Embedded Files
Ämne / Topic
Ämne / Topic
Writing small numbers using scientific notation.
Simplifying with negative exponents.
Inlärningsmål / Learning Goals
Inlärningsmål / Learning Goals
After this lesson you should know / understand....
After this lesson you should know / understand....
Whiteboard: I know... I understand...I can do...
Whiteboard: I know... I understand...I can do...
Write small numbers using scientific notation.
Write small numbers using scientific notation.
Simplifying exponents when one or more exponent is negative.
Simplifying exponents when one or more exponent is negative.
Google Slides & Videos
Google Slides & Videos
Lektionssteg / Steps in the lesson:
Lektionssteg / Steps in the lesson:
- Lektionsuppvärmning / Lesson warm up / Hook / Review from previous lesson
Lesson 1: (Writing number in scientific notation and standard form)
Lesson 1: (Writing number in scientific notation and standard form)
What is standard form and what is scientific notation?
What is standard form and what is scientific notation?
5 minutes to to discuss standard form and scientific notation in groups - learners will come up with a definition of the two concepts in their own words and provide examples. Groups will share their definitions and examples with the rest of the class.
5 minutes to to discuss standard form and scientific notation in groups - learners will come up with a definition of the two concepts in their own words and provide examples. Groups will share their definitions and examples with the rest of the class.
Lesson 2: (Writing scientific notation and standard form using negative powers).
Lesson 2: (Writing scientific notation and standard form using negative powers).
Writing a question in either standard form or scientific notation - when entering the class, the learners will receive a question on standard form or scientific notation, which they will need to complete. The learners will be called up at random to share their question and answer with the rest of the class.
Writing a question in either standard form or scientific notation - when entering the class, the learners will receive a question on standard form or scientific notation, which they will need to complete. The learners will be called up at random to share their question and answer with the rest of the class.
2. Introduktion till lektionen / Introduction to the lesson content
2. Introduktion till lektionen / Introduction to the lesson content
Standard form to Scientific notation.
Scientific notation to standard form.
Standard form to scientific notation - negative powers.
Scientific notation to standard form - negative powers.
3. Aktiviteter / Key Activities
3. Aktiviteter / Key Activities
Lesson 1: (Writing number in scientific notation and standard form)
Warm-up - What is standard form and what is scientific notation - learners will come up with a definition of the two concepts in their own words and provide examples. (Groups will share their definitions and examples with the rest of the class).
The teacher will show the learners a short video on scientific notation and standard form, as well as go through a slide show with the learners, based on converting between scientific notation and standard form (The teacher will pause and ask the learners questions on and to discuss certain slides, to keep the learners engaged).
The learners will apply the knowledge obtained in the lesson to worksheets. (Learners will be given the opportunity to work by themselves or with a partners).
Exit ticket - Learners will select one of the problems that they solved and come up to the board and explain their process on how they solved it.
How to Change Numbers Into and Out of Scientific Notation
Scientific notation is commonly used in chemistry and physics to represent very large or very small numbers. Changing numbers into and out of scientific notation isn't as hard as it looks.
Converting Numbers Into Scientific Notation
1
1
Add exponents together to show expanded multiplication.
Add exponents together to show expanded multiplication.
When numbers with exponents are multiplied by each other, you can represent the result easily by adding the exponents together.
When numbers with exponents are multiplied by each other, you can represent the result easily by adding the exponents together.
The base number remains unchanged.
The base number remains unchanged.
This rule only applies if the bases are the same.
This rule only applies if the bases are the same.
See these examples:
See these examples:
2
Cross out the original number's decimal point. This is the first step to beginning to convert the number into scientific notation. If you're working with the number 0.00004205, just write an "x" over the decimal point.
3
Add a new decimal point to the number so that there's only one non-zero digit in front of it. In this case, the first non-zero number is 4, so place the decimal point after the 4 so that the new number reads 000004.205.
This works for large numbers, too. For example, 10,090,250,000,000 would become 1.0090250000000.
4
Rewrite this number to drop any insignificant digits. Insignificant digits are any zeros that are not in between other, non-zero digits.
For example, in the number 1.0090250000000, the zeroes at the end are insignificant, but the zeros between the 1 and then 9, and between the 9 and the 2, are significant. Rewrite this number as 1.009025.
