Planering 5A/5B - Matematik Blueprint

Vad vi kommer jobba med:

Number Sense (Fractions and Decimals): Decimal and Number systems, introduction and review of fractions, positive and negative numbers, using all operations to solve calculations using decimal numbers.

Week 47: Checkpoint: Lesson 3 Friday

Week 48: Assessment: Lesson 3 Friday

Centralt innehåll

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.

Fractions and decimals

Numbers in fractions and decimals and their use in everyday situations.

Percentage

Numbers in percentage form and their relation to numbers in fraction and decimal form.

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.

Mathematical problem solving

Strategies for mathematical problem-solving in everyday situations

Mathematical questions

Mathematical formulation of questions based on everyday situations.

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v. 40

Week 40: Lesson 1: Introduction to the Decimal System

Decimal Numbers (decimatal)

Decimal numbers (decimatal) are numbers with parts of a whole number.

Review Place Value names and introduce new terms

Tenths - Tiondelar

Hundredths - Hundradelar

For example: 4 is a whole number, but 4.5 is not. We use a decimal in it to show the remaining part of the next whole number. So 4.5 is halfway between 4 and 5.

Students will order and compare decimal numbers.

Week 40: Lesson 2: Ordering and Comparing Decimals

Review place value terms from last lesson.

Students will have times to practice ordering decimal numbers from least to greatest as well as comparing decimals using the greater than and less than symbols.

This lesson, students will also learn to place decimal numbers on a number line. Understand the values of the decimal numbers will be very important for this lesson.

Week 40: Lesson 3: Rounding Decimal Numbers

This lesson we will discuss the rules for rounding. When your digit is 4 or less you round down. When the digit is 5 or greater you round the number up. This rule still applies for decimals as it does for whole numbers. We will practise rounding to the nearest whole number as well as to the nearest tenth.

Students may use number lines from the previous lesson to help them round the decimal numbers.

v. 41

Week 41: Lesson 1: Introduction to Fraction and Decimal Equivalents

Review Rounding Decimal numbers to the nearest whole number and tenth. Introduce a few examples of rounding to the nearest hundredth as well. The rules for rounding stay the same as with whole numbers.

Main input:

Students will be able to show understanding of fraction and decimal equivalents.

What is a fraction?

A fraction is a number that shows equal parts of a whole number or group.

It is made up of two parts, the numerator (täljare) and denominator (nämnare)

The denominator is how many total parts there are and the numerator shows how many parts we are discussing.

Week 41: Lesson 2: Calculate Fraction and Decimal Equivalents

Review writing fractions with denominators that are not 10 or 100

Last lesson we converted simple fractions of tenths and hundredths to decimals e.g. 1/10 = 0.1

In today's lesson we will convert more complex fractions and decimals.

How do you convert fractions to decimals?

Using a calculator, divide the numerator by the denominator.

If the decimal has many digits, round it to the nearest hundredth.

We will be using manipulatives during the lesson to visually display the calculations.

Regional All Staff Conference

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v. 42

Week 42: Lesson 1: Adding and Subtracting Decimals

Review steps for adding and subtracting whole numbers.

How do we add or subtract decimal numbers?

To solve these types of problems we will be using column addition or subtraction (med uppställning). It is important to line up the place values. The decimal helps us to line up the numbers correctly. Use the decimal to line up the units, tenths (tiondelar) and hundredths (hundradelar).

e.g.

2, 45

+ 1, 30

-------------

3, 75

Week 42: Lesson 2: Multiplying with Decimals

Review column multiplication (med uppställning)

When multiplying decimal numbers, we use the exact same method to multiply. When we have solved the problem, simply count how many digits are to the right (or behind) the decimal. In your final answer there must be the same amount of digits behind the decimal.

E.g.

Week 42: Lesson 3: Division with Decimals

Review steps for long division.

