Question

activity 1
the formula for the area of a circle is ( a=pi r^{2} ). use 3.14 for ( pi ). the radius for
each circle is given. find the area of the circle.
model ( r = 5 ) inches
( a=pi r^{2}=3.14 cdot 5^{2}=3.14 cdot 5 cdot 5 = 78.5 ) square inches

1. ( r = 2 ) inches
2. ( r = 4 ) inches
3. ( r = 6 ) inches
4. ( r = 10 ) inches

activity 2
find the value of ( n ) in each algebraic equation.

1. ( n + 10 = 8 + 4 quad n=)
2. ( 4 + 2 = n + 1 quad n=)
3. ( 3 cdot n = 32 - 2 quad n=)
4. ( n div 10 = 2 + 3 + 4 quad n=)
5. ( n - 12 = 6 + 6 quad n=)

activity 3 use tape diagrams to find the missing quantities.

1. the ratio of sugar cookies to chocolate cookies is 1 to 3. if there are

30 chocolate cookies, how many sugar cookies are there?
answer:

1. the ratio of peanut butter cookies to chocolate chip cookies is 3 to 2.

if there are 60 peanut butter cookies, how many chocolate chip cookies
are there?
answer:

1. the ratio of oatmeal cookies to chocolate mint cookies is 3 to 4. if there

are 80 chocolate mint cookies, how many oatmeal cookies are there?
answer:

Explanation:

Activity 1

Step 1: Calculate the area of each circle using the formula \(A = \pi r^{2}\)

• 1. For \(r = 2\) inches:
• Substitute \(r = 2\) and \(\pi=3.14\) into the formula \(A=\pi r^{2}\).
• \(A = 3.14\times2^{2}\)
• First, calculate \(2^{2}=4\).
• Then, \(A = 3.14\times4=12.56\) square inches.
• 2. For \(r = 4\) inches:
• Substitute \(r = 4\) and \(\pi = 3.14\) into the formula \(A=\pi r^{2}\).
• \(A=3.14\times4^{2}\)
• Calculate \(4^{2}=16\).
• Then, \(A = 3.14\times16 = 50.24\) square inches.
• 3. For \(r = 6\) inches:
• Substitute \(r = 6\) and \(\pi=3.14\) into the formula \(A=\pi r^{2}\).
• \(A = 3.14\times6^{2}\)
• Calculate \(6^{2}=36\).
• Then, \(A=3.14\times36=113.04\) square inches.
• 4. For \(r = 10\) inches:
• Substitute \(r = 10\) and \(\pi = 3.14\) into the formula \(A=\pi r^{2}\).
• \(A=3.14\times10^{2}\)
• Calculate \(10^{2}=100\).
• Then, \(A=3.14\times100 = 314\) square inches.

Activity 2

Step 1: Solve each algebraic equation for \(n\)

• 1. For \(n + 10=8 + 4\):
• First, simplify the right - hand side: \(8 + 4=12\).
• Then, solve for \(n\) using the equation \(n+10 = 12\). Subtract 10 from both sides: \(n=12 - 10=2\).
• 2. For \(4 + 2=n + 1\):
• First, simplify the left - hand side: \(4+2 = 6\).
• Then, solve for \(n\) using the equation \(n + 1=6\). Subtract 1 from both sides: \(n=6 - 1=5\).
• 3. For \(3\cdot n=32 - 2\):
• First, simplify the right - hand side: \(32-2 = 30\).
• Then, solve for \(n\) using the equation \(3n=30\). Divide both sides by 3: \(n=\frac{30}{3}=10\).
• 4. For \(n\div10=2 + 3+4\):
• First, simplify the right - hand side: \(2 + 3+4=9\).
• Then, solve for \(n\) using the equation \(\frac{n}{10}=9\). Multiply both sides by 10: \(n=9\times10 = 90\).
• 5. For \(n-12=6 + 6\):
• First, simplify the right - hand side: \(6 + 6=12\).
• Then, solve for \(n\) using the equation \(n-12=12\). Add 12 to both sides: \(n=12 + 12=24\).

Activity 3

Step 1: Use the ratio concept to find the missing quantities

• 1. For the ratio of sugar cookies to chocolate cookies is \(1:3\) and 30 chocolate cookies:
• Let the number of sugar cookies be \(x\). The ratio \(\frac{x}{30}=\frac{1}{3}\). Cross - multiply: \(3x=30\). Divide both sides by 3: \(x = 10\).
• 2. For the ratio of peanut butter cookies to chocolate chip cookies is \(3:2\) and 60 peanut butter cookies:
• Let the number of chocolate chip cookies be \(y\). The ratio \(\frac{60}{y}=\frac{3}{2}\). Cross - multiply: \(3y=120\). Divide both sides by 3: \(y = 40\).
• 3. For the ratio of oatmeal cookies to chocolate mint cookies is \(3:4\) and 80 chocolate mint cookies:
• Let the number of oatmeal cookies be \(z\). The ratio \(\frac{z}{80}=\frac{3}{4}\). Cross - multiply: \(4z=240\). Divide both sides by 4: \(z = 60\).

Answer:

• Activity 1:

1. \(12.56\) square inches
2. \(50.24\) square inches
3. \(113.04\) square inches
4. \(314\) square inches

• Activity 2:

1. \(n = 2\)
2. \(n = 5\)
3. \(n = 10\)
4. \(n = 90\)
5. \(n = 24\)

• Activity 3:

1. \(10\) sugar cookies
2. \(40\) chocolate chip cookies
3. \(60\) oatmeal cookies