In Module 4, Topic A, students build upon their understanding of the base ten system and their prior knowledge of place value strategies presented in Module 3. In Lesson 1, students relate 10 more and 10 less and 1 more and 1 less to addition and subtraction. They recognize that they must add and subtract like units and that the digit in the tens place changes when adding and subtracting 10, just as the digit in the ones place changes when adding or subtracting 1. Students see numbers in terms of place value units; 54 – 10 is 5 tens 4 ones minus 1 ten. They learn to record the addition and subtraction of multiples of 10 using arrow notation. In Lesson 2, students apply place value understanding to add and subtract multiples of 10 before counting on by tens. For example, when adding 20 to 43, they may count 53, 63. Students also develop flexibility in using related addition problems. For example, to solve 92 – 60, one student might think 9 tens – 6 tens is 3 tens, plus 2 is 32, while another starts at 60, adds on 3 tens, and then 2 ones to reach 92, so 32.
Module 4 culminates with Topic F, in which students think about and discuss the multiple strategies they have learned to represent and solve addition and subtraction problems. They share their reasoning as they link their drawings to two written methods, and discuss the similarities, differences, and efficacy of each approach. In Lesson 29, students learn the totals below written method. Throughout Grades 1 and 2, students decompose numbers into expanded form to recognize place value and to understand that they must add like units. These problems are written horizontally. Here, students use this prior learning to solve addition problems in a similar way. They decompose two- and three-digit numbers, then add like units and record the totals horizontally. They then transition into the vertical form of the method when they decompose the numbers mentally, add like units, and record the totals below. The totals below method gives students the option of adding from left to right or from right to left. Students explain how each step of their math drawing relates to this written method. In Lesson 30, students represent and solve problems using both the totals below and the new groups below methods (students used the latter method throughout the module). They relate both methods to their math drawings and discuss the differences and similarities between the two. In Lesson 31, students apply knowledge of addition and subtraction strategies to solve two-step word problems. Students are challenged to make sense of more complex relationships as they are guided through more difficult problem types, such as comparison problems. These problems will involve smaller numbers and will be scaffolded to address the heightened level of difficulty.
Module 4, Topic C parallels Topic B, as students apply their understanding of place value strategies to the subtraction algorithm, moving from concrete to pictorial to abstract. It is important to note that the algorithm is introduced at this level and is connected deeply to the understanding of place value. However, fluency with the algorithm is a Grade 3 standard. In Lesson 11, students use number disks on a place value chart to subtract like units (e.g., 76 – 43 is 7 tens – 4 tens and 6 ones – 3 ones). They practice modeling the standard subtraction algorithm within 100 without decompositions and then progress to problems that require exchanging 1 ten for 10 ones (e.g., in 76 – 47 students must recompose 7 tens 6 ones as 6 tens 16 ones). The use of manipulatives allows students to physically experience the renaming and understand the why behind recomposing a quantity. Lesson 12 builds upon this understanding as students relate manipulatives to a written method, recording recompositions in vertical form. In subtraction, a common error is for students to switch the top and bottom digits in a given place when renaming is necessary. They perceive the digits as a column of unrelated numbers, rather than part of a larger total, and simply subtract the smaller from the larger. Hence, many students would solve 41 – 29 as 28, instead of understanding that they can take 9 ones from 41 ones. To prevent this error and aid students in seeing the top number as the whole, students use a “magnifying glass” to examine the minuend. They draw a circle around the top number and add a handle. Before subtracting, they look inside the magnifying glass at the whole number and determine if each digit is big enough to subtract the number below it. If not, they decompose one of the next larger units to make ten of the unit they need. In Lesson 13, this is used in conjunction with the chip model; students record each change they make to their model simultaneously on the algorithm. In Lessons 14–15, students move to the more abstract dot drawings on their place value charts and follow the same procedure for decomposing a ten and relating it to the written method. Here, however, students subtract a two-digit subtrahend from a three-digit minuend (e.g., 164 – 36). This provides practice working with and drawing three-digit numbers without the complexity of decomposing a hundred. As in Topic A, Topic C closes with a lesson that focuses on one- and two-step word problems within 100. Students apply their place value reasoning, mental strategies, and understanding of compositions and decompositions to negotiate different problem types with unknowns in various positions. Because two different problem types (i.e., add to, take from, put together/take apart, compare) are often combined in two-step word problems, some quantities will involve single-digit addends, especially when students are working with the more challenging comparison problems. They are encouraged to be flexible in their thinking and to use drawings and/or models to explain their thinking. Students continue to use tape diagrams to solve word problems, relating the diagrams to a situation equation (e.g., 8 + ____ = 41) and rewriting it as a solution equation (e.g., 41 – 8 = ___), thus illustrating the relationship between operations. Students find success when using their mental strategies of making a multiple of 10 and counting on (e.g., 9, 10, 20, 30 40, 41) as they experience the relationships between quantities within a context.
In this interactive activity, students will be led through steps to write and solve addition and subtraction equations. There are teaching activities as well as practice activities available. A handout that reviews the steps taught during the activity can be printed. There is a karaoke song with printable lyrics that will help students learn the steps taught during the activity. After utilizing this resource, the students can complete the short quiz to assess their understanding.
This classroom resource provides a video that explains how to write and solve equations using information from word problems. There is a karaoke song with printable lyrics that will help students learn and review the steps taught during the video. After utilizing this resource, the students can complete the short quiz to assess their understanding.
Odd Squad agents Olive and Otto use addition and subtraction to figure out what's causing people in the park to be covered in plaids and stripes, especially when Otto is suddenly covered in yellow and white polka dots.