When we divide decimal numbers, the decimal place simply moves above the same place on the division line. Then we solve using the same original steps: divide, multiply, subtract, and bring down the next number. Now, if there is a remainder, we simply add a zero into the dividend and continue dividing until we reach zero remaining.

e.g.

v. 43

Week 43: Lesson 1: Continue Division with Decimals

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Week 43: Lesson 2: Review of Operations with Decimals

v. 44

Autumn Break

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Autumn Break

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Autumn Break

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v. 45

Week 45: Lesson 1: Working with Decimals and Mixed Operations

In this lesson, students will review using a range of operations with decimal values. We will review decimal place values, ordering, rounding and comparing decimals, as well as adding, subtracting, multiplying and dividing decimal numbers.

Students will also practise solving word problems involving decimal numbers.

Use RUCSAC to help you remember the steps to solving word problems:

Week 45: Lesson 2: Introduction to Percentages

In this lesson, students will learn to convert decimal numbers to percentages.

per cent means "of one hundred"

To convert a decimal to a percent, we must multiply the number by 100.

Week 45: Lesson 3: Percentages

In this lesson, students will review how to convert fractions to decimals. We will also practise converting between fractions, decimals, and percentages.

Multiply the denominator to make 10 or 100, multiply the numerator by the same number. Then move the decimal place.

You can also use long division:

Then simply multiply your number by 100 to find the percent.

We will also learn how to find the percent of a number. When we want to find a percentage from a total, we have to convert the percentage to a decimal number (divide by 100) and then multiply it by the amount. Example: what is 10% from 50, Convert 10 to ,1 and then multiply ,1 x 50 = 5

v. 46

Week 46: Lesson 1: Fractions as Division

Students will practise dividing proper and improper fractions to find decimal numbers. We will continue to practise converting these numbers to percentages as well to consolidate the methods before the checkpoint.

Week 46: Lesson 2: Introduction to Equivalent Fractions

Equivalent fractions are two fractions that are equal to one another e.g. 2/10 and 1/5

We need to multiply the numerator and denominator by the same number to find an equivalent fraction.

$Image result for equivalent fractions$

Week 46: Lesson 3: Equivalent Fractions

Students will review concepts from the last lesson, creating equivalent fractions.

We will use this idea of multiplying to make an equivalent fraction to order and compare fractions.

If the fractions have a common denominator, we simply use the numerator to order the numbers:

$Image result for ordering fractions$

If the fractions do not have a common denominator, we must use our knowledge of multiples, multiply the numerator and denominator by the same number to create a common denominator, to see which number is larger:

v. 47

Week 47: Lesson 1: Checkpoint Review

In this lesson,

Students will review the following topics from this unit:

ordering and comparing decimal numbers
rounding decimals to the nearest tenth and hundredth
adding and subtracting decimal numbers

** The rule for adding and subtracting decimal numbers is to line up the decimals and use column addition or subtraction for each place value.

Image result for adding and subtracting decimals

Week 47: Lesson 2: Checkpoint Review

In today's lesson, students will review the following topics from the unit:

multiplying and dividing decimals
converting fractions, decimals and percentages
finding percentages of amounts

Image result for percentages of amounts example

Week 47: Lesson 3: Checkpoint

The checkpoint will cover topics from the entire unit. It will be used to find which areas of the unit students require more practise and clarification before the assessment.

Topics will include:

ordering and comparing decimal numbers
rounding decimals
using decimal numbers in all basic operations
converting fractions, decimals and percentages
finding percentages of amounts
finding equivalent fractions
solving word problems

v. 48

Week 48: Lesson 1: Checkpoint Review

We will discuss the methods and solutions to the questions on the checkpoint. From this we will see the areas with misconceptions.

Students will be asked to correct any mistakes from their checkpoint and use them as a guide to study for the upcoming assessment.

Week 48: Lesson 2: Assessment Review

In this lesson, students will have the opportunity to solve a range of questions reviewing topics from the whole unit.

Week 48: Lesson 3: Assessment

Number Sense (Fractions and Decimals): Decimal and Number systems,

Topics will include:

ordering and comparing decimal numbers
rounding decimals
using decimal numbers in all basic operations
converting fractions, decimals and percentages
finding percentages of amounts
finding equivalent fractions
solving word problems