Addition: Using the number line

To solve this problem, we will follow these steps:

• Step 1: Start at the number 18 on the number line.
• Step 2: Add 2 in the first jump to reach 20.
• Step 3: Add another 2 in the second jump to reach 22.

Now, let's work through each step:

Step 1: We start at 18, as indicated by the initial position on the number line.

Step 2: For the first jump, we add 2 to 18, which gets us to 20.

Step 3: For the second jump, we again add 2 to 20, which brings us to 22.

Therefore, the solution to the problem $18 + 4$ using two jumps on the number line is $22$.

To solve $25 + 8$ using two jumps on a number line, we follow these steps:

• Step 1: Start at the number 25 on the number line.
• Step 2: Make the first jump by adding 5. This takes us from 25 to 30.
• Step 3: Make the second jump by adding the remaining 3. Move from 30 to 33.

By making these two jumps, we effectively add 8 to 25.

Therefore, the result of $25 + 8$ is $33$.

To solve the problem of adding $34 + 9$ using two jumps on a number line, follow these steps:

• Step 1: Start at 34 on the number line.
• Step 2: Make the first jump of $+6$ from 34, which lands you at 40.
• Step 3: Make the second jump of $+3$ from 40, landing you at 43.

Therefore, by completing the two jumps on the number line, we find that $34 + 9 = 43$.

The solution to the addition problem is $43$.

To solve $16 + 6$, we will proceed as follows:

• Step 1: Identify the numbers to add: 16 and 6.
• Step 2: Add the numbers: $16 + 6 = 22$.
• Step 3: Verify by recalculating or using a number line if needed.

Using our calculation, $16 + 6$ results in 22.

Therefore, the correct answer is $22$.

To solve this problem, we'll follow these steps:

• Step 1: Start at the number 17 on the number line.
• Step 2: Make the first jump of $+3$.
• Step 3: Make the second jump of $+4$.
• Step 4: Record the final position.

Now, let's work through each step:
Step 1: We begin at 17 and plan our jumps.
Step 2: The first jump of $+3$ takes us from 17 to $17 + 3 = 20$.
Step 3: The second jump of $+4$ takes us from 20 to $20 + 4 = 24$.

Therefore, the solution to the problem, using two jumps on the number line, is $24$.

To solve the addition problem $34 + 47$ using a number line, we'll follow these steps:

• Step 1: Start at the number 34 on the number line.
• Step 2: Add the tens from 47, which is 40. This takes us from 34 to 74.
• Step 3: Add the units from 47, which is 7. This takes us from 74 to 81.

Here's the detailed breakdown of each step:

Step 1: We start at 34.

Step 2: We add 40 (the tens from the number 47):
Adding 40 to 34 gives us $34 + 40 = 74$.

Step 3: We add 7 (the units from the number 47):
Adding 7 to 74 gives us $74 + 7 = 81$.

Therefore, the sum of $34 + 47$ is $81$.

Thus, the final answer is $\textbf{81}$, which corresponds to choice 3 in the given multiple-choice options.

To solve the addition problem $49 + 27$ using a number line, follow these steps:

• Start at 49 on the number line.
• Decompose 27 into tens and ones: $27 = 20 + 7$.
• First jump 20 units forward from 49: $49 + 20 = 69$. Now you're at 69.
• Next, jump 7 more units forward from 69. Break this into a jump of 6 then 1:
• Jump 6 units: $69 + 6 = 75$.
• Jump 1 more unit: $75 + 1 = 76$.

Thus, the final position on the number line is 76. Therefore, the solution to the addition is $76$.

To solve the addition problem $15 + 56$, we'll use jumps on a number line:

• Step 1: Start at 15 on the number line.
• Step 2: Break down the second number (56) into smaller, manageable increments. For simplicity, we can use increments of 10.
• Step 3: Make five jumps of 10 from 15. This will bring us to $15 + 50 = 65$.
• Step 4: Add the remaining 6 by jumping from 65 to 71.

This method effectively demonstrates that $15 + 56$ equals 71 by reaching the end point after all the incremental jumps on the number line.

Therefore, the solution to the problem is $71$.

To solve the problem of $18 + 67$ using a number line, we proceed with the following steps:

• Step 1: Start at number 18 as shown on the number line.
• Step 2: Break the number 67 into parts for easier addition: 60 and 7.
• Step 3: Jump 60 units forward from 18. This takes us from 18 to 78.
  Mathematically, this is $18 + 60 = 78$.
• Step 4: Jump 7 units forward from 78. Adding 7 to 78 gives us 85.
  Mathematically, this is $78 + 7 = 85$.

Thus, the total sum of $18 + 67$ is $85$.

To solve this problem using a number line, we will break down the addition of $26 + 38$ into smaller steps:

• First, start at the number $26$ on the number line.
• We can decompose the number $38$ into $30$ and $8$ for easier addition.
• From $26$, make a jump of $30$:
• $26 + 30 = 56$
• Next, add the remaining $8$ from the $38$:
• $56 + 8 = 64$

The final position on the number line after jumping is $64$.

Therefore, the solution to the problem $26 + 38$ is $\boxed{64}$.

To solve the problem $33 + \Box = 42$ using the number line, we will make strategic jumps:

First, jump from 33 to the nearest higher round number, which is 40:

• This first jump is $40 - 33 = 7$.

