2.2 Graphs, adding and subtracting

Mathematics

Mathematics in the world around us

Educator section

Memorandum

Critical and developmental outcomes:

The learners must be able to:

1. identify and solve problems and make decisions using critical and creative thinking;

2. work effectively with others as members of a team, group, organisation and community;

3. organise and manage themselves and their activities responsibly and effectively;

4. collect, analyse, organise and critically evaluate information;

5. communicate effectively using visual, symbolic and/or language skills in various modes;

6. use science and technology effectively and critically, showing responsibility towards the environment and the health of others;

6. demonstrate an understanding of the world as a set of related systems by recognising that problem-solving contexts do not exist in isolation;

7. reflect on and explore a variety of strategies to learn more effectively;

8. participate as responsible citizens in the life of local, national, and global communities;

9. be culturally and aesthetically sensitive across a range of social contexts;

10. explore education and career opportunities; and

develop entrepreneurial opportunities.

• Integration of Themes: Friends
• Social Justice, Human Rights and a healthy environment: “I am in Grade 2 with many other children. Each learner needs to be happy. The educator needs a suitable learning environment in order to teach us.”
• Discuss the learner’s responsibility to create such an environment.
• Taking turns on the jungle gym is important – why? Discuss safety, manners, co-operation, etc.
• Learners extend their number concept to 109 on the “jungle gym”. The activities include ordinals, names, symbols and counting forward and backward.
• Position is established by places in the classroom, using a floor map of the room.
• A graph is designed to be completed by collecting information.
• Addition and subtraction are extended to +4, -4, +5, -5, +6, -6, +7, -7.
• Bonds of 10 and 11 are discovered.
• Directions are given to draw and colour a shape.
• Measuring with thumbs and comparison of these measurements using the related vocabulary.

Leaner section

Content

Activity: graphs, adding and subtracting [lo 1.2, lo 1.4, lo 1.8, lo 1.10, lo 2.2, lo 5.1, lo 5.2, lo 5.4, lo 5.5]

I need to make a graph

The graph will help me find out …

- which is the longest.

- which is the shortest.

- which is the furthest.

- which is the nearest.

• For each thumb you counted, colour one block.

My graph on lengths

The length of…

• Now I can see…….

1. The ________________________ is the longest.

2. The ________________________ is the shortest.

3. The length of the cupboard is __________ than the length of the mat. (longer, shorter)

4. The length of the board is ___________ than the windows on the left. (longer, shorter)

Play with numbers

• Begin from 1. Draw a line from 1 to 2, from 2 to 3, etc, until you get to 40.

• Make each number one more and one less.

Rename numbers

• Can you show Sally different ways in which she can make her sum easier? Write or draw them here.

• Des has a plan.

• Liz has another plan.

• Let’s use the plan Des had.
• Use smaller numbers for the ones in circles.
• Rename them.
• Use arrows to say “gives me”.

• Do these sums in the same way by renaming the number in the circle.

Assessment

Learning Outcome 1: The learner will be able to recognise, describe and represent numbers and their 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 1.2: We know this when the learner counts forwards and backwards in:

1.2.1 ones from any number between 0 and 200;

1.2.2 tens from any multiple of 10 between 0 and 200;

1.2.3 fives from any multiple of 5 between 0 and 200;

1.2.4 twos from any multiple of 2 between 0 and 200;

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

1.4.1 whole numbers to at least 2-digit numbers;

1.4.2 common fractions including halves and quarters;

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

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 using concrete apparatus (e.g. counters);

1.10.4 number-lines;

Learning Outcome 2: The learner will be able to recognise, describe and represent patterns and relationships, as well as to solve problems using algebraic language and skills.

Assessment Standard 2.2: We know this when the learner copies and extends simple number sequences to at least 200.

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 (e.g. ‘how many learners are there in each classroom?’);

Assessment Standard 5.2: We know this when the learner sorts physical objects to one attribute chosen by the teacher;

Assessment Standard 5.4: We know this when the learner draws pictures and constructs pictographs that have a 1-1 correspondence between own data and representations;

Assessment Standard 5.5: We know this when the learner describes own or a peer’s collection of objects, explains how it was sorted, and answers questions about it.