Lesson 6.46.4 Small Group · Group 1
Start hereWords, worked example, and sentence starters
Learning target With my small group, I can write numerical expressions from a real situation and evaluate them using the order of operations, including powers — 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 |
|---|---|---|
| Numerical expressionSpanish: Expresión numérica | A math phrase built from numbers and operations, with no equal sign and no variable. | 4 × 9 + 3 × 6 |
| EvaluateSpanish: Evaluar | To find the single value an expression is worth by carrying out its operations in order. | 3 × 6 = 18 |
| Order of operationsSpanish: Orden de las operaciones | The agreed order for evaluating: grouping symbols, then exponents, then multiply and divide left to right, then add and subtract left to right. | 3 + 4 × 2² → 3 + 4 × 4 → 3 + 16 = 19 |
| PowerSpanish: Potencia | A short way to write repeated multiplication of the same factor, such as 2³ for 2 × 2 × 2. | 8 × 8 = 8^2 |
| BaseSpanish: Base | In a power, the number being multiplied by itself. In 2³ the base is 2. | In 8^2, the base is 8. |
| ExponentSpanish: Exponente | In a power, the small raised number that says how many times the base is used as a factor. | In 8^2, the exponent is 2. |
How it worksWorked examplewriting an expression from a situation
These numbers are not on your problems. The steps are. Follow them with your own numbers.
A group buys 4 tickets at $9 each and 3 programs at $6 each. Write an expression for the total cost, then find it.
- Name the parts. tickets: 4 at $9 programs: 3 at $6
- Write a product for each part. 4 × 9 and 3 × 6
- Join them with the operation the story needs. 4 × 9 + 3 × 6
- Evaluate. 36 + 18 = 54
Answer: The expression is 4 × 9 + 3 × 6, and the total cost is $54.
Now you trySame steps, your turn
The steps are the same as the worked example. The numbers are yours. Do the work.
A team buys 7 shirts at $11 each and 2 hats at $8 each. Write an expression for the total cost, then find it.
- Name the parts. shirts: at $ hats: at $
- Write a product for each part. × and ×
- Join them with the right operation.
- Evaluate. + =
Say it and write itSentence starters
Finish each sentence out loud with a partner. Then use them in your writing.
- The word tells me to multiply by .
- The expression for this situation is .
- I used a power because the same factor repeats times.
- An expression has no equal sign, so I only it.
Word bank numerical expressionevaluatepowerbaseexponentproductsumdifferenceeachin alloperationvalue
Watch outA common mistake
A common mistake with powers is multiplying the base by the exponent: reading 3² as 3 × 2 = 6 instead of 3 × 3 = 9. A second is evaluating strictly left to right, so 3 + 4 × 2 becomes 14 instead of 11. The order of operations exists so one expression has exactly one value: grouping symbols, then powers, then × and ÷ left to right, then + and − left to right.
Lesson 6.46.4 Small Group · Group 1
Group 1Supported practice
Learning target With my small group, I can write numerical expressions from a real situation and evaluate them using the order of operations, including powers — one step at a time, with support.
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1Complete each step, then write the final answer.
Ticket Number Price Cost Adult 3 $12 3 × 12 Child 5 3² dollars 5 × 3² Each row is one part of the expression. Ana buys 3 adult tickets at $12 each and 5 child tickets at 3² dollars each. Write and evaluate an expression for the total cost.
- 1Write one expression for the total cost.
- 2Find the power first. What is 3²?
- 3Multiply, then add. What is the total cost?
Final answer: -
2Complete each step, then write the final answer.
Order Work 1. Power 2⁴ = ? 2. Multiply 3 × ? 3. Subtract ? − 12 Powers, then multiply, then subtract. Mr. Lee buys 3 boxes of pencils. Each box has 2⁴ pencils. He gives away 12 pencils. Write and evaluate an expression for the pencils he has left.
- 1Write one expression for the pencils left.
- 2Find the power first. What is 2⁴?
- 3Multiply, then subtract. How many pencils are left?
Final answer: -
3Complete each step, then write the final answer.
Evaluate 4 + 2 × 3².
Show your workHint Find the power first. Then multiply. Add last.
Final answer: -
4Complete each step, then write the final answer.
Evaluate 5 × 15 + 2 × 20 + 3 × 2³.
Show your workHint Find 2³ first. Then do each multiplication. Add last.
Final answer: -
5Complete each step, then write the final answer.
Item Number Price Cost Water 6 $2 6 × 2 Pretzel 4 2² dollars 4 × 2² Add the two costs in one expression. A snack stand sells 6 waters at $2 each and 4 pretzels at 2² dollars each. Write and evaluate an expression for the total cost in dollars.
Show your workHint The expression is 6 × 2 + 4 × 2². Find the power before you multiply.
Final answer: -
6Complete each step, then write the final answer.
Kim evaluates 3 + 4 × 5². She adds 3 + 4 first and gets 175. Is she right? Find the correct value.
Show your workHint Add comes last. What must you do before you add?
Final answer:
Explain your thinkingKim added first and got 175. Why must you find the power and multiply before you add?
Sentence starter First I find ___ because ___. · Kim's answer is wrong because ___.