A wonder of addition and multiplication
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I will show you an interesting topic of math. I think you can understand if you are twelve years old or older.
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階差数列の和？について 数学B 数列
高校数学Bにおいては数列も学びます．数列の範囲においては，和（シグマ）の計算において，途中の項がバサバサ消えるような計算が出てきます．これについて私は，足し算は足し算でまとめて，引き算は引き算でまとめて計算した方がいいと思います．このスライドではその理由について述べています．
楽しい数式その1 ～1と9の不思議～
0×9+1=1
1×9+2=11
12×9+3=111
123×9+4=1111
1234×9+5=11111
...
123456789×9+10=1111111111
面白い式だと思いませんか？このスライドではこの式の種明かしをしたいと思います．
個人的な意見ですが，こういう式を小学校の算数の授業で教えると生徒が興味を示すと思います．
足し算と掛け算のマジック
ここでは足し算と掛け算を使った面白いネタを紹介します．
高度な数学の知識は使いません．小学校高学年の方でも理解できると思います．
もし可能であれば，紙と鉛筆を用意してください．
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2) Multiplication is initially taught through repeated addition and represented on number lines before moving to arrays to demonstrate commutativity.
3) Division is first taught as sharing and grouping using practical methods and models like Numicon before using repeated subtraction on number lines with and without remainders.
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1) The document outlines methods for teaching multiplication and division to KS1 students, including repeated addition, arrays, partitioning, equal sharing, and equal grouping.
2) Multiplication is initially taught through repeated addition and represented on number lines before moving to arrays to demonstrate commutativity.
3) Division is first taught as sharing and grouping using practical methods and models like Numicon before using repeated subtraction on number lines with and without remainders.
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1) The document discusses counting the number of possible patterns for number puzzle squares of different sizes.
2) It explains that the number of possible patterns for an N x N square can be calculated as N! factorial, and this value increases extremely quickly as N increases.
3) For colored puzzle squares without numbers, the number of possible patterns is the number of numbered patterns divided by the factorial of N, to account for identical patterns due to color permutations.
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The document summarizes key concepts from a 5th grade math unit on number theory, including:
- Identifying even and odd numbers and using arrays to represent multiplication
- Using divisibility tests to determine if a number is divisible by another
- Finding all the factors of a given number and identifying prime and composite numbers
- Writing numbers in exponential notation and relating square numbers to their square roots
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The document explains how to add and subtract fractions with the same denominator. It provides examples of adding fractions like 3/4 + 3/4 = 6/4 and subtracting fractions like 16/4 - 6/4 = 10/4. The key steps are to keep the same denominator and then add or subtract the numerators. The document ensures the reader understands the process by providing multiple examples and asking them to solve additional problems at the end.
Multiplication Table of 4.pdf
Multiplication table of 4 is one of the easy tables of mathematics. Memorize 4 times table with us and practice given questions for fast learning.
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This document contains instructions for several math tricks and puzzles. The 7-11-13 trick involves multiplying a 3-digit number by 7, 11, and 13 and writing the number twice to get the answer. The 3367 trick has a friend pick a 2-digit number and multiply it by 3367 then divide the answer by 3 to find the original number. The missing digit trick has a friend write a 4+ digit number, add the digits, subtract from the number, cross out a digit, and say the remaining digits for the solver to identify the missing digit.
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階差数列の和？について 数学B 数列
高校数学Bにおいては数列も学びます．数列の範囲においては，和（シグマ）の計算において，途中の項がバサバサ消えるような計算が出てきます．これについて私は，足し算は足し算でまとめて，引き算は引き算でまとめて計算した方がいいと思います．このスライドではその理由について述べています．
楽しい数式その1 ～1と9の不思議～
0×9+1=1
1×9+2=11
12×9+3=111
123×9+4=1111
1234×9+5=11111
...
123456789×9+10=1111111111
面白い式だと思いませんか？このスライドではこの式の種明かしをしたいと思います．
個人的な意見ですが，こういう式を小学校の算数の授業で教えると生徒が興味を示すと思います．
足し算と掛け算のマジック
ここでは足し算と掛け算を使った面白いネタを紹介します．
高度な数学の知識は使いません．小学校高学年の方でも理解できると思います．
もし可能であれば，紙と鉛筆を用意してください．
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Centrifugation is a powerful technique used in laboratories to separate components of a heterogeneous mixture based on their density. This process utilizes centrifugal force to rapidly spin samples, causing denser particles to migrate outward more quickly than lighter ones. As a result, distinct layers form within the sample tube, allowing for easy isolation and purification of target substances.
