Similarly the seven doesn't just represent seven, it represents seven tens or This three represents three ones, so it actually does represent three. But as I promised we're now going to extend our understanding and what we do is we put a decimal here which you've probably seen before at the right and the reason why we even need a decimal is to really tell us where our ones place is.
We say okay if we go right to the left of the decimal that's going to be our one space because once we start introducing decimals we can introduce as many spaces as we want to the right of the decimal. And so let's think about those a little bit. If when we went from hundreds to tens, notice we divided by ten, when we go from tens to ones, notice you divide by ten.
So what do you think this place over here is going to be called? Well what happens if you take one divided by ten? Well then you get a tenth so as you might imagine this is the tenths place. And then if you were to go one place to the right of that, what would this place be? And then if you were to go one space to the right we could keep doing this forever, but if we were to go one space to the right of that, what would it be?
And so for example if I were to extend this number instead of if just being , if I were to write This five doesn't just represent five, it represents five tenths or another way of writing five tenths you could write it like this 0. Or you could write it as five tenths. They are required to use the charted words and their plurals somewhere in their stories. Have the student share their stories with a partner. Display the stories. Activity 4 Show the students the MAB materials. Have the students discuss what is similar about these and the beans and containers.
Have students play Make and Take in pairs. Purpose: to have students composing and decomposing using pre-grouped place value materials Each pair has 15 tens and 1 hundred, a dice and recording materials. They make one group of 70 with their equipment and both use this for the game. Each student has a different target which they aim to be the first to reach: Player One must make by adding tens and Player Two must make 0 by subtracting tens.
Players take turns to roll the dice, model the number made and record the equation as they do so. For example: Player One, whose target is to make by adding tens, rolls 4 and adds 4 tens to 70, making He models this with materials, in the process exchanging 10 tens for Then Player Two, whose target is to make 0 by subtracting tens, rolls 5. She exchanges 1 hundred and 1 ten for 11 tens from which she subtracts 5, leaving 6 tens.
The game continues until one player has made or exceeded their target. Activity 5 Show the students an image of dots in a random grouping. Attachment 2. Have the students say how many dots they think there are. Ask them to justify their estimate. Tell them the total In pairs or small groups ask them to come up with ways to count the dots. Share approaches.
Hopefully one of the groups suggests grouping in tens. Give each group a copy of the dot image, and ask them to find out how many dots there are by circling into groups of Ask them to share how many tens 13 and how many left 3 , giving a total of Show the students a dot image of Attachment 2. Ask them to explain their thinking and make links to the ten groups of ten structure of the equipment they have been working with. Conclude the lesson by recording what has been learned, highlighting grouping of ten and ten times ten.
Emphasise that 10 is ten times bigger than 1 and that is ten times bigger than 10 and one hundred times bigger than 1. Session 2 SLO: Understand the structure of 3-digit numbers using a range of material representations and contexts. Activity 1 Have the students work in pairs. Each pair has access to MAB hundreds and tens equipment. Write on a chart a decade number, — Skip count together in tens to that number.
Have the other student in the pair check how many tens there are at the end of the count. For example, the students skip count in tens to They find this is 23 tens. Rua tekau 20, 2 tens ; toru tekau 30, 3 tens ;…rua rau , 2 hundreds ; rua rau, tekau , 2 hundreds, ten ; rua rau, rua tekau , 2 hundreds, 2 tens ; rua rau, toru tekau , 2 hundreds, 3 tens Have the students twice exchange ten 10s for one and model with hundreds and tens.
Activity 2 Explain to the students that the class is going to investigate the range of heights of the students in the class. Using MAB ones cubes, set the task for the students to each measure how long their pencils are in cubes, rounding to the nearest cube. Have them line the cubes along their ruler, confirm the length in centimetres and have them exchange ten singles for one ten as appropriate. Place the ten s and ones along the ruler once again for further confirmation.
Explain that the MAB equipment ones and tens only is now going to be used to measure how tall the teacher is because she needs to know this for her passport application. The teacher lies down and a marker is located at her head and feet. She resumes her position in front of the class. Ones can be used to complete the measure. The result is noted.
For example 17 tens and 4 ones. Students are asked to discuss with a partner if there is another way to say this. The students conclude that the teacher is 1 metre and 74 centimetres. Have the students describe the connection between the one hundred MAB flat and a 1 metre ruler. The students work in pairs to measure each other using 10 centimetre MAB rods, converting their measurements into metres and centimetres.
Activity 3 Have the students work in groups of four. Give each group — paperclips. Pose the challenge. Another group needs to see at a quick glance how many paperclips you have. Have the students visit the displays made by other groups. If they think the number of paperclips is immediately evident, each visiting student awards that group one coloured counter.
The groups return to their own display to see how others have voted. Discuss what the students did, highlighting the grouping decisions made by each group. Comment on those who used a tens and ones structure.
Recommended Worksheets Definition The topic of number changing is covered here.
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