Today I begin with the mountains (number bonds) that I introduced in a previous lesson. I remind students that the mountain helps us to figure out whether we are missing the whole or one of the parts in a number family, and to then create the number sentence we can use to find the missing number.
I draw the mountain on the board. I put a blank square at the top and two blank squares at the bottom (see attached drawing). I ask students where the biggest or tallest part of the mountain is (at the top) so we need to put the big number where? (at the top). If I have 2 numbers at the bottom they should add up to the number at the top. If I have 18 at the top of my mountain and 7 is one of the numbers at the bottom, how many more would I need to get to the top? (11). I ask if anyone can write a number sentence for the mountain? I let students come up to write several possible number sentences (18 - 7 = 11, 18 - ?= 7, 7 + 11 = 18).
Now I put the number 562 at the top of the mountain and I put 3 squares at the bottom. I put 500 in one and 2 in the last and leave the middle one open. I ask what would go there? (60). I say that the value of the 6 in the number at the top is 60 so I write 60 in the box. Could I write 6? Why not? Here I want students to begin to think about how the number can be broken into hundreds, tens and ones. This will help them visualize that the digits in the number stand for a number of ones, tens or hundreds. We add up the 500 + 60 + 2 to see if we get back to the top of the mountain.
I repeat this with several other 3-digit numbers. For each number I ask students to come up and fill in the missing numbers that I leave out.
I give each student a practice page to complete that has students fill in the mountains.
Today I want to provide students with another chance to practice taking larger numbers apart in order to add and subtract. This will prepare them to solve word problems independently. My goal is for students to attend to the structure of numbers (MP7) as they deepen their understanding of place value.
I begin today by inviting students to the rug. I tell them that now that we have made some mountains, we are going to figure out larger numbers using base ten blocks. Students will model the numbers with the blocks (MP4). I invite one student to be my partner. I ask her to count to 30 while I build with my base ten blocks. I build my tower out of my blocks as she counts. When she reaches 30 I stop building and look at my number. On my white board I write 300 (I used 3 hundreds blocks) + 40 (I have 4 tens rods standing) + 8 (I had 8 ones on my building). I look at what I have written (300 + 40 + 8) and I finish the number sentence (=348). I read my number sentence and answer aloud. I explain to the students that writing a number in this way is called the expanded form of the number. Now I invite my partner to build while I count. When she is done, she writes her number sentence and number next to mine. We add an alligator mouth (> or < symbol) to show who built the bigger number. We repeat the process again.
I tell students that they will build with a partner using the sets of base ten blocks in front of them. Each set contains 9 ones, 9 tens and 9 hundreds blocks. This prevents students from getting a number such as 800 + 110 + 15 and needing to regroup. I want them to understand the place value before they need to regroup. They will write their numbers in expanded form on the large paper as they build. I circulate around the room checking with students to monitor understanding. See: Trying to Count.
At the end of 15 minutes, I invite students to put their blocks away and return to their seats. I ask them for a thumbs up or down if they felt good about building and writing numbers.
Now I ask them to take out their math journals. I tell students that I am going to say a number and they should write that number in their math journals. I say the number 541. I ask students to take the number apart and write a number in expanded form (500 + 40 + 1). I remind them that this is like the mountains they built and like the base ten buildings. Next I ask them to write the number 243 beside the 541. I ask them to write this number in expanded form (200 + 40 + 3). Now I ask students to draw the <, >, or = sign (remember the alligator is always hungry and wants to eat the largest number) between the two numbers. Students need to attend to the structure of the number as they compare the hundreds, tens and ones to see which number is larger.
I repeat this with 2 other sets of 3-digit numbers.
To end the lesson today I ask each student to write a 3-digit number in his/her journal. (I know a lot of students will write 999 so I decide to ask them to compare with a partner to see who has the lowest digit in 2 out of the 3 places.)
I say, " would you turn to the person next to you. I want you to raise your hand if you have the lowest digit in the hundreds place of the two of you. (I wait for students to compare and decide who should raise his/her hand.) If you have a tie would either of you have the highest or lowest number? (No) so then neither of you would raise your hand. Now look at the ones place. Would the person with the lowest digit in the ones place raise his/her hand. And finally look at the tens place. Would the person with the HIGHEST number in the tens place raise his/her hand.
This is a quick check as I walk around the room as to whether students are correctly identifying the ones, tens and hundreds places in their 3 digit number.