In this unit the students form collections of 1000 objects. In doing this they examine the relationship between 1000 and smaller numbers, specifically 100 and 10.
- Develop an understanding of 1000 and the quantity for which it stands.
- Understand the relationship between 1000, 100 and 10.
As part of the work in this unit, the students will get to appreciate the size of 1000. It will take them some time to collect and display 1000 objects. In the process they will realise that 1000 is a reasonably large number. The size aspect of number is an important one. We need to have a ‘feel’ for how big numbers are so that we can appreciate everyday things such as how far it is to another town, how heavy things are or how much they cost.
In an effort to display their 1000 objects so that they are readily counted, the students will be encouraged to bundle the objects into groups of 10 and 100. This will help them see the relevance of the decimal counting system and the relationship between the numbers 10, 100 and 1000. A knowledge of the decimal system is fundamental to working with number, especially where the four operations of arithmetic are concerned. The advantage of this system over previous ones, such as that used by the Romans, is its efficiency in counting and calculating. This is all due to the fact that the system is based on the powers of ten – 101 = 10, 102 = 100, 103 = 1000, etc.
- Multilink cubes
- Stamps and ink pads
- Chart paper
- Possible items for collection (rice, beans, leaves, pebbles)
We begin our unit by making guesses about the number of beans in jars. We then work in pairs to decide how we are going to make a collection of a 1000 items.
- Show the class three jars (10 beans, 100 beans, 1000 beans).
I want you to think about how many beans might be in each of these jars. You can look closely at each jar but you can’t tip the beans out and count them. At the end of the week we will check your guesses.
- Give each student 3 pieces of paper and ask them to record their guess and then put this in the box beside each jar.
- As the students record their guesses ask questions which encourage them to explain the reasoning behind their guess.
How many do you think are in the jar? Why do you think that?
Which jar was the easiest to work out? Why? Have you seen that many before? Where?
- Ask for a volunteer to write 1000 on the board.
Can we write it any other ways?
- How big is a 1000?
Discuss the ideas that the students have about 1000.
- Tell the students that this week they are going to work with a partner to collect and display a thousand objects. Record on chart paper the students’ ideas for the 1000 collections.
- Discuss the ways that the collections might be displayed, for example:
- stamps in rows on chart paper;
- beans in bags;
- Seeds glued in groups of ten to paper.
- Ask the students to work in pairs to decide on a collection idea. They are to record how they are going to collect the items (from home or from school) and how they are going to display the items to share with others. As the students make their decisions ask questions that encourage them to think about the reasonableness of their choice. Although some may still make impractical choices refrain from direct intervention as an important part of the learning is developing a sense of the size of 1000.
Tell me how you think you can collect 1000 of those?
Where are you going to collect them? (home, school, friends)
How will you display them?
Will your collection cost very much?
Do you need help with your collection? What?
Over the next 2 to 3 days the students work with their partners to collect, make, count and display their collection of a 1000 objects.
- Tell the students that over the next three days they are to work with their partner to make their 1000 collection.
- As they work together ask questions that encourage the students to explain the counting strategies they are using. Expect that some pairs will group their objects from the start whereas others may count from one each time. If they do count from one ask them if they could think of ways to keep track of their counting.
How many objects have you collected?
How are you keeping track?
How many more do you need to collect?
Will you get to 1000 by Friday? How do you know?
How are you going to display your collection? Why are you doing it that way?
Will the others in the class be able to work out that you have a 1000 without having to count each object?
- At the end of each day ask the students to record on a piece of paper the number of objects that they have in their collection. Ask the students to share with the others in the class the groupings they are using to keep track of their collection.
- As the collections of 1000 are completed display these for everyone to look at and discuss.
In today’s session we create a 1000-block using multilink cubes. We do this by building it from sticks with 10 cubes.
- Show the class a box of multilink cubes.
- List the students' ideas on the board.
- Encourage the idea of grouping the cubes in groups (or sticks) of 10, then ask the students to form the cubes into sticks of 10.
Are there enough sticks here for 1000 cubes? Look at the collection of 10 sticks.
Are there enough sticks here for 1000 cubes?
How do you know?
How could we find out?
Ask the students to make collections of 100 with the 10-sticks.
Look at the 100’s collections. (As a class develop a name for the 10x10 cubes, for example; walls, panels.) Look at the 100's collections.( As a class develop a name for the 10x10 cubes, for example; walls, panels.)
Do we have a 100?
How many 100s do we need? How do you know?
How many 10s do we have in 1000? How do you know?