Maths Strategies

Throughout this week, we have been learning different types of strategies to solve multiplication and division problems;

1. Place value
2. Standard Algorithm
3. Rounding off/Rounding down
4. Rounding and Compensating
5. Guess and Check
6. Long division

and there’re still probably some that I left out. In the photo, on the right, I used rounding and compensating to solve the multiplication problems. On the left, I used guess and check to solve my division problems. I found these strategies very easy to use but I reckon I could’ve solve it faster using standard algorithm and long division. I would very much like to teach my learnings to the other students in my class.

Measuring Angles

This game helped me to understand how to use a protractor. I had to rotate the protractor to be in line with the red line and see what angle it was. I measured it accurately. I reckon this game would be useful to those people who still struggle using a protractor. It really does help you understand using a protractor properly.

Multiplying fractions

WALHT: Multiply Fractions

I played this online game to help me have a better understanding of multiplying fractions. If the answer was correct, you get 2 points, if you forgot to simplify you get 1 point, and if you get it completely wrong, then it doesn’t give you any points. I think I did alright in this game. I got one wrong and forgot to simplify once. This game was easier than I thought it would be. Next, I would like to try an online division of fractions game.

Math Man

In this game, I had to add and subtract fractions. I was Pac Man and the Ghost with the correct answer, I had to eat it. If I chose the wrong answer, I would lose a life. There are 3 lives in total. I was only able to reach level 7 and my score was 29. I found this game easy because this only had adding and subtracting fractions of the same denominators. I'd like to revise multiplying and dividing fractions with different denominators.

Fractions

In this game, I had to answer questions about which fraction was greater.As shown, I asnswered 20 questions and my score was 75. Every time I got an answer correct, my score went higher. But every time my answer was wrong, it went down. I found this activity easy because I already know my fractions. I would like to play this game again and see if I could beat my score.

Estimation Activities

My group was learning estimation of parts of a cob of sweetcorn. Norah and Stephanie were in my group. The closest estimation we had was for the row of kernels. We estimated 13 but the actual amount was 18. The rest of the estimations were wild guesses. The skill we had to use was rounding off.  I found this a little hard to work with because no one in my group had a netbook at the time. Next, I would like to revise algebraic expressions.

Maths - Patterns

WALT: solve problems involving patterns.

In the photos above, I was working in a group. For me, working in a group, is easier because we discuss the problem together and solve them. I enjoy working in a group, especially with my friends, because it’s easy to give off ideas and the problems would be solved faster if we work together.

Maths - Algebra

MATHS - ALGEBRA

Introducing Algebraic Expressions

         In maths, we use symbols to represent numbers, operations and formulae. It is important to understand how these are arranged.

         It is useful to be able to explain mathematical ideas using words. However, it is equally important to be able to use symbols - such as numbers (e.g. 5), letters (e.g. x) and signs (e.g. +).

         We often use x to represent some number in a mathematical calculation. Sometimes, we refer the letter x as a variable or a pronumeral.

 EXAMPLES

    x + 4 means a number with 4 added on.

    x - 20 means 20 less than x, or the result of taking away 20 from a number.

MULTIPLICATION & DIVISION

     The two symbols x and ➗ are not used very often in algebra.

     We leave out the multiplication sign.

EXAMPLE

5 lots of x, or 5 x X, is written as 5x.

EXERCISE 1.01

1. Match each algebra expression with an english phrase from the box.

1. x + 3     
2. x - 2
3. 5x
4. x + 5
5. 2x
6. 3x
7. x - 1

         2. Write down algebra expressions for the english expression.

1. A number with 10 added to it.
2. A number with 15 subtracted from it.
3. A number multiplied by 4.
4. A number multiplied by 7.

         3. Write down the english expression for each algebra expression.

1. 6x          B. x + 9

      C.   x - 12     D. 5x

         4. For each english expression, write down an algebra expression chosen from the box.

1. Ten times a number.                 
2. A number divided by 10.
3. Ten divided by a number.
4. Ten more than a number.
5. Ten less than a number.

         5.  Write down these expressions without using multiplication or division signs.

1. 6x         B. x ÷ 6           C. 20 x X         D. x ÷ 30        

     E. p x 9               F. 12 x y           G. 100 ÷ x         H. p ÷ 9    

         6.  Write an equivalent algebraic expression for each of these.

1. x take away 7.
2. Six more than x.
3. Twelve lots of x.
4. Ten less than x.
5. The number of cents in x dollars.
6. The number of days in x weeks.
7. The sum of p and q.

