เรียนเลข ม.๑ (เลขจำนวนเต็ม)

➕️ ➖️ เรียนเลข ม.๑ ✖️ ➗️ =❓️ ✔️ ❌️

Recently, I have spent time doing lessons in school math for year 7 (นักเรียนชั้นมัธยมศึกษาปีที่ 1; ~ 13 year old). I took some examples of content and learning/teaching activities. Perhaps, we can learn what our children are going through and why they are not doing well in math. More is about how the children are 'limited' in their learning and achieving better understanding of the math content and its applications in their future lives.

What are in the school curriculum for this Year 7 Mathematics?
[Internationally] most 7th grade math students will learn about numbers, expressions, equations & inequalities, and the steps involved in solving them. They will also learn about ratios, percents, probability, and statistics. Finally, they will learn geometric concepts (for examples surface area and volume of solids).[ See Note 2 for details]

Note 1) Examples of a class activities Guide (also called 'worksheet' / 'workbook').
A) https://cdn.gotoknow.org/assets/media/files/001/500/192/original_1721628499.pdf แบบฝึกทักษะคณิตศาสตร์.pdf
-- my comments:
Thai math language is “hard” but useful for communication.
Understanding the math concepts is perhaps much more useful for learning.

I think words like สมบัติการสลับที่ (commutative property), สมบัติการแจกแจง (distributive property) and สมบัติการเปลี่ยนหมู่ (associative property) force children into memorizing them. But the Royal Society (ราชบัณฑิตยสภา) had defined them. It is a problem, isn’t it?

- 1) page 14 : assertion that a x 0 = a = 0 x a is not correct, a x 0 = 0!

- 2) 'test before' is the same as 'test after'. So, before class, it is very likely that students would NOT do well in the test. After the class activities, unless the teaching/learning activities are really BAD, the students should do better. These tests are NOT showing results of learning or instructions.

B) https://www.leadedres.com.au/_files/ugd/f0332f_1ef43fc27c0146279526f5e784f780ab.pdf
-- my comments:
- 1) focus on concepts and examples for students to derive rules by themselves. No terminology.
- 2) students to work out extensions and applications of the rules they have together derived. No tests.

Note 2) In [Queensland, Australia] 7th grade math:
Unit 1: Proportional relationships. ...
Unit 2: Rates and percentages. ...
Unit 3: Integers: addition and subtraction. ...
Unit 4: Rational numbers: addition and subtraction. ...
Unit 5: Negative numbers: multiplication and division. ...
Unit 6: Expressions, equations, & inequalities.
7: Probability and statistics
8: Scale and copy
9: Geometry

For examples of worksheets :
https://www.leadedres.com.au/year-7-worksheets
https://www.leadedres.com.au/_files/ugd/f0332f_1ef43fc27c0146279526f5e784f780ab.pdf

Note 3) Precedence of mathematical operations in an expression:
The order of math operations within a math expression is summarized by an acronym 'BODMAS'. where
BODMAS stands for B-Brackets, O-Orders (powers/indices or roots), D-Division, M-Multiplication, A-Addition, S-Subtraction. So, terms in brackets, if any, will be evaluated first, terms with order, if any, (power and root) next, then terms in division, followed by terms in multiplication, then addition and last subtraction.

Perhaps, for Thai students the acronym ว ก ห ค บ ล (or วก หค +-) may be useful.

There is an alternative ordering: PEMDAS with Parenthesis, exponents, Mult, div, + -

Note 4) Examples of exercise questions to support student self-learning of math concepts
This worksheet is used to guide students to discover mathematical properties of numbers in various operations () ^ x ÷ + - [BODMAS, วก หค +-]. The tutor or teacher is to allow students to work on the worksheet alone by themselves or in small groups for some (40 minutes) duration of the class, but may initiate class discussions at any time to clarify or summarize issues. Names of mathematical property may be introduced after the drills are completed.

Note 5) Below is an example of worksheet for learning 'properties of integer operations'. The questions are designed to guide students to levels of learning from 'getting ready' to 'exploring' to 'understanding' to 'applying' to 'extending' (renovating). The exercise is given to urge students to consider real life use of mathematics. These questions require calculating, judging and reasoning in writing. Multiple choice style is considered 'easy for teachers' but not conductive for students learning and not easy for diagnosis of learning problems.

- Drill 1: getting ready
15 = 51 ...True | False; Why ... by convention 15=10+5; 51=50+1;

- Drill 2: Exploring
5 x 2 = 2 x 5 ...True | False; Why ...
2 x a = a x 2 ...True | False; Why ...
2 x (3 + 4) = (3 + 4) x 2 ...True | False; Why ...
3 x (4 - 2) = (4 - 2) x 3 ...True | False; Why ...
(1 + 2) x (5 - 3) = (5 - 3) x (1 + 2) ...True | False; Why ...
a x b = b x a ...True | False; Why ...
8 ÷ 2 = 2 ÷ 8 ...True | False; Why ...
a ÷ b = b ÷ a ...True | False; Why ...
a x (b ÷ c) = (b ÷ c) x a ...True | False; Why ...
3^2 = 3 x 3 ...True | False; Why ...
2^5 = 2 x 2 x .......
3^2 = 2^3 ...True | False; Why ...

- Drill 3: understanding
5 - 1 = 1 - 5 ...True | False; Why ...
a - b = b - a ...True | False; Why ...
8 ÷ 2 = 2 ÷ 8 ...True | False; Why ...
a ÷ b = b ÷ a ...True | False; Why ...
a x (1÷b) = b x (1÷a) ...True | False; Why ...
2 x (a + b) = 2a + 2b ...True | False; Why ...
2 x (a - b) = 2a - 2b ...True | False; Why ...
(2 + 1) x (a + b) = (2 + 1) x a + (2 + 1) x b ...True | False; Why ...
(2 + 1) x (a + b) = 2 x (a + b) + 1 x (a + b) ...True | False; Why ...
(2 + a) x (1 + b) = ....... + ........

- Drill 4: Applying
1+2+3+4 = (1+2)+3+4 = 2+(1+3)+4 = 2+(2+2)+(2+2) = .......
1+2+3+...+10 = .......
-1-2-3-...-10 = .......
1-2+3-4+5-6+7-8+9-10 = ........
-1+2-3+4-5+6-7+8-9+10 = ........

- Drill 5: Extending
10+20+30+...+100 = .......
2+4+6+8+10+...+20 = ........
1+3+5+7+9 = .......
11x39 = .......
3x(91-19) =.......

- Exercise: In real world
See the table in https://www.isranews.org/article/isranews/130404-isra-200.html
Fill in ....... to show the chain of events from 2,000 fish to 0 fish
2,000 ....... = 600
600 ....... = 400
... ....... = 200
... ....... = 150
... ....... = 50
.. ....... = 0

Is this chain of events reasonable? And why or why not?

เรียนเลข ม.๑ (เลขจำนวนเต็ม)

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