Next, jump from 40 to 42:

• This second jump is $42 - 40 = 2$.

Add the two jumps to find $\Box$:

• $\Box = 7 + 2 = 9$

Therefore, the solution to the problem is $9$.

To solve this problem using a number line and two jumps, follow these steps:

• Start at 24 on the number line.
• The first jump will move us to the nearest convenient round number, which is 30. This jump is $30 - 24 = 6$.
• From 30, we need to jump to 31. The second jump is $31 - 30 = 1$.
• Add the two jumps together: $6 + 1 = 7$.

Therefore, the number that fills the gap $\Box$ in the equation $24 + \Box = 31$ is $7$.

To solve the problem $81 + \Box = 98$ using two jumps along a number line, follow these steps:

• Step 1: Start at 81 on the number line.
• Step 2: Make the first jump from 81 to the next convenient round number: 90.
• Step 3: Calculate the increase from 81 to 90: $90 - 81 = 9$.
• Step 4: Make the second jump from 90 to 98.
• Step 5: Calculate the increase from 90 to 98: $98 - 90 = 8$.
• Step 6: Add both jumps to determine the total required increment: $9 + 8 = 17$.

The total increment needed to go from 81 to 98 using two jumps is $17$.

Therefore, the solution to the problem is $\Box = 17$.

To solve the problem $67 + \Box = 93$ using two jumps on the number line, follow these steps:

• Step 1: Identify the first jump to reach the next round number. From 67, the nearest round number is 70. This jump is $70 - 67 = 3$.
• Step 2: From 70, jump to the target number, 93. This jump is $93 - 70 = 23$.
• Step 3: Combine the two jumps to find the total amount needed to reach 93 from 67. Therefore, the total is $3 + 23 = 26$.

The number that satisfies $67 + \Box = 93$ is $26$.

To solve the problem $48 + \Box = 83$, we need to find the missing value that, when added to 48, equals 83. We'll visualize this using the number line and break this addition into two steps:

• Step 1: Start at 48. For simplicity, make the first jump to 50 (an easy round number that's close to 48). This jump is $2$ units: $48 + 2 = 50$.
• Step 2: Now, calculate the remaining distance to 83 from 50. This distance is $33$ because $50 + 33 = 83$.

By taking these two jumps, first adding 2 and then adding 33, the total addition is:

$2 + 33 = 35$.

Therefore, the missing addend in $48 + \Box = 83$ is $35$.

To solve this problem, follow these steps:

• Step 1: Calculate the difference from 33 to a rounded next number which is 40. The first jump is $40 - 33 = 7$.
• Step 2: From 40, calculate the difference to 68. The second jump is $68 - 40 = 28$.
• Step 3: Add the values of both jumps to find the total missing number.

Now, let's work through each step:
Step 1: From 33 to 40 is a jump of 7.
Step 2: From 40 to 68 is a jump of 28.
Step 3: The total added amount is $7 + 28 = 35$.

Therefore, the solution to the problem is $35$.

To solve the equation $24 + \Box = 45$ using two jumps on a number line, we will take the following approach:

• Step 1: Make the first jump from 24 to the closest higher round number, which is 30.
• Step 2: Calculate how much is needed to reach from 30 to 45.
• Finally, we combine the lengths of the two jumps to find $\Box$.

Now, let's calculate each step:

Step 1: The first jump from 24 to 30 is 6 units.

Step 2: From 30 to 45, the jump is 15 units.

Adding these two jumps: $6 + 15 = 21$.

Therefore, the number that completes the equation $24 + \Box = 45$ is $21$.

To solve the addition problem $46 + \Box = 55$ with two jumps on the number line, follow these steps:

• First, identify the starting point, which is 46, and the desired endpoint, which is 55.
• Make the first jump from 46 to the next higher round number. This number is 50 because it is the nearest round number greater than 46.
• The length of this first jump is calculated by subtracting 46 from 50, which is $50 - 46 = 4$.
• From 50, make the second jump to reach 55.
• The length of this second jump is obtained by subtracting 50 from 55, which is $55 - 50 = 5$.
• Add the lengths of both jumps to find the missing number $\Box$:
$\Box = 4 + 5 = 9$

Therefore, the solution to the problem is the missing number $\Box$, which is $9$.

To solve the problem of $87 + \Box = 92$ by using two jumps on the number line, we begin by identifying and making our jumps:

• First jump: Move from 87 to the nearest round number, which is 90. This jump is of size $90 - 87 = 3$.
• Second jump: Now move from 90 to 92. This jump is of size $92 - 90 = 2$.

Add the two jumps together:
First jump: 3
Second jump: 2
Total jump: $3 + 2 = 5$

Therefore, the value of the box ($\Box$) that satisfies the equation $87 + \Box = 92$ is $\Box = 5$ .

To solve the given problem, we need to find the missing number that, when added to 15, equals 37. We'll use a number line approach that involves taking two jumps.

First, we'll make a jump from 15 to the next round (friendly) number, which is 20. This first jump is:

$20 - 15 = 5$

Next, we'll make a second jump from 20 to 37. This second jump is:

$37 - 20 = 17$

Now, we'll add these two jumps together to find the total increase from 15 to 37:

$5 + 17 = 22$

Thus, the value of the missing number is $22$.

Therefore, the solution to the problem is $\Box = 22$.