You are participating in the pilot implementation of the Mathematical Framework - which requires the teaching of Mathematics for Understanding. Multiplication tables show the multiples of numbers – the answers to the multiplication of several 1 × 1 digit multiplications, depending on the number of the multiplication table.
Resources
The concrete number representations used in the TMU lesson plans as 'counters' for ones, tens and hundreds. Bottle caps are used as single counters (to count units), printed tens are used to count tens, and printed hundreds are used to count hundred places.
About the Lesson Plans and Resources
The assessment program proposed in the curricula is in line with CAPS as amended by Circular S1 of 2017 and the Provinces' responses thereto. Use all or a selection of these activities during the first week of the term before formal teaching of the numbered syllabuses begins.
Preparing to teach a lesson
It is important that you carefully plan how you will manage the pace of the lessons; otherwise, you will not be able to cover the entire content of the lesson. You have to set the pace - be guided by the average student and the recommendations in the curricula.
Lesson Plan Outline
Teacher’s notes
Lesson content – concept development (45 minutes)
Classwork activity and correction of homework (25 minutes)
You should try to answer all the daily math questions, but if you find that your students are struggling to complete them in ten minutes, do at least five questions. Complete the classwork activity each day by giving students the answers to the classwork, giving them time to write down corrections as and when necessary.
Homework activity (5 minutes)
Students should work individually first and then discuss with the rest of the group what they have done, based on what they have in their class book or worksheets.
Reflection (5 minutes)
The lesson activities below are for you to use on the first few days of school when students are still settling in and you are not quite ready to start the formal CAPS lesson plans that follow. These revision lesson activities will help you to keep students engaged in a meaningful way at the beginning of the term and to make observational notes about their mathematical knowledge development.
CAPS baseline framework
Number concept
Call on different students to come to the front and show you some different numbers. Start at other numbers that are multiples of 5 or ten and count in 5s and 10s.
Place value
You then discuss the place value and values of the digits in the number with the class.). First say the number as a whole number and then say it divided into tens and units.
Addition and subtraction
Repeated addition leading to multiplication
But when we work with larger numbers, we work with the numbers and the place value to figure out how much we have in total. To do this, you need to know your basic bonds and multiples very well – start learning them now.
Shapes and fractions
Q:What does it mean to divide a shape into two halves? you divide it into two parts of equal size). 2 Question: What does it mean to divide a shape into four. you divide it into four parts of equal size).
3-D objects
Take two boxes (of different sizes). Place the small box on top of the bog box. Show other representations of the shapes (next to, above, below, etc.) and allow students to describe the different positions using position words.
Measurement
Students rotate in groups so that each group has the opportunity to complete all activities. 1 Group 1: Give the group an A4 page and ask them to measure the length of the sides of the page with a pencil.
Data Handling
After students complete the table, ask them: How did the table help you organize the data. Explain that an icon is a way to represent data (drawing a graph to show what data you have collected).
Introduction: Numbers up to 1000
Numbers up to 999
3 CLASSROOM ACTIVITY AND HOMEWORK CORRECTION (25 MINUTES) Note: This activity does not include written work that can be marked as students need time to practice using the base ten groups. Note: This activity does not include written work that can be marked as students need time to practice using the base ten groups.
More numbers up to 999
Repeat the activity from the beginning with the base ten set on a place value table with other numbers that have a zero like ten or one, e.g. The other student must write down the number symbol represented by the base ten set in their class book.
Expanded notation
Ask the students to show the numbers on their place value table using their base ten sets, for example: 582. The students should then write (in their notebook) the number symbol that their base ten sets show.
Counting forwards and backwards up to 999
Make sure students read the numbers correctly – they should read the total values, not just the nominal values of the numbers they see. The other student must then count forward or backward from the selected starting number in 1s or 10s, as determined by the placement of the counters on the blocks.
Consolidation: Numbers up to 999
Multiples of 10
It is called an empty number line because it has no numbers and no markings. Ask the learners to help you fill in the numbers on the number line in increments of 10.
Assessment – Numbers up to 999
Assessment Criteria - Checklist: (1 mark for each criterion achieved) 1 Ability to count forward within 10 seconds in a range of numbers. 1 Ability to count down in 10s in a range of numbers 1 Ability to count down in 20s in a range of numbers 1 Ability to count down in 20s in a range of numbers 1 Ability to count down in 100s in a range of numbers 1 Ability to count down in a range of 100s in a range of numbers.
The number 1 000
So if we write the number symbol for 10 hundred in the same way as we wrote the other numbers on the board, it will look like this 1000. We say thousand instead because we are now talking about a 4 digit number and not a 3 -digit number.
The other student should represent the number by drawing the simple figures from activity 2.
Consolidation: Numbers up to 1000
We also added and subtracted in 10s and hundreds by counting forwards and backwards in 10s and 100s.
Sequencing and comparing numbers
Ask the students to indicate the direction that the numbers would increase on the number line in the previous activity.
Comparing, ordering and rounding off numbers
The small side of the sign indicates a smaller number, while the larger side of the sign indicates a larger number). The small side of the sign indicates a smaller number, while the larger side of the sign indicates a larger number).
By encouraging students to talk about their strategies, they will learn new (and more effective) strategies and thus improve their mathematical understanding. Ask the student to come to the board and write the remaining missing numbers.
