# ALEX Classroom Resources

ALEX Classroom Resources
Subject: Mathematics (2)
Title: Grade 2 Mathematics Module 4, Topic B
Description:

Subject: Mathematics (2)
Title: Grade 2 Mathematics Module 4, Topic D
Description:

In Lesson 17 of Module 4, Topic D, students extend the base ten understanding developed in Topic A to numbers within 200. Having worked with manipulatives to compose 10 ones as 1 ten, students relate this to composing 10 tens as 1 hundred. For example, students might solve 50 + 80 by thinking 5 ones + 8 ones = 13 ones, so 5 tens + 8 tens = 13 tens = 130. They use place value language to explain when they make a new hundred. They also relate 100 more from Module 3 to + 100 and mentally add 100 to given numbers. In Lesson 18, students use number disks on a place value chart to represent additions with the composition of 1 ten and 1 hundred. They use place value language to explain when they make a new ten and a new hundred, as well as where to show each new unit on the place value chart. In Lesson 19, students relate manipulatives to a written method, recording compositions as new groups below in vertical form. As they did in Topic B, students use place value language to express the action as they physically make 1 hundred with 10 tens disks and 1 ten with 10 ones disks. Working in partners, one student records each change in the written method step by step as the other partner moves the manipulatives. In Lessons 20 and 21, students move from concrete to pictorial as they use math drawings to represent compositions of 1 ten and 1 hundred. Some students may need the continued support of place value drawings with labeled disks, while others use the chip model. In both cases, students relate their drawings to a written method, recording each change they make to their model on the numerical representation. They use place value language to explain these changes. Lesson 22 focuses on adding up to four two-digit addends with totals within 200. Students now have multiple strategies for composing and decomposing numbers, and they use properties of operations (i.e., the associative property) to add numbers in an order that is easiest to compute. For example, when solving 24 + 36 + 55, when adding the ones, a student may make a ten first with 4 and 6. Another student may decompose the 6 to make 3 fives (by adding 1 to the 4).

Subject: Mathematics (2)
Title: Grade 2 Mathematics Module 4, Topic C
Description:

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.

Subject: Mathematics (2)
Title: Grade 2 Mathematics Module 4, Topic E
Description:

Module 4, Topic E begins with an extension of mental math strategies learned in first grade, when students learned to subtract from the ten by using number bonds. In Lesson 23, they return to this strategy to break apart three-digit minuends and subtract from the hundred. For example, in first-grade students solved 14 – 9 by restating the problem as 10 – 9 + 4. In second grade, students use the same strategy to restate 143 – 90 as 100 – 90 + 43. In Lesson 24, students use number disks on a place value chart to represent subtraction and develop an understanding of decomposition of tens and hundreds. This concrete model helps students see the answer to the question, “Do I have enough ones?” or, “Do I have enough tens?” When they do not, they exchange one of the larger units for ten of the smaller units. Repeated practice with this exchange solidifies their understanding that within a unit of ten there are 10 ones, and within a unit of a hundred there are 10 tens. This practice is connected to the strategies they learned with tens and ones; they learn that the only real difference is in place value. The strategies are also connected to addition through part-whole understanding, which is reinforced throughout. In Lesson 25, students move towards the abstract when they model decompositions on their place value chart while simultaneously recording the changes in the written form. Students draw a magnifying glass around the minuend, as they did in Topic C. They then ask the question, “Do I have enough ones?” They refer to the place value disks to answer and exchange a ten disk for 10 ones when necessary. They record the change in the written form. Students repeat these steps when subtracting the tens. Students use math drawings in Lesson 26 as they move away from concrete representations and into the pictorial stage. They follow the same procedure for decomposing numbers as they did in Lesson 25 with the number disks, but now they may use a chip model or number disk drawing. They continue to record changes in the written form as they work with their models. Topic E closes with the special case of subtracting from 200. Using number disks on a place value chart, students review the concept that a unit of 100 is comprised of 10 tens. They then model 1 hundred as 9 tens and 10 ones and practice counting to 100 both ways (i.e., 10, 20, 30…100 and 10, 20…90, 91, 92, 93…100). Next, they model the decomposition of a hundred either in two steps (as 10 tens then decomposing 1 ten as 10 ones) or one-step (as 9 tens and 10 ones) as they represent subtractions from 200. Students use this same reasoning to subtract from numbers that have zero tens. For example, to subtract 48 from 106, students model the decomposition of 106 as 10 tens 6 ones and as 9 tens 16 ones. Throughout the lesson, students relate their models to a written form step by step.

Subject: Mathematics (2)
Title: Grade 2 Mathematics Module 4, Topic F