A focused Grade 6 learning session for Exponents and Order of Operations using visual models, worked examples, strategy guidance, and a short mastery check.
Student goal: I can solve problems involving exponents and order of operations.
Exponents and Order of Operations means choosing a model, naming what each number means, and explaining the strategy.
Question: Which correctly describes the first step in evaluating \(5 + 4^2 \times 2\)?
Why it works: PEMDAS requires exponents before multiplication. The diagram shows the first step is evaluating \(4^2 = 16\). Then multiply: \(16 \times 2 = 32\). Finally add: \(5 + 32 = 37\).
Answer: \(37\)
Question: What is the value after Step 1 (parentheses)?
Answer: \(5^2 \times 2\)
Question: Evaluate: \(50 - 2^3 \times 5\)
Answer: \(10\)
Question: A student wrote: "\(2 + 3^2 = 5^2 = 25\)." What is the mistake?
Why it works: Apply the exponent first: \(3^2 = 9\). Then add: \(2 + 9 = 11\). The student incorrectly added before applying the exponent, treating it as \((2+3)^2\).
Answer: The exponent should be applied only to the base \(3\), not the sum.
Exponents and Order of Operations becomes easier when students connect the question to a model, use clear steps, and explain why the answer fits.
Understand the model before choosing the operation.
Use scratch paper. The explanation matters more than simply seeing whether the choice is correct.
Evaluate: \(3^2+2\times(5-1)\)
Answer B: \(17\)
Work inside the parentheses first: \(5-1=4\). Then exponent: \(3^2=9\). Then multiply: \(2\times4=8\). Finally add: \(9+8=17\).
What is \(2^4\) in expanded form?
Answer D: \(2\times2\times2\times2\)
An exponent shows how many times to multiply the base by itself. \(2^4\) means \(2\) multiplied \(4\) times, which is \(2\times2\times2\times2=16\).
Evaluate: \(5^3\)
Answer C: \(125\)
\(5^3 = 5 \times 5 \times 5 = 125\). The exponent 3 means we multiply 5 by itself 3 times (a cube).
What is \(6^2\)?
Answer B: \(36\)
\(6^2 = 6 \times 6 = 36\). A square exponent (power of 2) means multiply the base by itself once.
Evaluate: \(10^2 \div 5 + 3\)
Answer D: \(23\)
First, compute the exponent: \(10^2 = 100\). Then divide: \(100 \div 5 = 20\). Finally add: \(20 + 3 = 23\).
Which expression equals \(24\)?
Answer C: \(4^2 + 8\)
Evaluate each expression using order of operations. Choice C gives \(4^2+8=16+8=24\).
Evaluate: \((2+3)^2 - 5\)
Answer B: \(20\)
First, work inside the parentheses: \(2 + 3 = 5\). Then apply the exponent: \(5^2 = 25\). Finally subtract: \(25 - 5 = 20\).
What is \(4^3\)?
Answer C: \(64\)
\(4^3 = 4 \times 4 \times 4 = 64\). The exponent 3 tells us to multiply 4 by itself 3 times.
Evaluate: \(8 + 2 \times 3^2\)
Answer B: \(26\)
First, evaluate the exponent: \(3^2 = 9\). Then multiply: \(2 \times 9 = 18\). Finally add: \(8 + 18 = 26\).
Evaluate: \((6 - 2) \times 3 + 1\)
Answer C: \(13\)
Work inside the parentheses first: \(6 - 2 = 4\). Then multiply: \(4 \times 3 = 12\). Finally add: \(12 + 1 = 13\).
Which expression is equivalent to \(3 \times 3 \times 3 \times 3\)?
Answer C: \(3^4\)
The expression \(3 \times 3 \times 3 \times 3\) shows 3 multiplied 4 times. In exponential form, this is \(3^4\), where 3 is the base and 4 is the exponent.
