In this unit students form collections of 100 objects. In doing this they examine the relationship between 100 and smaller numbers, specifically 10.
- Develop an understanding of 100 and the quantity for which it stands.
- Count to 100.
- Understand the relationship between 100 and 10.
This unit explores the number 100, what it looks like, and the ways that it can be represented. As part of the work in this unit, the students will get to appreciate the size of 100. It will take them some time to collect and display 100 objects. In the process they will realise that 100 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 100 objects so that they are readily counted, the students will be encouraged to bundle the objects into groups of 10.
Associated Achievement Objectives
Listening, Reading, and Viewing - Ideas - makes meaning of texts by identifying ideas in some texts.
The learning opportunities in this unit can be differentiated by providing or removing support to students and by varying the task requirements. Ways to differentiate include:
- modelling the counting of items, using appropriate strategies, and with the aid of materials (e.g. Slavonic abacus, hundreds board)
- modelling examples of ways to display different kinds of items (in bags, stuck to a piece of paper, etc). If appropriate, students' work could be used as examples for other pairs
- strategically organising students into pairs and small groups in order to encourage peer learning, scaffolding, and extension
- working alongside individual students (or groups of students) who require further support with specific areas of knowledge or activities.
The activities in this unit can be adapted to be more interesting or relevant to your students by adding contexts that are familiar to them (i.e. that reflect cultural backgrounds, personal interests, or learning from other curriculum areas). For example, whilst each student can already choose their own collection to make with a partner, you might like to make the example collection something more meaningful to your students, such as shells if you are near the beach, or small pebbles from a local stream. You might be able to think of an authentic context, related to your learning, that involves counting 100 and that could be used to enhance the relevance of this unit (e.g. sheep farming, conservation of native birds, collecting cans for a can drive, laying out 100 cones for a sports day).
Te reo Māori kupu such as tatau (count), kotahi rau (100), and tekau (10) (as well as the kupu for other numbers used in counting sequences) could be introduced in this unit and used throughout other mathematical learning. You could also encourage students, who speak a language other than English at home, to share the words related to measurement that they use at home.
- Jar of 100 beans (or counters, sticks etc.)
- Multilink cubes
- Memo paper
- Stamps and ink pads
- Chart paper
- Possible items for collection ('collection of cars', 'rocks into rows', 'bowl of beans' etc)
Getting Started
We begin our unit by making guesses about the number of beans in jars. Do not tell the students how many beans are in the jar.
- Place a handful of beans in a container and ask students to estimate how many beans there are in the jar. Record students’ estimates on the board for all to see. Count the beans using skip counting techniques (or a technique that is currently relevant to your students) to see whose estimate was the closest. Repeat the activity, encouraging students to use their benchmarks to improve their estimations (e.g. if there are 10 beans here how many beans are in this jar? ).
- Show the class a jar with 100 beans in.
I want you to think about how many beans might be in this jar. You can look closely at the jar but you can’t tip the beans out and count them.
Encourage students to think about what 10, 20, 30 etc. beans looked like (as explored in the first step of this lesson).
Place your guess on a piece of paper and place it in a container. - 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? Have you seen that many before? Where? - Ask for a volunteer to write 100 on the board.
Can we write it any other ways? - How big is 100? Where have you seen 100 things?
Discuss the ideas that the students have about 100. - Tell the students this week they are going to work with a partner to collect and display a hundred objects.
- Record on chart paper the students’ ideas for the 100 collections.
Exploring
Over the next 2 to 3 days the students work with their partners to collect, make, count and display their collection of 100 objects. They may decide to display more than one collection of 100 depending on the time frame given. If you have thought of a relevant context in which this unit can be framed, introduce it in these sessions.
Nice warm up activities for the start of each day may include:
- using a 100 bead abacus to skip count in 10s as a line of the Slavonic abacus is pushed across
- using bead strings to model skip counting
- flipping 100 boards numbers as students count in 10s
- having student, in groups of 10, shows 10 fingers each to give students a feel for the size of 100.
Focus your English for the week on the same theme – groups of objects.
- Any books you have that include counting or groups would be suitable reading (Counting on Frank, by Rod Clement, and The 500 Hats of Bartholomew Cubbins, by Dr Seuss are fun examples).
- Students could be challenged to include the number 100 in their story writing.
- Students could write a letter to their parents explaining about their collection of 100 objects they are making.
- 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
- pop sticks bundled in tens
- toy cars in rows
- pebbles in bags
- 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 100.
Tell me how you think you can collect 100 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?
- Tell the students that over the next three days they are to work with their partner to make their 100 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?
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 100 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 100 are completed display these for everyone to look at and discuss.
Reflecting
Pull out the jar of 100 beans that was looked at in day one. How many beans do you think are in the jar? Ask students to record another estimate. Hand out the original estimates, compare the estimates with the second estimate. Was your estimate closer? How could these beans be organised to help make our estimates more accurate?
In today’s session we create a 100-block using multilink cubes. We do this by building it from sticks with 10 cubes.
- How many of these sticks will we need to make 100?
- 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.)
Extend the thinking by asking:
How many 100s do you think we might need to make 1000? How do you know?
How many 10s do we have in 1000? How do you know? - Ask students to turn the 100-block into a building. You might ask them to build their house, the classroom, the playground, their favourite place, or the local marae (i.e. something that is relevant to them).
Extension
Make 100 is a similar unit at Level 2 that focuses on making a thousand.
Dear parents and whānau,
In maths this week your child has been working with a partner to make a collection of 100 things (for example pop sticks, seeds, old used stamps) and to display the collection in a way that is easy to see that there are 100 objects. The purpose is for the students to develop a sense of just how big 100 is and to begin to understand how many tens there are in 100.
Please discuss their collection with your child and ask if they need some help to gathering items for their collection and display.