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Instructional Routine Activity

For use with small groups, partner pairs and independent work

[dvmd_table_maker tbl_title_mode=”on” tbl_title_text=”Evaluating Algebraic Expressions” tbl_frame_type=”none” tbl_chead_cell_align_horz=”center” _builder_version=”4.24.2″ _module_preset=”default” tbl_title_font=”|700|||||||” tbl_title_text_align=”center” tbl_tcell_text_font=”|600|||||||” tbl_chead_text_font=”|600|||||||” min_height=”436px” custom_margin=”||14px|||” global_colors_info=”{}”][dvmd_table_maker_item col_label=”I’ll tell you why” col_content=”I’ll tell you why… You are playing a guessing game of a number with your friends and you say: “I’m thinking of a number. If I double it and add six, I get the same answer as if I multiply it by five and subtract three. What is the number?” After a few trials, you tell them that the number you are thinking of is 12. They asked you to explain how you figured it out. You explain it to them one phrase at a time. Use the five algebraic expressions below to fill in the blanks in order to complete the sentences. i) 5n – 3 ii) 2n + 6 = iii) 2n iv) 2n + 6 = 5n – 3 v) 2n + 6 ” col_chead_cell_color=”#000000″ col_chead_cell_align_vert=”center” _builder_version=”4.24.2″ _module_preset=”default” col_chead_text_font=”|700|||||||” col_chead_text_font_size=”32px” global_colors_info=”{}”][/dvmd_table_maker_item][/dvmd_table_maker][dvmd_table_maker tbl_row_header_count=”0″ tbl_frame_type=”none” tbl_chead_cell_color=”#000000″ tbl_chead_cell_align_horz=”center” _builder_version=”4.24.2″ _module_preset=”default” tbl_chead_text_text_color=”#FFFFFF” custom_margin=”-18px|||||” custom_padding=”|0px||||” global_colors_info=”{}”][dvmd_table_maker_item col_content=”One phrase at a time: I’m thinking of a number If I double it And add six I get the same answer As if I multiply it by five and subtract three So the word problem translates to the equation What is the number?” col_column_max_width=”0.3fr” col_tcell_cell_align_horz=”left” col_chead_cell_align_horz=”left” _builder_version=”4.24.2″ _module_preset=”default” global_colors_info=”{}”][/dvmd_table_maker_item][dvmd_table_maker_item col_content=”The phrase translates to algebra as: Ok, let the number be “n” to “double something” means to multiply by two, so it translates to ______________ well, “add six” , translates to ___________ “same answer” suggests “equal”, so we put an equal sign and we get ___________ Next, “multiply it by five and subtract three” translates to __________, which goes on the right side of the equation. _____________________ If you solve the equation you get 12″ col_tcell_cell_align_horz=”left” col_chead_cell_align_horz=”left” _builder_version=”4.24.2″ _module_preset=”default” col_tcell_text_font=”||||||||” global_colors_info=”{}”][/dvmd_table_maker_item][/dvmd_table_maker]

