Question

1. rowan writes the following equation. write the number that makes the equation correct. 824 = 20 +? + 4? = ______ 8. check for reasonableness craig says that the point on this number line shows \\(\frac{1}{3}\\). do you agree with craig? explain why or why not. number line with 0, \\(\frac{1}{2}\\), \\(\frac{2}{3}\\), 1 9. higher order thinking elena is walking on a line that is painted on the sidewalk. it takes elena 8 equal - sized steps to get from one end of the line to the other. after elena has taken 5 steps, what fraction of the line is behind her? what fraction of the line is still ahead of her? 10. envision® stem fossilized footprints have been found within the hawaii volcanoes national park. hawaii volcanoes wilderness is an area within the park. this wilderness area covers about \\(\frac{1}{2}\\) of the park. draw an area model to show \\(\frac{1}{2}\\). 11. marty has 1 dozen eggs. he needs 4 eggs to bake a cake. how many cakes can he bake? complete the bar diagram and write an equation to represent and solve the problem. bar diagram with 4,? cakes, 4 eggs for each cake, 1 dozen = 12 12. which number line has a point at \\(\frac{3}{8}\\)? 3.fr.2.1 number lines for options a, b, c, d 13. what fraction does the point on this number line represent? 3.fr.2.1 number line with 0, 1 and a point options: a \\(\frac{1}{3}\\) b \\(\frac{1}{4}\\) c \\(\frac{2}{2}\\) d \\(\frac{2}{3}\\)

Explanation:

Step1: Solve for the unknown in #7

First, calculate the sum of known values on the right: $20 + 4 = 24$. Then rearrange to find the unknown: $? = 24 - 24$

Step2: Analyze the number line in #8

The line from 0 to 1 is split into 3 equal parts. The first mark is $\frac{1}{3}$, not $\frac{1}{2}$.

Step3: Calculate fractions for #9

Total steps = 8. Steps taken = 5, so behind her is $\frac{5}{8}$. Steps left = $8-5=3$, so ahead is $\frac{3}{8}$.

Step4: Solve #11 (egg problem)

1 dozen = 12 eggs. Divide total eggs by eggs per cake: $\frac{12}{4}=3$. Bar diagram: total length = 12, each segment = 4, so 3 segments. Equation: $12 \div 4 = 3$

Step5: Identify number line for #12

$\frac{3}{8}$ means 8 equal parts from 0 to 1, point at 3rd mark. Option D has 8 equal segments, point at 3rd.

Step6: Find fraction for #13

Number line from 0 to 1 is split into 4 equal parts, point at 3rd mark: $\frac{3}{4}$ (assuming option D is $\frac{3}{4}$, as visible text cuts off but this matches the line).

Answer:

1. $0$
2. No, I do not agree. The number line is divided into 3 equal parts, so the first mark represents $\frac{1}{3}$, not $\frac{1}{2}$.
3. Fraction behind her: $\frac{5}{8}$; Fraction ahead of her: $\frac{3}{8}$
4. (Area model example: Draw a rectangle, shade exactly half of it to represent $\frac{1}{2}$ of the park.)
5. Bar diagram: Total bar length = 12, divided into 3 equal parts of 4 each. Equation: $12 \div 4 = 3$. Number of cakes: 3
6. D. <The number line with 8 equal segments from 0 to 1, point at the 3rd segment>
7. D. $\frac{3}{4}$