Question 1
1.1
1.1.1. E
1.1.2. A
1.1.3. B
1.1.4. G
1.1.5. D
1.2
1.2.1. A, D & G
1.2.2. B, C, F & H
1.2.3. E, I & J
1.3
1.3.1. Addition, Substraction, multiplication and division.
1.3.2. Counting and Number recognition.
1.3.3. Grade 2
1.3.4. Grouping / term 3
1.3.5. Addition
1.4
1.4.1. E
1.4.2. C & G
1.4.3. A,D & H
1.4.4. B& F
2.1. C
2.2. Inverse operations are shown in the pictures. Addition is represented in
Image 1 by joining two 4-stud blocks to create an 8-stud block. Subtraction is
represented in Image 2 by minusing the 8-stud block with the 4 stud block
into two 4-stud block. These operations demonstrate how addition and
subtraction have an inverse relationship in which one operation undoes the
other to return to the initial state, Schafer, J. & Nel, I (2020).
2.3.
2.3.1. Sizwe and Thembi are building a LEGO tower, each bringing a 4-stud
block to form a big block for the first line of the tower. How many studs will
be on the new big block altogether?
2.3.2. Kinaesthetic activity: using learners bodies to get the sum or total.
Choose 4 pupils (representing 4 studs from one block) to come and
stand in front of the class, Schafer, J. & Nel, I (2020).
Then, choose another 4 pupils to join them, Schafer, J. & Nel, I (2020).
Ask the piupils: "How many pupils are standing in front of the class
altogether?” Schafer, J. & Nel, I (2020).
Allow the learners to explain addition in their own words, by providing
guidance through statements such as, “when you put 4 learners and 4
learners together, you have a total of 8 learners.” Schafer, J. & Nel, I
(2020).
2.3.3. Concrete Activity: learners using the real counting blocks to get the
sum.
LTSM: 4 blue and 4 green blocks (representing the number of studs)
Pair up the pupils and provide each pair with a set of 4 red blocks and
4 green blocks each.
Depending on their development level, learners can use counting all or
counting on, Schafer, J. & Nel, I (2020).
State to the class that, “Combining 4 blue blocks with the 4 green
blocks will give a 8 block tower.” Schafer, J. & Nel, I (2020).
Allow each pair to share their methond and the total number of studs
they counted with the class. All provide guidance through questions
and verbal statements, Schafer, J. & Nel, I (2020).
2.3.4. Semi-concrete Activity: using dot cards to get the sum
Divide the class into pairs and provide each pair with a two set of dot
cards each with 4 dots representing the LEGO block studs.
Depending on their development level, learners can use counting all or
counting on, Schafer, J. & Nel, I (2020).
Instruct each pair to put the 4 dots card with the other 4 dots card to
get 8 dots, representing the large block.
State to the class that, “Combining two dot cards with 4 dots each will
give 8 dots.” Schafer, J. & Nel, I (2020).
2.4.
2.4.1. Sizwe had a big LEGO block with 8 studs, made up of two 4-studded
LEGO blocks. He then took one 4-studded LEGO block and gave it to Thembi.
How many studs were left on Sizwe's block after giving one away?
2.4.2. Kinaesthetic activity: using learners bodies to get the differencel.
Choose 8 pupils (representing 8 studs from the large block) to come
and stand in front of the class, Schafer, J. & Nel, I (2020).
Then, Ask the 4 pupils to go back to their respective seats, Schafer, J. &
Nel, I (2020).
Ask the pupils: "How many pupils are still standing in front of the
class?” Schafer, J. & Nel, I (2020).
Allow the learners to explain substration in their own words, by
providing guidance through statements such as, “when you have 8
learners standing and 4 learners go back to their seats, only 4 learners
are left standing.” Schafer, J. & Nel, I (2020).
2.4.3. Concrete Activity: learners using the real counting /LEGO blocks to get
the diference.
Provide the learners with LEGO blocks (8), allow them to build a tower
using the provided blocks.
Then, ask the to take away 4 blocks from the tower and then ask them
how many blocks are in front of you, Schafer, J. & Nel, I (2020)
Depending on their development level, learners can use counting all or
counting on, Schafer, J. & Nel, I (2020).
State to the class that, “when taking away a 4 studded block from the
8 studded block, there will be a 4 studded block remaining.” Schwafer,
J. & Nel, I (2020).
2.4.4. Semi-concrete Activity: using dot cards to get the difference
Divide the class into pairs and provide each pair with a 8 dot cards
each representing the LEGO block studs.
Depending on their development level, learners can use counting all or
counting on, Schafer, J. & Nel, I (2020).
Instruct each pair to remove 4 dots cards from 8 dots cards,
representing the large block and ask them to count the remaining dot
cards
Allow the learners to manipulate the cards to get the difference while
guiding the with statement such as, “ when taking away 4 dots cards
from the 8 dot cards, you will get 4 dot cards.” Schafer, J. & Nel, I
(2020).