Instructional Routine – Sample Response

For use with small groups, partner pairs and independent work

[dvmd_table_maker tbl_title_mode=”on” tbl_title_text=”Evaluating Algebraic Expressions” tbl_frame_type=”none” tbl_chead_cell_align_horz=”center” _builder_version=”4.24.2″ _module_preset=”default” tbl_title_font=”|700|||||||” tbl_title_text_align=”center” tbl_tcell_text_font=”|600|||||||” tbl_chead_text_font=”|600|||||||” min_height=”436px” custom_margin=”||14px|||” global_colors_info=”{}”][dvmd_table_maker_item col_label=”I’ll tell you why” col_content=”I’ll tell you why… You are playing a guessing game of a number with your friends and you say: “I’m thinking of a number. If I double it and add six, I get the same answer as if I multiply it by five and subtract three. What is the number?” After a few trials, you tell them that the number you are thinking of is 12. They asked you to explain how you figured it out. You explain it to them one phrase at a time. Use the five algebraic expressions below to fill in the blanks in order to complete the sentences. i) 5n – 3 ii) 2n + 6 = iii) 2n iv) 2n + 6 = 5n – 3 v) 2n + 6 ” col_tcell_cell_color=”#FFFFFF” col_chead_cell_color=”#000000″ col_chead_cell_align_vert=”center” _builder_version=”4.24.2″ _module_preset=”default” col_chead_text_font=”|700|||||||” col_chead_text_font_size=”32px” global_colors_info=”{}”][/dvmd_table_maker_item][/dvmd_table_maker][dvmd_table_maker tbl_row_header_count=”0″ tbl_frame_type=”none” tbl_chead_cell_color=”#000000″ tbl_chead_cell_align_horz=”center” _builder_version=”4.24.2″ _module_preset=”default” tbl_chead_text_text_color=”#FFFFFF” custom_margin=”-18px|||||” custom_padding=”|0px||||” global_colors_info=”{}”][dvmd_table_maker_item col_content=”One phrase at a time: I’m thinking of a number If I double it And add six I get the same answer As if I multiply it by five and subtract three So the word problem translates to the equation What is the number?” col_column_max_width=”0.3fr” col_tcell_cell_color=”#FFFFFF” col_tcell_cell_align_horz=”left” col_chead_cell_align_horz=”left” _builder_version=”4.24.2″ _module_preset=”default” global_colors_info=”{}”][/dvmd_table_maker_item][dvmd_table_maker_item col_content=”The phrase translates to algebra as: Ok, let the number be “n” to “double something” means to multiply by two, so it translates to 2n well, “add six” , translates to 2n + 6 “same answer” suggests “equal”, so we put an equal sign and we get 2n + 6 = Next, “multiply it by five and subtract three” translates to 5n – 3, which goes on the right side of the equation. 2n + 6 = 5n – 3 If you solve the equation you get 12″ col_tcell_cell_align_horz=”left” col_chead_cell_align_horz=”left” _builder_version=”4.24.2″ _module_preset=”default” col_tcell_text_font=”||||||||” global_colors_info=”{}”][/dvmd_table_maker_item][/dvmd_table_maker]

Evaluating Algebraic Expressions

LESSON OBJECTIVES

When you complete this lesson, you will be able to:

  • Evaluate algebraic expressions
  • Evaluate formulas and other expressions

LESSON SUMMARY

When we are asked to “evaluate” an algebraic expression, we are told which numbers the letters stand for. Then, to figure out the value of the entire expression, we simply replace each letter with the number it stands for. For example, suppose we are told to evaluate the algebraic expression 3M + P if M = 2 and P = 8. We replace M with 2 and P with 8, and complete the problem as shown below.

  • 3M + P
  • 3(2) + 8
  • 6 + 8
  • 14

Self-Test

Use this test to check your understanding.

Evaluate these algebraic expressions:

  1. 7G – 5H, if G = 8, H = 6
  2. \(\frac{4S\;+\;T^2}V\) if S = 7, T = 6, V = 8

Compare your answers with those below.

Answers to Self-Test

  1. 26
  2. 8

Examples

These examples can help you master the new ideas in this lesson.

Evaluate each of the following algebraic expressions:

  1. 5v + y, if v = 3, y = 2.
  2. TS + R2 + , if R = 3, S = 7, T = 2.
  3. \(\frac{m}{2k}\) – n if k = 2, m = 8, n = -3.

Solution

To evaluate an algebraic expression we replace the letters by the numbers that we are told they equal. Then we find the value of the expression.

  1. 5v + y
    5(3) + 2
    15 + 2
    17
  2. TS + R2
    2(7) + 32
    14 + 9
    23
  3. \(\frac{m}{2k}\) – n
    \(\frac8{2(2)}\) – (-3)
    \(\frac84\) – (-3)
    2 – (-3)

To subtract a negative number, change the subtraction sign to addition, and change the negative sign to a positive sign.

2 + 3
5

Practice Problems

These problems will give you more experience with the material in this lesson.

  1. Evaluate each of the following expressions using these values: d = 2, e = 3, f = 1
    a) 4e + ef
    b.) fde
    c.)\(\frac{3e+f}d\)
  2. Evaluate each of the following expressions using these values: b = 3, s = -1, w = 4
    a.) w2 + 5s
    b.) bsw
  3. Evaluate each of the following expressions using these values: f = 2, g = 4, h = 1
    a.) 2g − 3hf
    b.) f + h
    c.) g + h + f2
  4. Using the formula E = RT (Earnings = hourly rate × number of hours worked), find the
    amount earned by each of the following people:
    a.) Jeff, who worked 35 hours at $9 an hour.
    b.) Diane, who worked 20 hours at $11 an hour.
    c.) Maria, who worked 18 hours at $12.50 an hour.

Answers to Practice Problems

  1. a.) 15
    b.) -4
    c.) 5
  2. a.) 11
    b.) -7
  3. a.) 3
    b.) 3
    c.) 9
  4. a.) 315 dollars
    b.) 220 dollars
    c.) 225 dollars

CollegeReadyMath’s Algebra I Intervention Program includes the following:

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