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This is very close! Lets read the problem again. What do we know? Alex has 53 nickels and SOME dimes. We also know that there are 71 coins all together. So, we need to figure out how many dimes he has in total. We can use a number line to help us visualize this problem. If we know he has 53 nickels, we can draw 53 on the number line. We also know he has 71 coins all together, so we can put that on the number line. To figure out how many dimes he has, we must figure out how many dimes are in between 53 and 71. We can count how many jumps it takes to get to 71. Lets count together. We get 18! We can double check this by adding 53 nickles and 18 dimes. This equals 71 coins all together. So, we know that Alex has 18 dimes! Great job!

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I see how you are trying to solve this problem and I love your thinking! Let's try it a different way and see if we can get a different answer. First, make a number line. Number lines are a great way to visualize different math strategies like addition and subtraction. So what do we know in this problem? We know that Alex has 53 nickels and un unknown amount of dimes. We also know that 53 + however many dimes he has will get us 71 because he has 71 coins all together. So we can start at 71. Since we're doing subtraction, we are going to start at the largest number. Then we can count down the number line until we get to the number 53. I find it easiest to count down by 10s first. So 10 less of 71 is 61. Now that you're at 61, you can count down by numbers in the 1's space. I like to subtract to get numbers in the 10s or 5s space. So what do you want to subtract next? I agree, I think subtracting 1 from 61 is a good idea to make 60. What do you want to subtract next? Good! Subtracting 5 from 60 gets us to 55, which is an easy number to add and subtract from. Now how can we get 55 to be 53? Good! Subtracting 2 from 55 makes 53. So now we can add all of these numbers that we subtracted from 71 to get how many dimes Alex has. The addition equation is 10+1+5+2. Let's add the first two numbers. 10+1=11. Now the next two numbers. 5+2=7. Finally 11+7 equals what? Very good, 18! So we know that Alex has 18 dimes because we did subtraction on the number line. Good work!

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You are really close but we should look back to see to double-check your math. It's okay it happens it's part of the learning progress. Let's see what we know. We know Alex has 71 coins and 53 times. We also know that we are looking for the number of dimes they have. We also know this is a subtraction problem because we are finding the difference between dimes and nickels.  We start by setting up the equation. 71- ??= 53. In order to find the missing part is by putting it in a fact-family. Now it's 71-53. We then separate it into tens and ones. Like the picture shows. We then solve it using the standard algorithm. We got 18 dimes.

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I love your thinking! You are on the right track! I see you used standard algorithm for addition to solve your problem. That is a great strategy for solving this equation! Let's try this problem using standard algorithm one more time together. When we add 8+5 we get 13. We have to remember the ones place value only goes up to 9 so we have to carry or regroup any time we have an amount greater than 9! As you can see we will regroup our 10 to the tens column and drop our three below the ones column. Now we can add the 3+7 but don't forget to add in that 1 we regrouped to the tens column! All those together equal 11! When we write those answers in the correct place value column we get 113! Great Job!
If you ever need to check your work to make sure you regrouped or carried correctly you can use the counting on method. You find one of the numbers (Usually the higher number) on a number line and you can add the other number using the number line as a reference. For example I added +10, +10, +10, +8 to get to 113! These are quick mental math addition problems we both were able to add in our minds! Well Done! -JB

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We know that Alex has 53 nickels and some dimes. He has 71 coins all together. To find how many dimes he has, we have to subtract 71-53. The student forgot to borrow from the 10s place when subtracting. It is not possible to take 3 away from 1.

