Question

spaced practice board

1. use a strategy to solve-

64 × 32 =

1. find the volume. explain how you know. image of cube grid
2. a rectangle is 25 feet long. its area is 375 square feet.

what is the width of the rectangle?
what is the perimeter of the rectangle?

1. how many unit cubes would it take to make a model of a rectangular prism that is 6 units long × 4 units wide × 2 units high?

a 14 unit cubes
b 22 unit cubes
c 24 unit cubes
d 48 unit cubes

1. the bar model shows the comparison 24 is 6 times as many as 4.

bar model: one 4, six 4s making 24
decide if each equation represents the comparison. choose yes or no for each.
table: 6×4=24 (a/b), 24−6=4 (c/d), 24=4×6 (e/f), 6+4=24 (g/h), 4×4=24 (i/j), 24×6=4 (k/l)

1. tcap review

count the unit cubes to find the volume of the solid below.
image of 3d shape
a 24 cubic units
b 28 cubic units
c 32 cubic units
d 48 cubic units
murfreesboro city schools

Explanation:

Question 7:

Step1: Break down 64 and 32

We can use the distributive property (area model) to multiply \(64\times32\). Break \(64\) into \(60 + 4\) and \(32\) into \(30+2\).

Step2: Multiply each part

• Multiply \(60\times30 = 1800\)
• Multiply \(60\times2=120\)
• Multiply \(4\times30 = 120\) (Wait, the original drawing has 90, maybe a typo, correct should be \(4\times30 = 120\), but let's follow the correct method)
• Multiply \(4\times2 = 8\)

Step3: Add the products

Now add all the products: \(1800+120 + 120+8=2048\)? Wait, no, the correct breakdown for \(64\times32\) using area model:
\(64\times32=(60 + 4)\times(30+2)=60\times30+60\times2 + 4\times30+4\times2=1800 + 120+120 + 8=2048\). But the handwritten work has some errors, but the correct way:
Alternatively, \(64\times32 = 64\times(30 + 2)=64\times30+64\times2=1920+128 = 2048\)

Step1: Recall the volume formula for a rectangular prism

The volume \(V\) of a rectangular prism is given by \(V=\text{length}\times\text{width}\times\text{height}\)

Step2: Identify the dimensions

From the figure, length \(l = 5\), width \(w=3\), height \(h = 3\)

Step3: Calculate the volume

\(V=5\times3\times3=45\)? Wait, no, looking at the figure again, the front face has \(5\) columns and \(3\) rows (height). Wait, maybe the dimensions are: length \(= 5\), width \(= 3\), height \(= 3\)? Wait, no, the figure shows a rectangular prism with length \(5\), width \(3\), height \(3\)? Wait, no, let's count the cubes:
In each layer (height = 1), the number of cubes is \(5\times3 = 15\). There are 3 layers (height = 3), so total volume \(=15\times3=45\). Wait, but maybe the figure has length \(5\), width \(3\), height \(3\). So volume is \(5\times3\times3 = 45\) cubic units.

Step1: Recall the area formula for a rectangle

The area \(A\) of a rectangle is given by \(A=\text{length}\times\text{width}\), so \(\text{width}=\frac{A}{\text{length}}\)

Step2: Substitute the given values

Given \(A = 375\) square feet and \(\text{length}=25\) feet. So \(\text{width}=\frac{375}{25}=15\) feet

Part 2: Find the perimeter of the rectangle

Answer:

\(2048\)

Question 8:

To find the volume of the rectangular prism (the cube - like structure with layers), we can count the number of unit cubes along each dimension. From the figure, we can see that:

• Length: Let's assume the number of cubes along the length is \(5\) (since there are 5 columns)
• Width: Let's assume the number of cubes along the width is \(3\) (since there are 3 rows in the base layer)
• Height: Let's assume the number of cubes along the height is \(3\) (since there are 3 layers)