I Like Toys

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Purpose

In this unit we explore ways to pose and answer investigative questions about our favourites by gathering and analysing data and discussing the results.

Achievement Objectives
S1-1: Conduct investigations using the statistical enquiry cycle: posing and answering questions; gathering, sorting and counting, and displaying category data; discussing the results.
Specific Learning Outcomes
• Pose investigative questions with support from the teacher.
• With the teacher decide on how to collect the data to answer the investigative question.
• Sort objects into categories for display.
• Make a display of the data collected (pictograph).
• Make statements about data displays.
Description of Mathematics

In this unit the students begin by brainstorming areas for investigation. Young students' areas of interest are likely to focus on themselves and the activities that they are engaged in. Using the students and their interests is a recurring technique used in junior classes. It provides students with contexts that are meaningful and motivating. With the teacher investigative questions are posed about categorical data.

In this unit we use favourites as the theme for the investigations. Much of the data collected at level one will be real objects. In this unit we begin by posing an investigative question about our favourite toys. Once the data (toys) are collected together they can be sorted into categories ready for display. It is important that the students are involved in deciding how to sort the objects. We then draw pictures of other favourites and use them to make displays.

Once more we stress the importance of letting the students decide how to sort and display the data. In this unit we photocopy the drawings so that each pair of students gets the opportunity to make decisions about how the data should be sorted and displayed. The follow-up discussion of the displays will involve the students making statements about the number of objects in each of the categories. In this unit we do not attempt to get the students to formalise their displays into pictographs. However the thinking carried out in this unit means that the students would be ready to use pictographs in future statistics units.

The learning opportunities in this unit can be differentiated by providing or removing support to students and by varying the task requirements. Ways to support students include:

• reducing the number of favourites in the data set for students who are beginning to count one-to-one when they are doing individual or small group work
• extending by recording two types of favourites on data cards so that they can sort in two ways, e.g. by favourite food and by favourite drink.

The context, about favourites, for this unit can be adapted to suit the interests and experiences of your students by selecting favourites of interest to your students.

A te reo Māori term that can be introduced in this unit is rōpū (group). Counting in te reo Māori could be used throughout the sessions.

Required Resource Materials
• Paper for drawing (cut A4 sheets into 8 pieces)
• Chart paper
• Scissors
• A favourite toy from home
• Copymaster 1
Activity

Session 1

1. The previous day or previous week ask the students to bring their favourite toy to school. Ensure there are spare toys in the classroom for children who are unable to bring one or forgot. As an alternative, you could ask students to draw a picture of their favourite toy.
2. We begin the week by looking at all the toys the students have brought to school. Ask the students, seated in a circle, to introduce their toy to the class.
Let’s try to find out about our favourite toys. The investigative question we are exploring is "What are the favourite toys of the children in our class?"
3. Write the investigative question up on the board or a chart.
4. Ask a student to put their toy in the centre of the circle.
Do any of you have toys that could belong with this one? Is there some way that your toy is like this one? How does your toy belong? Who has one that doesn’t belong? Why not?
5. Continue until all the toys are sorted into categories. Together count the toys in each group.
Four of us brought dolls or action men. Three of us brought balls to kick. Six of us brought toys with wheels. Two of us brought soft animals etc
6. Record statements on the board or a chart, for example, "Four of us like dolls the best.
7. Send home the family and whānau letter regarding answering the investigative question "What are the favourite fruits of our class and their families?"
8. Conclude the session by exploring the investigative question "Which of the toys of Māori children played with 100 years ago do we like best?”
9. Introduce the photos (Copymaster 1) and ask the students if they know what the toys could be (A. cat's cradle, B. poi, C. kite, D. stilts and E. spinning top). Compare these traditional toys with ones you might play with today. What are the differences and similarities?
10. Have a copy of the photos on the wall and ask your students to  children put a dot underneath the traditional toy they think would be their favourite toy if they lived long ago.
11. Leave the activity open as you challenge the students to write statements to answer the investigative question "Which of the toys of Māori children played with 100 years ago do we like best?” Encourage students to use both statements about individual toys (for example, "The most popular toy is the stilts because eight of us chose that"), and comparative statements (for example, "More people liked the spinning top than the kite.")

