Planering 6C/6D - Matematik Blueprint

What we will be doing:

We will be learning about

Interpreting Graphs

Averages

Extracting Data (mode, charts)

Making Graphs and Interpreting Graphs

Probability in Words and Numbers

Planning Data Collection

Core content

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.

Probability

Probability, chance and risk based on observations, experiments or statistical material from everyday situations. Comparisons of probability in different random trials.

Combinatorial analysis

Simple combinatorial analysis in concrete situations.

Tables and diagrams

Tables and diagrams to describe the results of investigations. Interpretation of data in tables and diagrams.

Measures of central tendency

Measures of central tendency - average, mode and median and how they are used in statistical investigations.

Abilities

formulate and solve problems using mathematics and also assess selected strategies and methods,

use and analyse mathematical concepts and their interrelationships,

choose and use appropriate mathematical methods to perform calculations and solve routine tasks,

apply and follow mathematical reasoning, and

use mathematical forms of expression to discuss, reason and give an account of questions, calculations and conclusions.

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 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.

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

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

w. 5

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

Week 5: Lesson 2: Interpreting Graphs

Objective (Teaching Point):

Organize data using a tally chart / frequency table
Understand and use frequency tables.
Understand and draw a bar chart
Interpret pictograms

Frequency tables

Here is a clip introducing tally charts.
We will construct a tally chart together on the board
The tally chart on the board will have three labelled columns - 'categories', 'tally' and 'total' as well as a title.
Once we complete it as a class the students will be asked to complete their own.

Bar charts

Make sure students understand how to read a bar graph. You can make your own bar graph here.
Or display this bar graph to explain how it can be read.
Before continue, ask if anyone else has any questions on either bar graphs or frequency tables. If no one has any questions work in small groups to complete the rest of the section.

Pictograms

Display this pictogram and analyze it will the class

Work In Class:

Textbook: Page 6, 7, 8 #Q. 1 - 6

Activity

Play the Bitesize Interpreting data activity. The students can fill in the tally/frequency chart, bar chart and pictogram on the activity.

Extension

Ask the children to work through the Bitesize interpreting data quiz or to complete the interpreting data worksheet (PDF 65KB).

Week 5: Lesson 3: Interpreting Graphs: Part 2

Objective (Teaching Point):

Construct and interpret bar-line graphs
Construct and interpret compound bar charts
Construct and interpret dual bar charts

Lesson:

Explain the three types of charts we will be working with today: Line Graphs, Compound Bar Charts, Dual Bar Charts

Line Graph

Display this worksheet on the board and ask them to answer the questions. Discuss.
Romme Alpin - Ski centre - WEATHER (Discuss) Click on 5-day forecast
Another worksheet - Harder

Compound Bar Charts

A compound bar chart combines sets of information on one bar chart.
Do the first one as example on the board. Ask them to construct the graphs 2 & 3. Discuss.

Dual Bar Charts

Here, you can give them the information to construct the bar graph and hence answer the questions.

Work In class

Construct a double bar graph.

Extension:

Ask them to be creative and create their own question / problem and after that construct a bar chart.

Conclusion:

Students should know the difference between line graphs, compound bar charts, and dual bar charts. They should be able to read and interpret each type of graph, and they should be able to construct these graphs after being given data in a frequency table.

Week 5: Lesson 4: Pie Charts

Objective (Teaching Point):

Interpret pie charts using knowledge of fractions and percentages

Lesson:

Begin by explaining pie charts and how the sections within a pie chart always add up to 100% if dealing with percentages, or add up to 1 if dealing with fractions. Draw this on the board so they can visualize it. Start by drawing a line through the centre of the pie chart to show 50% (½) of the chart. Draw another line to further divide the pie chart into 4 equal sections of 25% (¼ each).

Now draw another pie chart on the board with 10 equal parts. Ask them what percentage each section represents. What fraction? Shade in 4 of the sections and ask them what it now represents.

Hand out this worksheet and make sure they understand that 30 students voted for their favorite field trip. The graph shows the percentage of students that voted for each field trip, so they will need to figure out the number of students based on the percentages. Start with the Nature Preserve; it has 50% of the votes. They should easily deduce that 15 out of the 30 students voted for the nature preserve. Let them try to figure out the rest themselves, but go over the questions at the end.

Students can try this worksheet when they are done.

w. 6

Week 6: Lesson 1: Probability

Lesson Objective: Understand and use the probability scale, be able to list all of the possible outcomes of an event, and find the probability of equally likely outcomes.

Intro:

What Is probability?

