1. 1. add 2. triple 3. decrease 4. prove Tie to LO
Activating Prior Knowledge – Notes
Write an equivalent word(s) for the word.
1. add
2. triple
3. decrease
4. prove
Tie to LO

2. Today, we will write equations using symbols.
Learning Objective
Today, we will write equations using symbols.
CFU

3. Concept Development – Pair Share
𝐁. 𝟏,𝟏𝟓𝟕= 𝒙 𝟐 + (𝒙+𝟐) 𝟐 𝒙+𝟐 −𝒙
A. The number 1,157 is the sum of the squares of two consecutive odd integers divided by the difference between the two consecutive odd integers.
How are these two related?
Which representation do you prefer?
CFU

4. Concept Development – Notes #1 & 2
1. Using letters to represent numbers in mathematical statements was introduced by Rene Descartes in the 1600s.
2. Use of letters, or symbols, to represent numbers not only brought clarity to mathematical statements, it also expanded the horizons of mathematics.
CFU

5. Concept Development – Notes #3 & 4
3. Using symbols saves time and labor.
𝟏,𝟏𝟓𝟕= 𝒙 𝟐 + (𝒙+𝟐) 𝟐 𝒙+𝟐 −𝒙 vs.
The number 1,157 is the sum of the squares of two consecutive odd integers divided by the difference between the two consecutive odd integers.
4. Notice that x is just a number. This is a symbolic statement about numbers.
CFU

6. Concept Development – Notes #5 & 6
5. Writing symbols is simpler than writing words, as long as everyone is clear about what the symbols mean.
6. When we write mathematical statements using letters, we say we are using symbolic language.
CFU

7. Concept Development – Notes #5 - 7
7. An equation is a statement of equality between two expressions.
Expressions
4+r – w ÷ 6
Equations
4+r = – 5 = 𝑥 w ÷ 6 = 2w - 5
CFU

8. Concept Development Review –
Word Phrases
Expression + –  
a number plus 5
sum of a number and 5
n + 5
5 more than a number
subtract 11 from a number
difference of a number and 11
x – 11
11 less than a number
3 multiplied by a number
3  m or 3m
product of 3 and a number
7 divided into a number
or a  7 a 7
quotient of a number and 7
CFU

9. Skill Development/Guided Practice – Notes #8
A whole number has the property that when half the number is added to 15, we get the number itself.
𝟏 𝟐 𝒙+𝟏𝟓=𝒙
CFU

10. Skill Development/Guided Practice – Notes #9
A whole number has the property that when the square of half the number is subtracted from five times the number, we get back the number itself.
𝟓𝒙− 𝒙 𝟐 𝟐 =𝒙
CFU

11. Skill Development/Guided Practice – Notes #10
Paulo has a certain amount of money. If he spends six dollars, then he has 𝟏 𝟒 of the original amount left.
𝒙−𝟔= 𝟏 𝟒 𝒙
CFU

12. Skill Development/Guided Practice – Notes #12
The sum of three consecutive integers is 372.
What does consecutive mean?
𝒙+𝒙+𝟏+𝒙+𝟐=𝟑𝟕𝟐
𝟑𝒙+𝟑=𝟑𝟕𝟐
CFU

13. Skill Development/Guided Practice – Notes #13
The sum of three consecutive odd integers is 93.
What does odd consecutive mean?
𝒙+𝒙+𝟐+𝒙+𝟒=𝟗𝟑
𝟑𝒙+𝟔=𝟗𝟑
CFU

14. About 6 minutes and then we will review.
Independent Practice –
About 6 minutes and then we will review.
1. The sum of four consecutive even integers is -28.
𝒙+𝒙+𝟐+𝒙+𝟒+𝒙+𝟔=−𝟐𝟖
𝟒𝒙+𝟏𝟐=−𝟐𝟖
CFU

15. Independent Practice – Back of Notes
2. A number is four times larger than the square of half the number.
𝒙=𝟒 𝒙 𝟐 𝟐
CFU

16. Independent Practice – Back of Notes
3. Steven has some money. If he spends nine dollars, then he will have 𝟑 𝟓 of the amount he started with.
𝒙−𝟗= 𝟑 𝟓 𝒙
CFU

17. Independent Practice – Back of Notes
4. The sum of a number squared and three less than twice the number is 129.
𝒙 𝟐 +𝟐𝒙−𝟑=𝟏𝟐𝟗
CFU

18. Independent Practice – Back of Notes
5. Miriam read a book with an unknown number of pages. The first week she read five less than 𝟏 𝟑 of the pages. The second week she read 171 pages and finished the book. Write an equation that represents the total number of pages in the book.
𝟏 𝟑 𝒙−𝟓+𝟏𝟕𝟏=𝒙
CFU

19. Closure - Paper CFU 1. What did we learn today?
2. Why is this important to you?
3. Why do we write mathematical statements using symbols?
Write each of the following statements using symbolic language.
4. When you square five times a number you get three more than the number.
5. Monica had some cookies. She gave seven to her sister. Then, she divided the remainder in half, and she still had five cookies.
CFU