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We present the JWST discovery of SN 2023adsy, a transient object located in a host galaxy JADES-GS
+
53.13485
−
27.82088
with a host spectroscopic redshift of
2.903
±
0.007
. The transient was identified in deep James Webb Space Telescope (JWST)/NIRCam imaging from the JWST Advanced Deep Extragalactic Survey (JADES) program. Photometric and spectroscopic followup with NIRCam and NIRSpec, respectively, confirm the redshift and yield UV-NIR light-curve, NIR color, and spectroscopic information all consistent with a Type Ia classification. Despite its classification as a likely SN Ia, SN 2023adsy is both fairly red (
�
(
�
−
�
)
∼
0.9
) despite a host galaxy with low-extinction and has a high Ca II velocity (
19
,
000
±
2
,
000
km/s) compared to the general population of SNe Ia. While these characteristics are consistent with some Ca-rich SNe Ia, particularly SN 2016hnk, SN 2023adsy is intrinsically brighter than the low-
�
Ca-rich population. Although such an object is too red for any low-
�
cosmological sample, we apply a fiducial standardization approach to SN 2023adsy and find that the SN 2023adsy luminosity distance measurement is in excellent agreement (
≲
1
�
) with
Λ
CDM. Therefore unlike low-
�
Ca-rich SNe Ia, SN 2023adsy is standardizable and gives no indication that SN Ia standardized luminosities change significantly with redshift. A larger sample of distant SNe Ia is required to determine if SN Ia population characteristics at high-
�
truly diverge from their low-
�
counterparts, and to confirm that standardized luminosities nevertheless remain constant with redshift.
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A wonder of addition and multiplication
- 1. A wonder of addition and multiplication Enjoy math!
- 2. • Hello everyone! • I will show you an interesting topic of math. • I think you can understand if you are twelve years old or older. • Let’s start!
- 3. Take a pencil and paper if you can. Choose three or more positive integers and write them on the left-hand side of the paper. ( In this case, I chose the four positive integers, 3, 4, 4 and 5. ) 3 4 4 5
- 4. Next, choose a integer on the left-hand side of the paper. ( In this case, I took 3. ) 3 4 4 5
- 5. Then, write the product of the numbers that you didn’t choose on the left-hand side on the right-hand side. 3 4 4 5 4×4×5 = 80
- 6. Then, subtract 1 from the number that you chose. 3 4 4 5 2 80
- 7. Repeat the same thing again and again until 0 appears on the left-hand side. 3 4 4 5 2 80
- 8. In this case, there are four numbers, 2, 4, 4 and 5 on the left-hand side at this time. Assume that you took 4 on the left-hand side. 3 4 4 5 2 80
- 9. Then, you should write the product of the numbers that you didn’t choose. 3 4 4 5 2 80 2×4×5 = 40
- 10. Then, you should subtract 1 from the number that you chose on the left-hand side. 3 4 4 5 2 3 80 40
- 11. Repeat the same thing again and again until 0 appears on the left-hand side. 3 4 4 5 2 3 80 40
- 12. 3 4 4 5 2 3 80 40
- 13. 3 4 4 5 2 3 80 40 2×3×4 = 24
- 14. 3 4 4 5 2 3 4 80 40 24
- 15. 3 4 4 5 2 3 4 80 40 24
- 16. 3 4 4 5 2 3 4 80 40 24 3×4×4 = 48
- 17. 3 4 4 5 2 3 4 1 80 40 24 48
- 18. 3 4 4 5 2 3 4 1 80 40 24 48
- 19. 3 4 4 5 2 3 4 1 80 40 24 48 3×4×4 = 48
- 20. 3 4 4 5 2 3 4 1 0 80 40 24 48 48 The number 0 appears.
- 21. 3 4 4 5 2 3 4 1 0 80 40 24 48 48 240 Now, calculate the sum of the numbers on the right-hand side. In this case, the sum is 80 + 40 + 24 + 48 + 48 = 240. There is an interesting fact. Can you find it? ＋
- 22. Now, calculate the product of the numbers that you chose at first. In this case, I chose the numbers 3, 4, 4 and 5 at first, so the product is 3 4 4 5 2 3 4 1 0 80 40 24 48 48 240 3×4×4×5 = 240. That’s interesting, isn’t it? ＋
- 23. If it is interesting for you, change the numbers and try again. Thank you for watching!!