LI: To be able to identify the value of each digit in decimal places.
We are starting a new unit this week: decimals!
- It is important to remember that not all numbers are whole numbers as we showed with fractions. Another way of writing part of a whole number is through decimal places.
- Numbers that have digits to the right of a decimal point are numbers between whole numbers.
- Any digit immediately to the right of the decimal point are called tenths.
- Any digit immediately to the right of the tenths place value are called hundredths.
- Any digit immediately to the right of the hundredths are called the thousandths.
- Each time we move further to the right of the place value, the value of the numbers become ten times smaller.
Study the number 25.391
- What place value is the 1 in?
- The thousandths! There is one thousandth in 25.391 which can also be shown as 1/1000
- What place value is the 3 in?
- The tenths! There are three tenths in 25.391 which can also be shown as 3/10
- Finally, what place value is the 9 in?
- The hundredths. There are nine hundredths in 25.391 which can also be shown 9/100.
LI: To be able to identify each digit in a number up to three decimal places
In today's lesson, you shall be continuing to develop your understanding of decimal numbers up to three places. However, you will be using your reasoning skills to identify a number from clues given about that number.
- Recap from yesterday: what is a decimal number? What are the place values to the right of the decimal called and can you put them in order?
- Which decimal numbers below contain four tenths?:
6.466 1.47 4.105 4.09 3.794 1.420 9.742
- Today's activity focuses on using what you know about a number and decimal place values to solve a riddle. Each clue is focused on the place value of a digit. An example is given below to help you:
1. The hundredths digit is an odd number greater than 1 and less than 5.
2. The hundredths digit is half of the tenths digit.
3. It is a decimal number less than 5 with four digits.
4. The ones digit is greater than 3.
5. The ones digit is double the thousandths digit.
- The number I am thinking of is 4.632. Did you manage to work it out? If not can you now spot how we came to the answer from the clues provided?
LI: I can multiply and divide numbers by 10, 100 and 1000.
It is important to understand that when we multiply or divide, we do not always need to use column multiplication or the bus stop method. When it comes to multiplying or dividing numbers by a value of 10, 100 or 1,000, we can use our place value knowledge to aid us instead.
- If we multiply a number by 10, it is getting ten times bigger. What do you notice about the calculation and answer here: 25 x 10 = 250?
- Many people assume we have simply added a zero but does this always work and is it how we should remember how to solve questions when multiplying by 10, 100 or 1,000?
- The answer is no! We are not simply adding a zero, two zeroes or three zeroes. We are making our number greater by 10, 100 or 1,000. We are moving each digit in the number across a number of place values to the left hand side.
- It is similar in division, only this time the numbers are being made smaller by 10, 100 or 1,000. Each digit moves to the right a number of place values.
- It is important to remember this, especially when it comes to multiplying or dividing by decimal numbers. If we added a zero then we would not always be moving each digit the correct number of places.
- For example: 2.4 x 10 = 24 (if we added a zero instead, we may end up with an answer of 20.4 or 2.40).
- The number of zeros in the multiplier or divisor tells us how many place values we move to the left or to the right. 10 = one place; 100 = two places and 1,000 = three places.
LI: To be able to multiply and divide numbers by 10, 100 and 1,000.
Recap on yesterday's lesson. How do we know how many places to move each digit? How do we know whether to move the digits to the left or to the right?
- Today, you are going to continue developing your skills of multiplying and dividing by 10, 100 and 1,000 but will have to do so across multi-step calculations.
- On your activity sheet, you will see questions such as: 3.2 x 10 x 10 x 5 x 10.
- This can be completed in many small steps, however using our prior knowledge of place value and multiplication by 10 we can make this calculation easier.
- 10 x 10 x 10 = 1,000. Therefore, we can now change the calculation to read: 3.2 x 1,000 x 5.
- This is now easier for us to do as there are less steps to consider.
- 3.2 x 1,000 tells me that I need to move how many places to the left?
- Three! Because there are three zeroes in 1,000. This gives us the answer of 3,200 as we move each digit to the left three times.
- Now we need to multiply our answer by 5 to solve the complete calculation.
LI: I can multiply one-digit numbers with up to two decimal places by whole numbers.
- Look at the word problem below:
Rhys is going into town on the bus with his five friends.
Each bus ticket costs £1.54.
How much will six bus tickets cost altogether?
- The calculation we are going to need to solve from this word problem is 1.54 x 6
- What method would you use to solve this calculation?
- Short multiplication is the method we will need to use to solve this.
First, set your calculation out correctly with one number in each square. Use a ruler to draw your lines.
Step 1: Calculate the hundredths digit.
Multiply the 4 hundredths by 6.
4 × 6 = 24 hundredths.
We can only put hundredths in the hundredths column.
We write the 4 hundredths in the hundredths column.
We need to regroup the 20 hundredths into 2 tenths.
Step 2: Calculate the tenths digit.
Multiply the 5 tenths by 6.
5 × 6 = 30 tenths.
We need to add on the 2 tenths that we wrote under the line.
30 + 2 = 32 tenths.
We can only put tenths in the tenths column.
We write the 2 tenths in the tenths column.
We need to regroup the 30 tenths into 3 ones.
We write the 3 under the bottom line of the ones column.
We write the 2 under the bottom line of the tenths column
Step 3: Calculate the ones digit.
Multiply the 1 by 6.
1 × 6 = 6.
We need to add on the 3 ones that we wrote under the line.
6 + 3 = 9.
We write the 9 ones in the ones column.
We have used a written formal method to calculate £1.54 × 6 = £9.24
Awards we have received so far.