Expressions and patterns (Uttryck och mönster)

Ämne / Topic

Lesson 1: Introduction to Algebra

Lesson 2: Expressions and patterns - Developing expressions from real-world scenarios and completing patterns involving numbers and shapes.

Inlärningsmål / Learning Goals

Lesson 1: Introduction to Algebra (recap of what was learnt in year 8)

Lesson 2: Turn word problems into algebraic expressions

Complete numerical and pictorial patterns

Google Slides & Videos

Lektionssteg / Steps in the lesson: 

1. Lektionsuppvärmning / Lesson warm up / Hook / Review from previous lesson

Lesson 1- (Introduction to Algebra)

Warm-up activity on the value of expressions.

Material: 2 dice of a different colour

Number of participants: 2 - 3 per group.

Instructions:

1. Determine which of the dice gives the value of x and which gives you the value of y.

2. One person in the group starts by throwing both dice.

3. Once they have done this, they select an expression from the expression bank.

4. Calculate the value of the expression and write down the result.

5. Once player one has gone, it will be the turn of player. Player 2 once they have thrown the dice may choose any equation from the equation bank.

6. Player 2 calculates the value of the expression they chose and writes it down.

Rules:

1. Players can only select on expression once and cannot change their expression, once it has been chosen.

2. The game continues in the same way until all participants have chosen all five expressions.

3. When all five rounds are over, each player adds their results together. Whoever has the greatest sum, WINS!

Lesson 2: (Expressions and patterns)

Labelling parts of an algebraic equation:

Using the words from the word bank label the parts of the equation below:

Coefficient

operator

variable

constant

4 x  -  7  =  5

Two numbers multiply together to make 10. They add together to make -7.

Can you write this as an algebraic expression?

Can you solve for the two unknown numbers?

2. Introduktion till lektionen / Introduction to the lesson content 

Lesson 1 (Introduction to algebra):

The main part of the lesson, will start with the learners watching a video on algebra (see attached).

While the video is playing, the teacher will stop it at various points and ask learners questions on what was said, to gauge their understanding and keep them active in the lesson.

Lesson 2 (Expressions and patterns)

How many sticks will we need to build a 100 triangles?

Material: sticks used for building/making the pattern

Number of participants: 3 - 4 per group

Instructions:

1. Build a triangle using three of the sticks.

2. Build a second triangle using another two sticks.

3. Continue the pattern using the following number of sticks: 3, 5, 7, 9, 11...

Solving the equation:

Process:

What do you notice when we are building a new triangle?

3. Aktiviteter / Key Activities 

Sequences

A sequence is a list of numbers that follow a pattern. We can define this pattern with an nth term rule or a recurrence relation. We will also define the terms increasing sequence, decreasing sequence and periodic sequence. We will also define an arithmetic and geometric progression, both of which will be studied in more detail later on.

Lesson 1 (Introduction to Algebra):

How to Understand Algebra

Understanding algebra can seem tricky at first. But if you build up a strong basic knowledge of beginner math facts and learn some of the “language” of algebra, you can understand it much more easily. The basic steps for solving algebra problems involve performing simple operations in small steps that “cancel” the original problem. Doing these steps carefully and in order should get you to the solution.

Knowing Your Objectives in Algebra

4.  Stängning / Closure / Summary of lesson

The learners will answer answer the questions below and share their answers with the class.

Question 1:

One day the temperature was 4 degrees in Åre.

Ar the top of Åreskutan mountain, the temperature was lower.

For each meter that the height increased, the temperature was 0.01 degrees colder.

a. Draw an expression of how many degrees the temperature was at a height of ym above Åre village.

b. At what altitude above Åre village was the temperature at - 3 degrees?

Question 2:

5. Kolla vad eleverna kan / Check for understanding / Exit ticket

• Learner complete the question below and hand their answer to the teacher upon leaving the class.

• 2, 8, 14, 20....

• a. Write an expression for the nth number in the sequence.

• b- Calculate the 8th term in the sequence.

• c. Calculate the 100th number in the sequence.