MATHEMATICS

Bonny and Tommy are road users too

EDUCATOR SECTION

Memorandum

Division with a remainder but without the regrouping (decomposition) of the tens is taught. This demands much work in the range of the tables. The learners need to understand this stage very well before they work with higher numbers. Testing of the tables is essential.

In Module 5, the number concept is expanded to 800. In addition and subtraction, two- and three-digit numbers are introduced. Multiplication is done with regrouping of tens. Division with a remainder, but without regrouping or breaking up of tens, is taught. Initially it is only done in the number range of the tables. The learners need to have a very good understanding of this before it can be extended to larger numbers. Testing of tables remains extremely important.

Here the learners are exposed to other ways of summarising data. An oral discussion of possible changes and the results thereof is necessary.

Ensure that the learners realise that they need to cover the distance between the school and their homes at least twice daily: They come to school and have to go home again.

The learners need to find out what the distance between home and school is before they do the work on this page.

This is the first Grade 3 Module to expose learners to determining particular points on a graph so that they can draw the graph, and for working with 2 sets of data on the same graph. You therefore need to be doubly sure that they understand how this is done. Easier examples could be discussed in preparation for the exercise.

Precede this with a discussion on what a bus looks like from the front and from the rear before you let the learners attempt the drawings.

Counting in 8’s must be done before the table at the bottom of this page is completed.

Learners must discover the relationship (pattern). There are similar patterns on p. 11.

This worksheet is simply aimed at determining the level of thinking involved with operations requiring addition and subtraction and finding out where special attention is required. The work sheet does not have to be completed in one session.

Concrete work is necessary to explain the regrouping of tens during multiplication.

Ensure that the learners understand the patterns where division is involved before expecting them to complete the exercises.

Here we deal with division with a remainder. Explain that it is sometimes impossible to divide the remainder into fractions, simply because of the nature of the problem.

E.g. 1 fried or boiled egg can be divided but 1 uncooked egg cannot be divided and shared.

This is written as the remainder (rem.).

Begin with work in the number range of the tables (to tenth multiple). You will need much concrete work and lots of repetition, because it is very important that the learners understand what they are doing before you go on to larger numbers.

The learners must do research in books and pamphlets about the different traffic signs and discuss them before they complete the signs.

Many pictures and different objects with these shapes are required to ensure that the learners recognise all the shapes.

Make the learners aware of the fact that there is no easy way of folding or dividing for obtaining fifthsof 2-D shapes. This must be determined by measuring.

It may be necessary to help the learners to determine the location of the first square that must be coloured in. Do not offer help if they are able to find it independently.

Encourage learners to tell where they live and how they would explain the route to their home to someone else. Help them to explain an easy route to find a certain room in the school.

LEANER SECTION

Content

ACTIVITY: Distance [LO 1.1, LO 1.3, LO 1.4, LO 1.8, LO 1.9, LO 1.10, LO 3.5, LO 5.1, LO 5.2, LO 5.3, LO 5.4, LO 5.5]

All of us are road users: pedestrians, cyclists, drivers of vehicles, or passengers. It is important to know and obey traffic rules and road signs.

Figure 1

Find out how each of the learners in your class gets to school in the morning. Place a dot in the relevant circle for each of the learners.

Use this information to complete the following sentences.

Most of the learners come _______________________________________________

The fewest learners come ________________________________________________

• Write down 3 things that could happen to change the information that you have gathered.

_____________________________________________________________________

_____________________________________________________________________

_____________________________________________________________________

• Suppose that all the learners in your class came to school by bicycle.

How many bicycles would there be? ______________ bicycles.

How many wheels would there be? ______________ wheels.

• There are 10 bicycle racks outside the school building and 25 bicycles are parked in each bicycle rack. How many bicycles are there alltogether? ______________ bicycles.

How many wheels are there in alltogether? ______________ wheels.

Suppose that there are only 13 bicycles in 1 of the bicycle racks. How many bicycles and wheels would there be in all? ______________ bicycles and ______________ wheels.

Bonny and Tommy live 500 m from the school and walk to and from school every day. They cross the street at the scholar patrol.

• How far do they walk each day?

They walk ____________________________________________________________

• How far do they walk in 4 weeks?

They walk ____________________________________________________________

• This morning 418 feet crossed the street at the scholar patrol. How many learners crossed over at the zebra lines? _______________________ learners.

• Find out:

1. How far from the school is your home?

2. How far do you walk or ride each day?

3. How far do you walk or ride in one school week?

4. How far away is the learner who lives furthest from the school?

5. How far away is the learner who lives nearest to the school?

6. Calculate the difference between the two distances:

• Ask your educator to help you to summarise the information:

___________________ learners living closer than ½ km.

___________________ learners living between ½ and 1km from the school.

___________________ learners living between 1 and 1½ km from the school.

___________________ learners further than 1½ and 2 km from the school.

___________________ learners further than 2 km from the school.

Here is a graph showing the distances for the learners in the twins’ class. Their graph is drawn in black and marked with an A. Record your own class’ information on the same graph. Draw your graph using a red pencil and mark it with B.

