Lesson 6.56.5 Small Group · Group 1
Start hereWords, worked example, and sentence starters
Learning target With my small group, I can write an algebraic expression for a real situation and evaluate it for a given value of the variable — one step at a time, with support.
Start hereWords for this lesson
Read each word before you begin. Say it out loud.
| Word | What it means | Example |
|---|---|---|
| VariableSpanish: Variable | A letter that stands for a number that is unknown or can change. | the m in 14m + 35 |
| Algebraic ExpressionSpanish: Expresión algebraica | A math phrase that has at least one letter. | 14m + 35 |
| CoefficientSpanish: Coeficiente | The number in front of a letter, like the 3 in 3x. | In 14m, the coefficient is 14. |
| ConstantSpanish: Constante | A fixed number in an expression or equation that does not change. | the 35 in 14m + 35 |
| Like termsSpanish: Términos semejantes | Terms with the same letter raised to the same power, like 2x and 5x. | 4x + 2x = 6x (like terms, same variable); but 4x + 2y cannot be combined (different variables) |
| SubstituteSpanish: Sustituir | To replace a variable with a given number before working out the value. | For s = 30: 4.25s + 23.50 → 4.25 × 30 + 23.50 |
How it worksWorked examplewriting an expression with a variable
These numbers are not on your problems. The steps are. Follow them with your own numbers.
A club buys a $14 shirt for each member and pays one $35 setup fee. Write an expression for the total cost.
- Name the unknown. Let m = the number of members.
- Write the part that changes. $14 for each member → 14m
- Write the part that stays the same. one-time fee → 35
- Join them with the operation the story needs. 14m + 35
Answer: The expression is 14m + 35, where m stands for the number of members.
Now you trySame steps, your turn
The steps are the same as the worked example. The numbers are yours. Do the work.
A camp charges $9 for each craft kit and one $20 registration fee. Write an expression for the total cost.
- Name the unknown. Let = the number of craft kits.
- Write the part that changes. $9 for each kit →
- Write the part that stays the same.
- Join them with the operation.
Say it and write itSentence starters
Finish each sentence out loud with a partner. Then use them in your writing.
- I let stand for .
- The coefficient shows the amount for each .
- The constant happens only .
- My expression for this situation is .
Word bank variablealgebraic expressioncoefficientconstanttermeachone-timeperstands fordefinetotalunknown
Watch outA common mistake
A common mistake in Write Algebraic Expressions is treating 'each' or 'per' as if it means add instead of multiply, and attaching the variable to the wrong number. For 'a $25 setup fee plus $8 per hour, h,' students often write 25 + 8 + h (adding all three numbers) or 25h + 8 (multiplying the flat fee by h) instead of the correct 8h + 25. Since $8 applies per hour, it must multiply the variable (8h), and the flat $25 fee is a constant added only once — check that the per-unit rate, not the flat fee, is the number multiplied by the variable.
Lesson 6.56.5 Small Group · Group 1
Group 1Supported practice
Learning target With my small group, I can write an algebraic expression for a real situation and evaluate it for a given value of the variable — one step at a time, with support.
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1Circle the letter of the best answer. Show how you know.
Rosa writes “4 less than a number n” as 4 − n. Which expression is correct?
- An − 4
- B4 − n
- C4n
- Dn + 4
Hint Try a number. If n is 10, what is 4 less than 10?
Show your work
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2Complete each step, then write the final answer.
Words Math $8 for each class 8c $20 to join, one time + 20 Turn each part of the words into math. A gym costs $20 to join, paid one time. Each class costs $8. Let c be the number of classes. Write an expression for the total cost. Then find the cost for 6 classes.
- 1Write the cost of c classes.
- 2Add the join fee one time. What is the expression?
- 3Substitute c = 6. What is the total cost?
Final answer: -
3Complete each step, then write the final answer.
Words Math starts with 50 gallons 50 loses 3 gallons each hour − 3h This time the changing part is taken away. A tank has 50 gallons of water. It loses 3 gallons each hour. Let h be the number of hours. Write an expression for the water left. Then find the water left after 4 hours.
- 1How much water is lost in h hours?
- 2Write the expression for the water left.
- 3Substitute h = 4. How many gallons are left?
Final answer: -
4Complete each step, then write the final answer.
Evaluate 5n + 2 when n = 7.
Show your workHint Put 7 in place of n. 5n means 5 × n.
Final answer: -
5Complete each step, then write the final answer.
Evaluate 4.5m + 12 when m = 8.
Show your workHint Replace m with 8. Multiply 4.5 × 8 before you add.
Final answer: -
6Complete each step, then write the final answer.
p 1.75p + 4.50 10 ? Put 10 in place of p. Each slice of pizza costs $1.75. Delivery costs $4.50, paid one time. Let p be the number of slices. The cost is 1.75p + 4.50 dollars. What is the cost for 10 slices?
Show your workHint Replace p with 10. Multiply 1.75 × 10. Then add the delivery fee.
Final answer:
Explain your thinkingIn 8c + 20, why is the 8 next to the c, but the 20 is added alone?
Sentence starter The 8 is next to c because ___. · The 20 is added one time because ___.