         7.  Show the meanings of these expressions by including multiplication signs.

1. 4p        B.  6p - 1

      C.  pq         D.  2 + 3p

         8.  Rewrite these expressions, showing all the implied multiplication and division signs.

1. 12 x          B.  x/6  

      C.  cd             D.  7/y

         Substitution [replace the variable (letter or symbol) with a number to work out the value]

        If x = 7, then x + 3 = 10.

         But if x = 24, then x + 3 = 27.

          The number represented by x + 3 depends on the value of x.

EXERCISE 1.02

1. The value of x is 8. Calculate each of these expressions.

1. x + 2 =             B.  x + 10 =             C.  x + 27 =             D.  x + 6 =

     E.  x + 8 =              F.  x + 1 =                G.  2 x X =              H.  4 x X =

1. 7 x X =             J.  3x =                    K.  10x =                L.  9x                          

     M.  x ÷ 4 =             N.  x/2 =                   O.  x/8 =                  P.  48/x =

         2.  A car factory uses a rule to decide how many tyres it needs to purchase when it is assembling cars. The rule is:

    The number of tyres = 5 x the number of cars

    The manager writes down this rule as:

    Number tyres = 5x

1. What does x stand for in this expression?
2. The factory is assembling 60 cars. How many tyres does it need to purchase?
3. What is the value of 5x when x = 40?

    EXERCISE 1.03

1. Here a = 4, b = 5, c = 13 and d = 28. Calculate the value of each of these expressions.

1. a + b          B.  a + c + d          C.  d + b

     D.  b - q           E.  c - b                 F.  d - a

         2.  An airline provides two types of dinner on a flight - chicken and fish. The total number of meals served on a plane can be worked  out using the rule c + f. What is the value of c + f when:

1. c = 41 and f = 35?
2. c = 56 and f = 29?

         3.  Sounds Unlimited use this rule to work out the number of CD’s they sell each week: Number sold = number in shop at start of week - number in shop at end of week.

1. Explain what x stands for in this rule.
2. Explain what y stands for in this rule.
3. Calculate the value x - y when x = 20 and y = 7.
4. Explain in words what you have worked out in part c.

SIMPLIFYING ALGEBRAIC EXPRESSIONS

There are two ways we can show multiplication:

1. with at ‘times’ symbols (x),
2. by placing the letters, or number and letter, next to each other.

                          

Example

    Each of these are equivalent.

                     

Using the x symbol	Simplified
2 x X	2x
p x q	pq

Here are the rules writing multiplication expressions as simplified as possible.   

Rule	Example
Any number in the expression are multiplied	4 x 2x = 8x
If there is more than one letter, they are written in alphabetical order	3d x 5c = 15cd
Numbers are placed in front of letter when multiplying	p x 2q = 2pq

Exercise 1.04

Simplify these expressions.

1. 4 x 3x                  8.  4c x2d                15.  4d x 2c x e
2. 2 x 5x               9.  2g x 3f               16.  3 x 2a x 5
3. a x c                10.  p x 2a               17.  1 x 10q x 1
4. 3 x p                11.  2a x 4b              18.  2 x 4p x 2q x r
5. 1 x d                 12.  q x 2p x 3r        19.  4a x b x 2c
6. 7 x 2x                 13.  f x 2d x 5e        20.  q x r x p  
7. b x a                 14.  3o x q x 2p

     Expressions with like terms

Like terms are those that have the same combination of letters. For example 3ab, -5ba and ab are all like terms. Other examples of like terms are: (a) x2, 3x2, -5x2   (b) ac2e, -3ac2e, 5ac2e

                                                              

Unlike terms have different letter combinations. For example (a) ab and bc are unlike terms. (b)  x and 2x are unlike terms because the powers of x are different.

          Complete the Statements

• A algebraic ___________ is made up of __________ and operators such as +, -, x, ÷ and ().

• A ______ is made up of numbers and letter symbols but not operators.

    For Example,

1. 3a + 4b - a is an ______          b. 3a, 4b and 5 are _______ in the expressions.

      c.   3a and a are called ______ because the both contain a number and the letter symbol a.

                                                                                      Choose your answer from: expression, term,

                                                                                                                                                          like term

Like terms can be added and subtracted

Examples

1. 5 dogs + 7 dogs = 12 dogs      

            5d + 7d = 12d

     2.     14 pigs - 6 pigs =  8 pigs

             14p - 6p = 8p

     3.     8 mangoes  + 5 apples - 3 mangoes - 2 apples = 5 mangoes + 3 apples

             8m + 5a - 3m - 2a = 5m + 3a

     4.     6x2y + 5x2y = 11x2y

     5.     3x + 5 + 6x - 2 + 7 + y = 9x + 10 + 9x + y