Figure 2

Bonny and Tommy are very exited, because Grades 3, 4 and 5 are going on a netball and rugby tour.

This is the bus in which they will travel.

• Copy it in the blocks that are provided.

Figure 3

• Now draw the bus, first as you will see it from the front and then from the back.

Figure 4

• Bring empty cartons and other scrap material to school to build your own bus.

Use your own method for solving the following problems.

• There will be 120 players and 8 coaches on the tour. Each bus may only transport 35 passengers. Draw the buses that will be needed to transport everyone.
• Divide the players and the coaches among the buses to place the same number of players and coaches in each bus. Write the numbers on the buses you have drawn. How many seats will be empty in each bus? ________________
• A rugby team has 15 rugby players. How many players are there in the 5 rugby teams altogether? There are __________________________________
• There are 7 netball players in a netball team. How many players are in the 5 netball teams altogether? There are __________________________________
• The other players are the reserves. How many reserves are there?
• There are __________
• They leave on Thursday and will be away for 3 nights. On which day will they return? _____________________________________________________
• Each player has to contribute R100 to cover a portion of the costs. Bonny and Tommy will each take along R50 in pocket money.

What will the twins’ parents have to pay, including the pocket money, to let them go on the tour?______________________________________________

Bonny and Tommy and all the other players enjoyed the tour thoroughly, but there are a couple of calculations to be done.

• Here is a representation of the route to help you with the calculations.

Figure 5

During the tour they travelled 400 km altogether. On the first day they travelled 120 km, on the second day they travelled 102 km and 103 km on the third day. How far did they travel on the last day to get back to the school?

• Number sentence: ________________________________________
• On the last day: ____________________________________

The cost of the fuel came to R150 for each 100 km that the bus travelled.

What was the price of the fuel for one bus for the whole bus tour?

• Number sentence:________________________________________
• R ______________________________________________

What was the total cost of the fuel for all the buses?

• R _____________________________________________

• Suppose each bus travelled 80 km in an hour. Complete the table:

Table 1

hours	1	2	3	4	5	6	7	8	9	10
km	80

Figure 6

• Make use of the number line and write the number halfway between:

100 ……………………… 300

400 ……………………… 500

150 ……………………… 250

300 ……………………… 350

250 ……………………… 300

200 ……………………… 600

700 ……………………… 800

550 ……………………… 650

400 ……………………… 450

750 ……………………… 800

Figure 7

• How quickly can you fill in all the answers?

Figure 8

• Write down all the 3-digit numbers that you can make with the numbers 3, 7 and 8.

_____________________________________________________________________

• Arrange the numbers from the mosttothe least and circle the uneven numbers.

_____________________________________________________________________

• Write the uneven numbers with their number names.

_____________________________________________________________________

• Round off the even numbers to the nearest ten.

_____________________________________________________________________

• Halve the rounded off numbers.

_____________________________________________________________________

Figure 9

Think!

Figure 10

Assessment

Learning Outcome 1:The learner will be able to recognise, describe and represent numbers and their relationships, and to count, estimate, calculate and check with competence and confidence in solving problems.

Assessment Standard 1.1: We know this when the learner counts forwards and backwards in:

1.1.1 the intervals specified in grade 2 with increased number ranges;

Assessment Standard 1.3: We know this when the learner knows, reads and writes number symbols and names from 1 to at least 1 000;

Assessment Standard 1.4: We know this when the learner orders, describes and compares numbers;

Assessment Standard 1.8: We know this when the learner can perform calculations, using appropriate symbols, to solve problems;

Assessment Standard 1.9: We know this when the learner performs mental calculations;

Assessment Standard 1.10: We know this when the learner uses the following techniques:

1.10.1 building up and breaking down numbers;

1.10.2 doubling and halving;

1.10.3 number-lines;

1.10.4 rounding off in tens.

Learning Outcome 3:The learner will be able to describe and represent characteristics and relationships between two-dimensional shapes and three-dimensional objects in a variety of orientations and positions.

Assessment Standard 3.5: We know this when the learner recognises and describes three-dimensional objects from different positions;

Learning Outcome 5:The learner will be able to collect, summarise, display and critically analyse data in order to draw conclusions and make predictions, and to interpret and determine chance variation.

Assessment Standard 5.1: We know this when the learner collects data (alone and/or as a member of a group or team) in the classroom and school environment to answer questions posed by the teacher and class (e.g. ‘how many learners walk to school?’);

Assessment Standard 5.2: We know this when the learner sorts, orders and organises own and supplied data by one or more attributes for a particular reason. chosen by the teacher;

Assessment Standard 5.3: We know this when the learner draws pictures and constructs pictographs and bar graphs that have a 1-1 correspondence between own data and representation;

Assessment Standard 5.4: We know this when the learner reads, interprets and reports on information in own and a peer’s representations of data.

Assessment Standard 5.5: We know this when the learner reads and interprets data presented in simple tables and lists.