Question

you divided and shaded models to show fractions. first, divide the shape into eighths.

Explanation:

Step1: Understand the Goal

We need to divide the square (the shape) into eighths. Eighths mean dividing the shape into 8 equal parts.

Step2: Plan the Division

A square can be divided into eighths by first dividing it into halves, then each half into quarters, and then each quarter into eighths, or by using horizontal and vertical lines. Alternatively, we can use 3 horizontal lines (to make 4 rows) and 3 vertical lines (to make 4 columns), but wait, no—wait, to get 8 equal parts, we can divide the square into 8 equal rectangles. Let's think: 8 equal parts. So, if we divide the square into 2 rows and 4 columns (2×4 = 8) or 4 rows and 2 columns (4×2 = 8), or 8 equal triangles. But the most straightforward way for a square is to use 3 horizontal lines and 1 vertical line? No, wait, 8 equal parts. Let's do 4 horizontal lines? No, wait, 8 equal parts: 8 = 8×1, 4×2, 2×4. So, to divide the square into eighths, we can draw 3 horizontal lines (to create 4 rows) and 1 vertical line? No, that would be 4×2 = 8? Wait, no: if we draw 1 horizontal line, we have 2 parts. Then, draw 3 vertical lines, we have 2×4 = 8 parts. Yes, that works. So, first, draw a horizontal line through the middle of the square (dividing it into top and bottom halves). Then, draw 3 vertical lines, equally spaced, to divide each half into 4 equal columns. So each half (top and bottom) is divided into 4 columns, so total 2×4 = 8 equal rectangles. Alternatively, draw 3 horizontal lines (dividing the square into 4 rows) and 1 vertical line (dividing into 2 columns), so 4×2 = 8 equal rectangles.

Step3: Execute the Division (Using the + Buttons)

Looking at the buttons: the + buttons are for adding lines. The left + button is for vertical lines? Wait, the left + button is on the left side of the square, so maybe it's for adding vertical lines. The top + button is for adding horizontal lines. Let's start by adding horizontal lines. First, click the top + button to add a horizontal line through the middle (dividing the square into top and bottom halves). Then, click the top + button again to add another horizontal line, dividing the top half into two, and the bottom half into two (now we have 4 horizontal strips). Then, click the top + button a third time to add a third horizontal line, dividing each of the 4 strips into two, so now we have 8 horizontal strips? Wait, no, 3 horizontal lines would create 4 horizontal strips. Wait, no: number of regions = number of lines + 1. So 1 horizontal line: 2 regions. 2 horizontal lines: 3 regions. 3 horizontal lines: 4 regions. Wait, that's not right. Wait, no: if you have a square, and you draw n horizontal lines, equally spaced, you get n + 1 horizontal strips. So to get 8 equal parts, we need 7 lines? No, that can't be. Wait, maybe the square is being divided into 8 equal triangles. Alternatively, the problem is using a different method. Wait, the initial square is a white outline on a blue background. The + buttons: left + is vertical, top + is horizontal. Let's try adding vertical lines first. Click the left + button to add a vertical line, dividing the square into left and right halves. Then click the left + button again to add another vertical line, dividing each half into two (now 4 vertical columns). Then click the left + button a third time to add a third vertical line, dividing each column into two (now 8 vertical columns? No, 3 vertical lines would create 4 columns. Wait, this is confusing. Wait, the goal is to divide the shape into eighths, so 8 equal parts. Let's think of the square as having area 1, so each part should have area 1/8. So, the correct way is to divide the square into 8 equal parts. Let's use horizontal and vertical lines. Let's add 3 horizontal lines (to make 4 rows) and 1 vertical line (to make 2 columns), so 4×2 = 8 parts. So, first, click the top + button to add a horizontal line (row 1). Then click the top + button again (row 2). Then click the top + button a third time (row 3). Now we have 4 rows. Then click the left + button to add a vertical line, dividing the square into 2 columns. Now we have 4 rows × 2 columns = 8 equal rectangles. Yes, that works. So, using the top + button 3 times (to get 4 rows) and the left + button 1 time (to get 2 columns) will divide the square into 8 equal parts (eighths).

Answer:

To divide the square into eighths, follow these steps:

1. Click the top + button (horizontal line) three times to create 4 equal horizontal strips.
2. Click the left + button (vertical line) once to create 2 equal vertical columns.

This results in \( 4 \times 2 = 8 \) equal parts (eighths).

(Note: Alternatively, use 1 horizontal line and 3 vertical lines: 2 rows × 4 columns = 8 parts. Adjust button clicks accordingly.)