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Ffocws dysgu

Dysga ddatrys hafaliadau un cam, gan ddefnyddio llythrennau i gyflwyno ‘anhysbysion’.

Mae'r wers hon yn cynnwys:

• cyflwyniad i hafaliadau
• dau weithgaredd

Learning focus

Learn to solve one step equations using letters to present ‘unknowns’ with integer solutions.

This lesson includes:

• an introduction to equations
• two activities

Beth yw hafaliadau?

Mae hafaliadau wedi eu ffurfio o ddau fynegiad â hafalnod rhyngddyn nhw, ee:

x + 2 = 1

I ddatrys hafaliad, mae angen i ti ganfod gwerthoedd y rhifau coll.

Enghraifft - 'Dw i’n meddwl am rif, adio pedwar, a’r ateb yw saith.'

Dyma sut mae ysgrifennu hwn ar ffurf algebraidd:

x + 4 = 7

Mae x yn cynrychioli’r rhif y gwnest ti feddwl amdano.

Mae x + 4 = 7 yn enghraifft o hafaliad algebraidd. Mae x yn cynrychioli rhif anhysbys.

Rhaid mai 3 yw’r rhif y gwnest ti feddwl amdano yn gyntaf (3 + 4 = 7). Felly, x = 3 yw'r ateb i'r hafaliad x + 4 =7.

What are equations?

Equations are made up of two expressions on either side of an equals sign, such as:

x + 2 = 1

To solve an equation, you aim to find the value of the missing number.

Example- 'I think of a number, add four, and the answer is seven.'

Written algebraically, this statement is x + 4 = 7 * where x represents the number you thought of.*

x + 4 = 7 * is an example of an algebraic equation where* x represents the unknown number.

The number you first thought of must be 3 (3 + 4 = 7). Therefore, x = 3 is the solution to the equation x + 4 = 7.

Cydbwyso’r hafaliad

Mae hafaliad fel clorian bwyso – dylai’r ddwy ochr bob amser fod mewn cydbwysedd perffaith. I ddatrys yr hafaliad mae angen canfod gwerth y rhifau coll a gwneud yr un gweithrediad ar y ddwy ochr.

Enghraifft 1

Dychmyga dy fod yn ceisio canfod faint o losin sydd yn y bag hwn.

Balancing the equation

An equation is like a weighing scale - both sides balance because they represent the same amount. To solve the equation you need to find the value of the missing number by performing the same operation on each side.

Example 1

Suppose you are trying to find out how many sweets are in the bag shown here.

O dynnu tair losinen o’r ddwy ochr, mae’r glorian yn dal yn gytbwys.

By subtracting three sweets from each side, the scales remain balanced.

Galli di weld nawr fod un bag yn gywerth â dwy losinen, neu, o’i ysgrifennu’n algebraidd:

x + 3 = 5

Tynna 3 o'r ddwy ochr i gael:

x = 2

You can now see that one bag is equivalent to two sweets. Written algebraically, this is:

x+ 3 = 5

Subtract 3 from both sides, to give:

x = 2

Enghraifft 2

Yn yr achos hwn, mae dau fag o losin yn gywerth â chwe losinen:

Example 2

In this case, two bags of sweets are equivalent to six sweets.

I ganfod beth sy’n gywerth ag un bag, rhanna’r ddwy ochr yn ei hanner:

To find the equivalent of one bag, divide both sides by two.

O’i ysgrifennu’n algebraidd:

2x = 6

Rhanna’r ddwy ochr â 2, i gael:

x = 3

Written algebraically, this is:

2x = 6

Divide both sides by 2 to give:

x = 3

Gweithgaredd 1 / Activity 1

Gwna'r symiau isod. Darllena'r cyflwyniad eto os wyt ti angen help.

Do the sums below. Read the introduction again if you need help.

1. x + 5 = 9

2. x + 12 = 18

3. x + 18 = 22

4. 7 + x = 12

5. 15 + x = 20

Gweithgaredd 2 / Activity 2

Datrysa'r hafaliadau isod. Er mwyn dod o hyd i'r ateb, cofia rannu â'r rhifau eraill yn y swm.

Solve the equations below. In order to find the answer, remember to divide with the other numbers in the sum.

1. 2a = 8

2. 3b = 15

3. 6c = 60

4. 4c = 28

5. 5b = 35

Nodiadau i rieni

Ar ddiwedd y wers bydd disgyblion:

• wedi cael cyflwyniad i waith hafaliadau
• yn gallu deall sut i ddod o hyd i werth x mewn gwaith hafaliadau
• yn gwybod sut i gydbwyso hafaliadau

Notes for parents

After the lesson, pupils will:

• have had an introduction to work on equations
• be able to understand how to find the value of x in equations
• know how to balance equations