Question 3
3.1. In the Foundation Phase, mathematical graphics are used to help
students integrate their language and math knowledge, which improves their
ability to come up with new solutions and adjust representations to fit
changing circumstances, Bouwer, 2023. This helps students solve problems
creatively and take responsibility for learning conceptually challenging
material, Bouwer, 2023.
3.2. There are 6 lollipops to be shared equally among 3 girls. How many
lollipops will each girl receive?
3.3. Because the learner can comprehend the idea of equal sharing, apply
division to solve the problem, and interpret the visual representation of the
three girls sharing the lollipops, the learner has a good understanding of the
word problem. This learner is able to make a connection between conceptual
and mathematical knowledge, Schafer, J. & Nel, I (2020).
3.4. Supporting Grade R learners in transitioning towards written
mathematics involves the utilization of the following strategies; Kinaestetic
activity( using learners bodies to learner), concrete activity(use of concrete
LTSMs to learner) and semi concrete activity ( use of e.g. picture cards or dot
cards), Schafer, J. & Nel, I (2020).
3.5. 6 lollipops ÷ 3 girls = each girl will receive 2 lollipops. Therefore 6 ÷ 3 =
2
Question 4
4.1. The commutative property in mathematics states that the order of
numbers being added does not change the result, Schafer, J. & Nel, I (2020).
The lines "1 for you and 4 for me" and "4 for you and 1 for me" in the
provided rhyme illustrate the commutative property of addition. The
commutative property of addition is demonstrated by the fact that, no
matter which order the apples or pears are distributed, the total stays the
same (5).
4.2. The commutative property also applies to multiplication in mathematics.
This property states that changing the order of the numbers being multiplied
does not change the result (Khan Academy (n.d.)).
For example, in multiplication
a × b = b × a; where a and b are any 2 non zero whole numbers
3x4=4x3
(source: Khan Academy (n.d.))
4.3.
4.3.1. Objective: Teaching Grade R students the commutative property of
addition through the use of rhymes and other LTSMs.
4.3.2. Let the learners recite the following rhyme to start: "5 red apples on
the tree, 1 for you and 4 for me! 5 green pears on the tree, 4 for you and 1
for me!", and encourage the learners to role-play the distribution of the
fruits as stated in the rhyme, (Engage education, 2023)).
Resources:
Learners bodies ( singing and role-playing), Schafer, J. & Nel, I (2020).
4.3.3.
Learners should be divided into pairs or small groups, and each group
should be given the following concrete resources, Schafer, J. & Nel, I
(2020): five red and green toy apples, five red and green toy pears,
and a tree prop or image of a tree.
Ask the learners to physically arrange the fruits on the tree according
to the rhyme:
“5 red apples on the tree, 1 for you and 4 for me!”
“5 green pears on the tree, 4 for you and 1 for me!”
Ask the learners to work through the exercise, lead conversations
about the following: How the fruits are sorted and distributed according
to the rhyme. Learners should be encouraged to rearrange the fruits
and note that the sum stays constant in order to demonstrate the
commutative property, Williams P.M & Gonzalez, K. (2023). Make use of
the concrete resources to show that altering the addendum's order has
no effect on the total quantity, Williams P.M & Gonzalez, K. (2023).
Resources:
Red and green toy apples
Red and green toy pears
Tree prop
4.3.4. Make Use of dot cards with arrangements representing the numbers 1,
4, and 5 from the rhyme. As they role-play the distribution, have learners
match the dot cards to the appropriate fruits on the tree. This activity
reinforces the connection between the number dot arrangements and the
physical and numerical representations of the fruits on the tree, Baroody, A.J,
(2017).
Resources: Dots Cards, Schafer, J. & Nel, I (2020).
4.3.5 Reference List:
Baroody, A.J.(2017).The Use of Concrete Experiences in Early Childhood
Mathematics Instruction. Available online at:
http://dx.doi.org/10.1016/bs.acdb.2017.03.001 [Accessed 04 August 2024].
Engage education. 2023. Learning Styles: Kinaesthetic Learner
Characteristics – Engage Education. Available online at: https://engage-
education.com/blog/learning-styles-kinaesthetic-learner-characteristics/
[Accessed 05 August 2024].
Khan Academy (n.d.)). Commutative property of multiplication review
(article). Available online at: https://www.google.com/url?
sa=t&source=web&rct=j&opi=89978449&url=https://
www.khanacademy.org/math/arithmetic-home/multiply-divide/properties-of-
multiplication/a/commutative-property-review&ved=2ahUKEwjy49610-
CHAxXxa0EAHegMIv44ChAWegQIBhAB&usg=AOvVaw3qWahCN1iuYwqz_Xey
QOL1[Accessed 05 August 2024].
Schafer, J. & Nel, I (2020). R-MAT221. Mathematics Learning in Grade
R1.SANTS Private Higher Education Institution. Pretoria: BusinessPrint.
Williams P.M & Gonzalez, K. (2023). Commutative Property of Addition |
Overview & Examples. Available online at:
https://study.com/academy/lesson/cumulative-property-of-addition-definition-
example.html [Accesse 05 August 2024].