Session 2

In this session we collect sets of data to use in investigations in the following sessions. If you have time available at the end of the session you may wish to start analysing one of the sets.

1. Let’s think about some other favourites that we can investigative with the class this week.
2. With the students, discuss different objects and items that we could explore to see what our favourites are.  Collect the ideas on the board or chart.
3. Choose three favourites to explore with the class this week.
Possible favourites include: food, colour, drink, number, animal.
4. With the students, pose investigative questions to explore. For example: What are the favourite foods of the children in our class? What colours do Room 30 students like best? What are our class’s favourite numbers? What animals do the children in Room 2 have as favourites?
5. Discuss with the students that we need to collect data from each of them to answer the three investigative questions.  With the students, pose survey questions for each of the investigative questions.  For example: What is your favourite food? What colour do you like the best? What number is your favourite? What is your favourite animal?
6. Write each of the three survey questions on an envelope. Pin the envelopes up where everyone can reach them.
7. Ask the students to draw an answer for each of the survey questions onto the prepared pieces of paper (A4 cut into 8 pieces). If they are able, ask them to write their answer beside the picture. Circulate and help those who are unable to write their answers beside the picture.
8. Put the named pictures (answers) in the appropriate envelope.

Sessions 3 and 4

In preparation for the next two days, make a set of picture sheets for each pair by photocopying the answers from session 2 (8 per sheet of A4). It is worth taking the time to make copies as it gives everyone the opportunity to sort and display the data.

1. Each day select one of the investigative questions to explore. Take the envelope that contains the student responses to the associated survey question. Spread the pictures out on the mat for the students to look at.
Do you see any that are like yours?
Which ones are different to yours?
2. Ask the students for ideas for sorting the pictures.
3. Sort the pictures according to one of the suggestions, for example, sort foods with others of the same type, for example, ice-creams, fruit, cakes, chips, fish
4. Together count the pictures in each collection.
5. Have the students return to their seats to work with their partners. Give each pair a set of the photocopied answers prepared for the day’s investigative question.
6. Each pair needs to cut the pictures apart and then decide how to sort them.
7. As the students work ask questions that focus on the approach they are taking to sort the pictures:
How are you sorting the pictures?
How many categories or groups have you got?
Is it easy to decide where to put the pictures? Why/Why not?
8. Once the pictures are sorted get the students to glue their pictures onto chart paper that have the investigative question already written at the top. Encourage students to make statements about what their displays shows. Help them write statements about their display if they are unable to write their own statements.
9. At the end of each session ask the students to share their posters. Ask questions, such as in point 10 above, and 2, 3, and 4 below, and offer models of appropriate language to support the students to effectively talk about the process of making their display and what is presented on it.

Session 5

We begin today’s session by getting the students to select their favourite investigation to display on the classroom walls.

1. Let's look at all the great statistical investigations that we did this week.
2. Spend some time looking at the displays and asking the students to tell you what the display is saying about the investigative question.  For example, if the investigative question was "What fruit do Room 30 students like best?", then the teacher would say Can you tell us what your display is saying about the fruit that Room 30 students like best?
How many chose that favourite (e.g. fruit)?
Which things are favourites? How do you know? How does your display show that?
3. Conclude the session by exploring the investigative question "What are the favourite fruits of our class and their families?"  Gather together the fruit pictures that families drew.
4. Talk about ways to sort the fruit pictures. Choose four or five types and then discuss the use of an "other fruit" category.
5. When you have agreed on ways to sort the fruit let the students add their families’ pictures to categories. Glue the pictures onto a chart to make a display.
6. Leave the activity open as you challenge the students to write statements to answer the investigative question "What are the favourite fruits of our class and their families?" They can add these to the display during their own time in the next week or so.
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