2.NBT Boxes and Cartons of Pencils Alignment 1: 2.NBT.A.1 Domain NBT: Number and Operations in Base Ten Cluster Understand place value. Standard Understand that the three digits of a three-digit number represent amounts of hundreds, tens, and ones; e.g., 706 equals 7 hundreds, 0 tens, and 6 ones. Understand the following as special cases: Pencils are packed 10 in a box. A classroom carton has 10 boxes. Jem has 1 carton and 4 boxes. How many pencils does Jem have all together? Lee needs to pack 370 pencils. How many boxes does Lee need? If Lee puts the boxes in cartons, how many cartons can he completely fill? Ms. Kato needs 10 pencils for each of her 26 students. If she can only buy boxes, how many boxes does she need? She finds out that it is cheaper to buy pencils in cartons. How many cartons should she buy? How many additional boxes will she need? Commentary: This task is a kernel for an instructional task that could be elaborated with commentary about teaching strategies and examples of student work. When this website is fully functional, teachers will be able to submit tasks and related materials for review. Illustrative Mathematics invites teachers to help us with this. Solution:Answers Jem has a total of 140 pencils. To pack 370 pencils, Lee needs 37 boxes. If he puts the boxes in cartons, he can completely fill 3 cartons and will have 7 boxes left over. Ms. Kato needs 10 pencils for each of her 26 students. If she can only buy boxes, she needs 26 boxes. She can buy 2 cartons and will need 6 additional boxes. Alternatively, she can buy 3 cartons, but she will have some boxes left over.
456 is, in fact, less than 500 because 456 has four 100 s (a four in the hundred’s place) and some tens and ones that total less than one hundred, while 500 has five 100 s (a five in the hundred’s place). True. It reads, “Four hundreds and 9+3=12 ones is less than 491 .” 12 ones is the same as one ten and three ones, so let’s rewrite the previous sentence. “Four hundreds, one ten, and two ones is less than 491 .” 412<491 412 is, in fact, less than 491 . Although both numbers have four 100 s (fours in the hundred’s place), 412 only has one ten (a one in the ten’s place), while 491 has nine tens (a nine in the ten’s place). False. It reads, “Three hundreds and four tens is less then seven tens, nine ones, and two hundreds.” 340<279 340 is, in fact, greater than 279 because 340 has three 100 s (a three in the hundred’s place), while 279 has two 100 s (a two in the hundred’s place). False. It reads, “Seven ones and three hundreds is greater than 370.” 307>370 307 is, in fact, less than 370 . Although both numbers have three 100 s (threes in the hundreds place), 307 has no 10 s (a zero in the ten’s place), while 370 has seven 10 s (a seven in the ten’s place). False. It reads 2 hundreds + 7 tens = 3 hundreds - 2 tens 270=280 While both numbers have 2 hundreds (a two in the hundreds place), 270 has 7 tens (a seven in the tens place) while 280 has an 8 in the tens place. Therefore 270<280 2.NBT Comparisons 2 Alignment 1: 2.NBT.A.4 Domain NBT: Number and Operations in Base Ten Cluster Understand place value. Standard Compare two three-digit numbers based on meanings of the hundreds, tens, and ones digits, using > , =, and < symbols to record the results of comparisons.