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That was an awesome try, but this is actually a subtraction problem! So first we know that Barbara starts with 158 paper dolls, and that she ends with 201 paper dolls by the end of the problem. So our goal is to find how many dolls her sister brought her to reach a total of 201. Using base 10 blocks we can show these big numbers. 158 is shown with one flat (100), 5 rods (10s) and 8 units (1s), and that plus an unknown number will equal 201, which is two flats (100s), and one unit (1s). We can then turn our addition problem into a subtraction problem to find our missing value. When we subtract, we will take 158 away from 201. In order to do that we have to turn 201 into one flat (100), 9 rods (10s), and 12 units (1s). As you can see in the picture, you then take away the flat (100), five rods (10s), and 8 units (1s), which represents 158. What you get when your done crossing them out is 4 rods (10s) and 3 units (1s). So our final answer is 43. Barbara's sister gave her 43 paper dolls!- SO

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This is the other picture for my response- SO

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Let's use base 10 blocks together. First, we know that we have to use addition to find the answer to this problem. For 38, we would have 3 tens and 8 ones. For 75, we would have 7 tens and 5 ones. Please sort that out for me. Good! Now, we can break this problem apart. If we have 3 tens and 7 tens, we can combine those together to add them. What number did you get? I got 30+70=100. Nice job! Now, let's add our ones together. What did you get? 8+5=13. Perfect! Since we now have our tens place and ones place figured out we can add it all together. What do we have? 100+13=113. Amazing, now can you show me how to break apart the 113 with the base 10 blocks? Sure, I got 100+10+13+113. Wonderful, you got it! Let's move on to the next problem!
-K.N.

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Good Job! You're on the right track. Let's work it out together to see how you arrived at 103 using base 10 blocks. So it says Carl gave 38 carrot sticks to Monica so let's take 38 and put on on the table. Good Job now let's see what Monica already had. It says Monica had 75 carrot sticks with her already, and saved the 38 for later. Let's take 75 and put it on the table. Ok good job. So we know that the 38 is from what Carl had, and the 75 is what Monica originally had. Let's add them together. Let's count up the tens to see how many tens we have in total. Alrighty so we see that we have 30+70 what does that equal? 100! Good Job! Could we use a 100 base block with this? Now let's add up the ones. 8+5. We see that wee have 13, how many groups of ten can we make? 1, good job! Now lets count how many ones we have left. Ok so we see that we have 3 ones left. Now let's look at what we have. So we have one group of hundred, one group of tens, and 3 ones. What is our answer. 113. Amazing! Let's continue the good work!

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If we know we have 53 nickels, and we think that we have 22 dimes let's add 53 and 22 to see if that gets us to our total. I want you to try this on your paper while I demonstrate. So, we can break 22 into 20 and 2, adding each piece one at a time to get to the answer. First, let's take 53 and add 20 to it on your paper, hold up your answer when you're done... You got 73 and I got 73 perfect! Ok, next, let's take 73 and add in our remaining 2, so we are doing 73+2, go ahead and do that on your paper and hold up the answer when you're done. 75, spot on, I also got 75! Can you read back in the problem for me how many coins in total Alex had? Exactly right, Alex had 71 coins in total! Is 71 greater than or less than our 75? Less than, exactly, so since we know that we went to high over the total, do you think that we guessed too many or too little dimes? Too many exactly, so since we know that we had two many dimes, let's try the problem again, knowing that our actual number of dimes is less than our first try. I'm gonna do the problem on my sheet, while you try again on yours and then we will compare answers! -MS

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https://apps.mathlearningcenter.org/number-pieces/?jvb7atua
Need to regroup our unit (yellow blocks). 8 units plus 5 units equals 13 units. We know that 13 is made up of 1 ten rod and 3 units blocks. We add this to our flat (red block) and get 113 carrots total.
ID

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a.Alex has 53 nickels and some dimes. He has 71 coins all together.  How many dimes does he have?  (22 dimes)

b.There were 158 paper dolls at Barbara’s house. Her sister brought some more. Then there were 201. How many paper dolls did her sister bring?  (359 paper dolls)

c. Carl gives 38 carrot sticks to his friend Monica.  Monica has 75 carrot sticks on her party plate and puts the 38 carrot sticks in her ice box for later.  How many does carrot sticks does she have?  (103 carrot sticks.)