Question

question
robert used a ratio table to solve the following problem. read the problem, then identify strategy by filling in the blank below.
a car has 4 wheels. how many wheels are there for 4 cars?

cars	1	2	4
wheels	4	8	16

answer
the best description for the strategy that he used is
submit answer
options: counting on, doubling, multiplying

Explanation:

Step1: Analyze the ratio table

The table shows the number of cars and corresponding wheels. For 1 car, wheels = 4. For 2 cars, wheels = 8 (which is 4×2), and for 4 cars, wheels = 16 (which is 4×4).

Step2: Identify the strategy

- Counting on: Involves adding sequentially, not applicable here as we're not adding step - by - step in a counting - on way.
- Doubling: From 1 car (4 wheels) to 2 cars (8 wheels) is doubling, but from 2 cars to 4 cars is also doubling (8 to 16). However, the underlying operation is multiplication (number of cars × 4 wheels per car). But looking at the table, from 1 to 2 (×2) and 2 to 4 (×2) in cars, and wheels also ×2 each time. But the most accurate description of the relationship between cars and wheels is multiplying (number of cars × 4). But wait, the options: Let's re - evaluate. The number of wheels is 4 times the number of cars. So the strategy is multiplying (since wheels = 4×cars). But also, the table shows that when cars double (1 to 2 to 4), wheels double (4 to 8 to 16). But the core operation here is multiplication. Wait, but the options are counting on, doubling, multiplying. Let's check the values:
For 1 car: 4 wheels. For 2 cars: 4×2 = 8 (which is doubling 4 to 8). For 4 cars: 8×2 = 16 (doubling 8 to 16). So the strategy of getting from 1 to 2 to 4 cars and corresponding wheels is doubling. Wait, no: 1 car → 4 wheels; 2 cars → 4×2 = 8 wheels (multiplying by 2); 4 cars → 8×2 = 16 wheels (multiplying by 2). But the relationship between cars and wheels is wheels = 4×cars, which is multiplication. But the way the table is filled, from 1 to 2 (×2) and 2 to 4 (×2) in cars, and wheels follow the same multiplication by 2. But the problem is about the strategy Robert used. Let's see: The ratio of wheels to cars is 4:1. So for n cars, wheels = 4×n. So the strategy is multiplying. But wait, the table shows that when cars go from 1 to 2 (×2), wheels go from 4 to 8 (×2), and from 2 to 4 (×2), wheels go from 8 to 16 (×2). So it's also doubling. But which is more appropriate? Let's check the options. The correct strategy here is multiplying, because the number of wheels is 4 times the number of cars. But also, the table uses doubling as a way to get from 1 to 2 to 4. Wait, maybe I made a mistake. Let's re - examine: 1 car has 4 wheels. 2 cars: 4 + 4 = 8 (which is doubling 4). 4 cars: 8+8 = 16 (doubling 8). So the strategy of adding the same amount (4 wheels per car) is multiplication, but the way the table is built is by doubling. But the key relationship is wheels = 4×cars, so the strategy is multiplying. But wait, the options: Let's check the values again. The number of wheels is calculated as 4 (wheels per car) multiplied by the number of cars. So the strategy is multiplying. But the table also shows doubling. Wait, maybe the intended answer is multiplying, but let's check the options. Wait, the problem is to identify the strategy. The ratio table is based on the multiplication of the number of cars by 4. So the best description is multiplying. But wait, when we go from 1 to 2 cars, we multiply the number of cars by 2 and the number of wheels by 2 (doubling). But the fundamental operation is multiplication (number of cars × 4 wheels per car). So the correct option is multiplying? Wait, no. Wait, 1 car: 4 wheels. 2 cars: 4×2 = 8 (multiplying the number of cars by 2, and wheels by 2). 4 cars: 8×2 = 16 (multiplying by 2 again). So the strategy of building the table is doubling (each time we double the number of cars, we double the number of wheels). But the relationship between cars and wheels is multiplicative (wheels = 4×cars). So which option is correct? Let's see the options:

- Counting on: Not applicable, as we're not counting up from a number.
- Doubling: From 1 to 2 cars (wheels double from 4 to 8), from 2 to 4 cars (wheels double from 8 to 16). So this is a doubling strategy.
- Multiplying: Wheels = 4×cars, so multiplying the number of cars by 4.

But in the table, the number of cars is 1, 2, 4. The number of wheels is 4, 8, 16. So 1×4 = 4, 2×4 = 8, 4×4 = 16. So it's multiplying (by 4). But also, 4×2 = 8, 8×2 = 16. So both doubling and multiplying are involved. But the question is about the strategy Robert used. The problem is about the relationship between cars and wheels, which is a multiplicative relationship (wheels = 4×cars). So the strategy is multiplying. Wait, but the table is built by doubling the number of cars and doubling the number of wheels. So maybe the intended answer is doubling? Wait, no. Let's check with the numbers:

For 1 car: 4 wheels.

For 2 cars: 4×2 = 8 (multiplying the number of cars by 2, and wheels by 2 - which is doubling).

For 4 cars: 8×2 = 16 (doubling again).

But the formula is wheels = 4×cars, which is multiplication. So which is it? The options are counting on, doubling, multiplying.

Counting on: No, because we're not counting up from a number by 1s.

Doubling: Yes, because each time the number of cars doubles, the number of wheels doubles.

Multiplying: Yes, because wheels = 4×cars.

But which is more accurate? Let's see the problem statement: "Robert used a ratio table to solve the following problem". A ratio table for a proportional relationship (wheels and cars are proportional with a constant of proportionality 4). The strategy of using a ratio table for a proportional relationship is based on multiplication (or division). But in this case, the way the table is filled (1, 2, 4 cars and 4, 8, 16 wheels) shows that when the number of cars is multiplied by 2 (from 1 to 2, from 2 to 4), the number of wheels is also multiplied by 2. So this is a doubling strategy (multiplying by 2 each time the number of cars doubles). But the core relationship is multiplication by 4. Wait, maybe the answer is multiplying. Wait, no. Let's calculate:

Number of wheels = number of cars × 4.

For 1 car: 1×4 = 4.

For 2 cars: 2×4 = 8.

For 4 cars: 4×4 = 16.

So the operation is multiplying the number of cars by 4. So the strategy is multiplying.

But the table also shows doubling. However, the key mathematical operation here is multiplication (4 wheels per car, so total wheels = 4×number of cars). So the correct option is multiplying? Wait, no, the table is built by doubling the number of cars (1→2→4) and doubling the number of wheels (4→8→16). So the strategy of building the table is doubling. But the relationship between cars and wheels is multiplicative. This is a bit confusing. Let's check the options again. The three options:

- Counting on: Incorrect, as we're not counting up by 1s.

- Doubling: When cars go from 1 to 2 (double), wheels go from 4 to 8 (double); when cars go from 2 to 4 (double), wheels go from 8 to 16 (double). So this is a doubling strategy.

- Multiplying: The number of wheels is 4 times the number of cars, so it's multiplying.

But which is the best description? The problem is about the strategy Robert used. Since the ratio table is based on the proportional relationship where wheels = 4×cars, the strategy is multiplying. But the way the table is filled (using 1, 2, 4) is by doubling the number of cars. However, the fundamental operation is multiplication. So the correct answer is multiplying? Wait, no, let's see the values:

1 car: 4 wheels (4×1)

2 cars: 8 wheels (4×2)

4 cars: 16 wheels (4×4)

So the operation is multiplying the number of cars by 4. So the strategy is multiplying.

Answer:

The best description for the strategy that he used is multiplying. So the answer is "multiplying".