplying and Dividing

-Decimals

-Rounding

-Order of Operations

-Negative Numbers

-Square Numbers and Simple Roots

Week 39 Lesson 4: Review of Checkpoint and Skills

Lesson Objective: The students will review their checkpoints

The students will correct their checkpoints and practice skills that will be on the test.

Skills that will be focused on...

-Adding and Subtracting

-Multiplying and Dividing

-Decimals

-Rounding

-Order of Operations

-Negative Numbers

-Square Numbers and Simple Roots

w. 40

Week 40 - Lesson 1

Review for the test

Week 40 - Lesson 2

Review for the test.

Numbers

What we will be doing:

Core content

Abilities

Knowledge requirements

Core concepts

Core questions

Week 34 - Lesson 1 - Introduction and Diagnostic Test (NP)

Week 34 - Lesson 2 - Addition and Subtraction (NP)

Week 34 - Lesson 3 - Multiplying and Dividing by 10/100/1000 (NP)

Week 34 - Lesson 4 - Review and Word Problems

Week 35 - Lesson 1 - Written Multiplication (NP)

Week 35 - Lesson 2 - Division (NP)

Week 35 - Lesson 3 - AW

Week 35 - Lesson 4 - Review and Word Problems

Week 36 - Lesson 1 - Order of Operations (NP)

Week 36 - Lesson 2 - Order of Operations Cont. (NP)

Week 36 - Lesson 3 - Adding and Subtracting Decimals (NP)

Week 36 - Lesson 4 - Rounding (NP)

Week 37- Lesson 1 - Multiplying Decimals

Week 37 - Lesson 2 - Dividing Decimals

Week 37 - Lesson 3 - Adding and Subtracting Negative and Positive Numbers.

Week 37 - Lesson 4 - Adding and Subtracting Negative and Positive Numbers Continued.

Week 38 - Lesson 1 - Multiplying and Dividing Negative Numbers

Week 38 - Lesson 2 - Order of Operations with Negatives

Week 38 - Lesson 3 - Order of Operations with Negative Numbers and Decimals

Week 38 - Lesson 4 - Review

Week 39 Lesson 1: Square Numbers and Simple Roots

Week 39 Lesson 2: ORIENTEERING

Week 39 Lesson 3: Checkpoint

Week 39 Lesson 4: Review of Checkpoint and Skills

Week 40 - Lesson 1

Week 40 - Lesson 2

Coming soon