In the number 000004.205, the leading zeros are insignificant. Rewrite this number as 4.205.
9
9
Round your number as much as necessary. This depends on how certain you need to be in your answer. For example, 1.009025 x 1013 might be better off as 1.009 x 1013 or even as 1.01 x 1013, depending on how accurate you need to be.
Round your number as much as necessary. This depends on how certain you need to be in your answer. For example, 1.009025 x 1013 might be better off as 1.009 x 1013 or even as 1.01 x 1013, depending on how accurate you need to be.
Lesson 2: (Writing scientific notation and standard form using negative powers).
Lesson 2: (Writing scientific notation and standard form using negative powers).
Warm-up - Writing a question in either standard form or scientific notation - when entering the class, the learners will receive a question on standard form or scientific notation, which they will need to complete. The learners will be called up at random to share their question and answer with the rest of the class.
The teacher will go through a slide show and notes with the learners on how to convert between standard form and scientific notation with negative powers. (The teacher will pause and ask the learners questions on and to discuss certain slides, to keep the learners engaged).
The learners will apply the knowledge obtained in the lesson to worksheets. (Learners will be given the opportunity to work by themselves or with a partners).
Exit ticket - Learners will select one of the problems that they solved and come up to the board and explain their process on how they solved it.
Converting Numbers from Scientific Notation
Converting Numbers from Scientific Notation
1
1
Decide if you will be moving the decimal point to the left or to the right. If the exponent on the "x 10" part of the number is positive, then you will be moving the decimal places to the right; if the exponent is negative, you will be moving the decimal places to the left.
Decide if you will be moving the decimal point to the left or to the right. If the exponent on the "x 10" part of the number is positive, then you will be moving the decimal places to the right; if the exponent is negative, you will be moving the decimal places to the left.
2
Write down how many places you would need to move the decimal. In the case of the number 5.2081 x 1012, you will be moving the decimal point over five spaces to the right. If the exponent is a -7, you move left seven places; if the exponent is a 5, move right five places.
3
Move the decimal point over, adding zeroes for every empty space. You may have to add them in front of or behind the number, depending on whether you are moving left or right. If you're moving the decimal point over 12 spaces to the right from the number 5.2081, then the new number becomes 5208100000000.
4
Write the new decimal point after you've moved over the correct amount of spaces.
5
Add commas to any number over 999. Go through the digits, from right to left, putting a comma in front of every group of three digits. For example, 5208100000000 becomes 5,208,100,000,000.
4. Kolla vad eleverna kan / Check for understanding / Exit ticket
4. Kolla vad eleverna kan / Check for understanding / Exit ticket
Lesson 1: (Writing number in scientific notation and standard form).
Exit ticket - Learners will select one of the problems that they solved and come up to the board and explain their process on how they solved it.
Lesson 2: (Writing scientific notation and standard form using negative powers).
Exit ticket - Learners will select one of the problems that they solved and come up to the board and explain their process on how they solved it.
5. Avslutning / Closure / Summary of lesson
5. Avslutning / Closure / Summary of lesson
Discussing learners answers and why they chose to convert from standard form to scientific notation and visa versa in the way that they did.
Resurser & Materiel / Resources & Materials
Resurser & Materiel / Resources & Materials
http://webbapp.liber.se/matematikboken-z/#
Textbook Practice 1:
Ett pg. 31 no. 1089 abc, 1090 abc, 1091 ab, 1093.
Två pg. 32 no. 1096 abc, 1097, 1098, 1099.
Tre pg. 33 no. 1103 abc, 1104 abc, 1105.
Fyra pg. 33/34 no. 1107 abc, 1108 abc, 1109 abcd, 1110, 1111.
Textbook work 2:
ETT pg.38 - 1113 abc, 1114 abc, 1116 abc, 1118
TVÅ pg.39 - 1120 abc, 1121 abc, 1123 abc, 1124 abc, 1125
TRE pg.40 - 1127 abc, 1128 abc, 1130 abc, 1131 abc, 1132 abc
Fyra pg.41 - 1135 abc, 1137, 1138 ab, 1139 abc
Unit 1.5 Small numbers and powers of 10 answers.pdfUnit 1.5 Practice Questions.pdfPage updated
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