Probability is the study of random events. The theory of probability is an important branch of mathematics with many practical applications in the physical, medical, biological and social sciences. An understanding of this theory is essential to appreciating weather reports, medical findings, political doings and the state lotteries.

Probability: the chance or possibility that something will happen or the measure of likeliness that something will occur.

Probability is usually expressed as a ratio of the number of likely outcomes compared with the total number of outcomes possible. Ask students if they can give an example of probability.

It can be shown by the...

successful outcomes

total number of possible outcomes which is a fraction. This fractions can be converted to decimals and percentages.

Lesson:

Probability Scale: You can use a probability scale to show the outcome of an event in words or values between 0 and 1.

A value of 0 means the event is impossible.

A value of 1 means the event is certain.

A value of ½ means the event has an even chance of occurring.

A value between 0 and ½ is considered unlikely.

A value between ½ and 1 is considered likely.

This website gives a great example and an interactive part: http://www.bbc.co.uk/bitesize/ks3/maths/handling_data/probability/revision/2/

Go over a few more examples with your students until they understand the concept of the probability scale.

Begin to explain how to find probability of a die as an example.

There are six possible different outcomes. It can show either 1, 2, 3, 4, 5 or 6

What are the total number of outcomes when we roll it once.

What is the probability of rolling a 1?

What is the probability of rolling a 2?

What is the probability of rolling a 3?

What is the probability of rolling a 4?

What is the probability of rolling a 5?

What is the probability of rolling a 7?

What is the probability of rolling a 2 or 3?

What is the probability of rolling a 1, 4 or 6?

What is the probability of rolling an even number?

Once the students understand the concept of the die, have them go over this worksheet:

Probability with numbers: http://www.math-aids.com/cgi/pdf_viewer_8.cgi?script_name=probability_numbers.pl&prob1=1&prob2=2&prob3=3&language=0&memo=&answer=1&x=144&y=17

Week 6: Lesson 2: Probability Real Life Word Problems

Lesson Objective: to continue to build the students knowledge of probability.

To help students understand probability, work on the following problem as a class:

Probability of a deck of cards: http://www.math-aids.com/cgi/pdf_viewer_8.cgi?script_name=probability_cards.pl&prob1=1&language=0&memo=&answer=1&x=77&y=15

Probability of using a spinner: http://www.math-aids.com/cgi/pdf_viewer_8.cgi?script_name=probability_spinner.pl&denom_6=1&denom_8=1&dtype-1=1&dtype-2=1&language=0&memo=&answer=1&x=126&y=28

Begin to give the students problems such as this...

1. I have a bag containing 8 different colored tennis balls. There is 4 orange balls, 2 blue balls, and 2 red balls. For each of the following questions give your answer in words and in numbers found on the probability line.

What is the probability of removing a blue ball?

__________________________________________

What is the probability of removing a yellow ball?

__________________________________________

What is the probability of removing an orange ball?

__________________________________________

2. This time the bag has 4 orange balls, 2 blue balls, 2 red balls, 1 green ball and 1 pink ball. For each of the following questions give your answer in words and with your best estimate of the number.

What is the probability of removing a green ball?

__________________________________________

What is the probability of removing an orange ball?

__________________________________________

What is the probability of removing a blue ball?

__________________________________________

Go over these problems and make sure the students understand... then use this worksheet

https://www.superteacherworksheets.com/probability/probability_TZQNR.pdf?up=1466611200

Lesson Cancelled Due to National Tests.

Week 6: Lesson 3: Experimental Probability

Lesson Objective: Have the students apply their knowledge of probability into experiments.

The experimental probability is the observed probability in an experiment, while the theoretical probability is hypothesized.

Start off by conducting an experiment together on the board.

Use flipping a coin as an example. When we flip a coin there is a 50% chance, or ½ chance that it will land on heads. If we were to flip a coin 10 times, the theoretical probability of the coin landing on heads would be 5 out of 10, or ½. This is, in theory, what should happen.
Now flip a coin 10 times and record the results in a tally chart on the board. The results you get from this experiment is the experimental probability. It will probably not be ½. The experimental probability is the observed probability in an experiment, while the theoretical probability is hypothesized.

Before each activity, have students first think about the theoretical probability before they conduct the experiment.

Roll and Tally: https://docs.google.com/a/engelska.se/document/d/1ktwb9IX0DnfSOEW9UzRegqn_h8LciNHH0Yx0RgSJD_A/edit?usp=sharing

Rock Paper Scissors: https://www.education.com/worksheet/article/rock-paper-scissors-probability/

Worksheet: http://www.massillonschools.org/Downloads/Prob_ws_47.pdf

w. 7