Consolidation: Numbers up to 1000
Addition and subtraction of multiples of 10
Show students the connection between the number sentence and the place value table and their simplified pictures (or base ten groups). Show students the connection between the number sentence and the place value table with a base ten bag.
Introduction: Addition and subtraction
Mental maths – addition
Have students check the answer using a base ten set if the answer they have is different. After students have had a chance to work with 20 number combinations, repeat the above steps with a different number, for example.
Mental maths – addition with carrying
This is an effective strategy to use when addition problems require students to make a ten. Ask some students to share their strategies with the class and discuss the strategies students have suggested.
Mental maths – subtraction
Clearly show the connection between the simplified images and the numerical representation of the number.
Consolidation: Mental maths
Mental maths – subtraction with borrowing
Now add the 7 that remains after we split 17 into tens and ones.
Assessment – Mental maths with 2-digit numbers
Addition using the column method
Draw 86 and 43 vertically
Write the answer
First we used simplified drawings and then we started learning how to use the column method.
Addition using the column method and a number line
Draw 78 and 56 vertically
What is the difference between the column method we used in Activity 1 and the number line method we used now. First we used simplified drawings and the column method, then we learned to add using a number line.
Consolidation: Addition
Addition using various strategies
Ask a student to come up and write on the board to show the class how they would use the number line to solve the problem. What is the difference between the column method we used first and the number line method we used now.
Assessment – Addition
3 Can add from in the number range 0–50 by counting from the first number 4 Can add 2-digit and 3-digit numbers using the column method using a base ten set 5 Able to add 2-digit numbers and 3-digit numbers using the column method using a base ten set. 6 Able to add 2-digit and 3-digit numbers using the column method and a number line.
Subtraction using the column method
Draw 138
Since we can’t subtract 5 from 3 in tens place, exchange 1 hundred to 10 tens (borrowing)
Write the answer
The first step is to line up the numbers vertically in the hundreds, tens, and ones. This is very important as it is common for students to simply say "We can't subtract 5 from 3, so we'll subtract 3 from 5").
Subtraction using the column method
Draw 136
Since we can’t subtract 9 from 6 in the ones place, exchange 1 ten to 10 ones (borrowing)
Since we can’t subtract 4 from 2 in tens place, exchange 1 hundred to 10 tens (borrowing)
Write the answer
We borrow or exchange the hundred for 10 tens, so we end up with 12 tens). Remember to talk about crossing out one hundred and writing ten at the top of the tens place.
Consolidation: Addition and subtraction
Subtraction using the column method
Students still need to be aware of what to do when there is a zero in the tens place. We looked at what happens when there is a zero in the tens or ones.
Subtraction using various strategies
Ask one student to demonstrate the simplified picture strategy on the board, one student to demonstrate the column method, and one student to demonstrate the use of the number line. Today we solved subtraction problems using simplified drawings, the column method and number lines.
Assessment – Subtraction
3 Able to subtract in the number range 0–50 by counting from the first number 4 Able to subtract 2-digit and 3-digit numbers using the column method using a base ten set 5 Able to subtract 2-digit and 3- digit numbers using the column method using a base ten kit and. 6 Able to subtract 2-digit and 3-digit numbers using the column method and a number line 7 Able to subtract 2-digit and 3-digit numbers competently and can choose from a variety of.
Addition and subtraction using the column method
In the column method, you had to carry any numbers to the tens or hundreds column. In the column method, you had to borrow any numbers from the tens or hundreds column.
Consolidation: Addition and subtraction
Word problems
You always follow the steps to solve word problems like writing the word problem on the board, to read the problem, to let students read the problem themselves to understand the problem. You need to draw the bar graphs on the board to help students solve the problems.
Revision of addition and subtraction
Because the answer to the addition problem is 351, which is the same as the larger number in our subtraction problem). The answer in the addition problem is the same as the larger number answer in the subtraction problem.
Assessment – Addition and subtraction
We learned how to use addition to check whether our solution to a subtraction problem is correct.
Introduction: What’s the missing number?
What’s the missing number? Part 1
To find the missing number, we need to go backwards on the arrow above.
Consolidation: Missing Numbers
What’s the missing number? Part 2
Assessment – What’s the missing number?
Introduction: Number patterns
Counting in 2s and 4s
Do this by looking at each number in the 2's pattern to see if there is a match with a number in the 4's pattern.
Consolidation: Number patterns
Ask students to draw squares of how the patterns were made by counting in 4s, starting at 400 and counting to 600. Ask why it was easy to show the rest of the pattern. all the numbers are placed in two straight lines - the 5's line and the 10's line.).
Flow diagrams and tables
Ask students what pattern they notice. model that the output numbers are all multiples of 3).
Number patterns, flow diagrams and tables
Solve this problem by having students record their answers in a table and flowchart.
Assessment – Number patterns
Scoring criteria – Checklist: (1 mark for each criterion achieved) 1 Able to count in 2 s in the number range. 1 Capable of counting in 3 seconds in the number range 1 Capable of counting in 4 seconds in the number range 1 Capable of counting in 5 seconds in the number range 1 Capable of counting in 20 s in the range of Numbers 1 Able to count in 25 s in the range of Numbers.
Consolidation: Number patterns, flow diagrams and tables