ALEX Classroom Resource

  

Grade 2 Mathematics Module 4, Topic E

  Classroom Resource Information  

Title:

Grade 2 Mathematics Module 4, Topic E

URL:

https://www.engageny.org/resource/grade-2-mathematics-module-4-topic-e

Content Source:

EngageNY
Type: Lesson/Unit Plan

Overview:

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.

Content Standard(s):
Mathematics
MA2019 (2019)
Grade: 2
12. Add and subtract within 1000 using concrete models or drawings and strategies based on place value, properties of operations, and/or the relationship between addition and subtraction; relate the strategy to a written method.

a. Explain that in adding or subtracting three-digit numbers, one adds or subtracts hundreds and hundreds, tens and tens, ones and ones; and sometimes it is necessary to compose or decompose tens or hundreds.
Unpacked Content
Evidence Of Student Attainment:
Students:
  • add and subtract within 1000.
  • explain their reasoning using concrete models or drawings, or using strategies based on place value, properties of operations, and/or the relationship between addition and subtraction.
  • relate the strategy used to a written method (symbolic and numeric recording of the steps used).
Teacher Vocabulary:
  • Compose
  • Decompose
Knowledge:
Students know:
  • how to count to 1,000.
  • how to identify hundreds, tens, and ones.
  • how to compose numbers.
  • how to decompose two digit numbers.
  • how to record strategies for solving addition and subtraction problems.
Skills:
Students are able to:
  • add and subtract within 1000.
  • model addition problems using visual models.
  • record strategies for solving addition problems.
  • communicate the relationship between models and symbolic (numeric) representations.
Understanding:
Students understand that:
  • relationships between models of addition/subtraction problems and written strategies of those models can be used to justify solutions.
Diverse Learning Needs:
Essential Skills:
Learning Objectives:
M.2.12.1: Define regrouping, total, sum, difference and solve.
M.2.12.2: Add and subtract two two-digit numbers with and without regrouping.
M.2.12.3: Determine the value of the number in the ones, tens, hundreds and thousands place using concrete models or drawings and strategies based on place value.
M.2.12.4: Match the number in the ones, tens, hundreds and thousands position to a pictorial representation or manipulative of the value.
M.2.12.5: Model written method for recording horizontal and vertical addition and subtraction problems.
M.2.12.6: Represent two- and three-digit numbers with multiple models.
Examples: models—base ten blocks, number lines, linking cubes, straw bundles.
M.2.12.7: Recall single-digit addition and subtraction facts.
M.2.12.8: Add and subtract within 20, e.g., by using objects or drawings to represent the problem.

Prior Knowledge Skills:
  • Notice same/different and some/all.
  • Recognize numerals from 1-50.
  • Add one to a set of objects (up to 10 objects).
  • Given small groups of objects, create larger groups by combining the small groups.
  • Understand ten and 1 (ten 1's =10).
  • Put together two small groups of objects to create a larger group.
  • Subtract one from a set of objects (up to 10 objects).
  • Given a group of objects (20 or less), divide the group into smaller groups in various ways.
  • Take away objects from a large group to create two smaller groups.
  • Understand number words.
  • Establish one-to-one correspondence between numbers and objects when given a picture a drawing or objects.
  • Rote count to 10.
  • Understand amount words, such as more, less, and another.
  • Begin to understand that parts of an object can make a whole.

Alabama Alternate Achievement Standards
AAS Standard:
M.AAS.2.10 Using vocalization, sign language, augmentative communication, or assistive technology, identify the meaning of the + sign (add, plus, put together) and the sign (subtract, take away, take from) and the = sign (equal, the same as); compose and decompose numbers up to 20 using objects, pictures, drawings, or numbers.


Mathematics
MA2019 (2019)
Grade: 2
14. Explain why addition and subtraction strategies work, using place value and the properties of operations.

Note: Explanations may be supported by drawings or objects.
Unpacked Content
Evidence Of Student Attainment:
Students:
  • solve addition and subtraction problems using objects, pictures, words and numbers. Explain and justify strategies for adding and subtracting.
Teacher Vocabulary:
  • Properties of operations
Knowledge:
Students know:
  • strategies for finding sums and differences.
  • physical (manipulative) models and pictorial models (place value blocks, lines and dots, bundles and sticks, etc.) for representing numbers using place value concepts.
Skills:
Students are able to:
  • use logical reasoning, place value concepts and vocabulary, and properties of numbers and operations to justify strategies for finding sums and differences.
Understanding:
Students understand that:
  • relationships between models of addition and subtraction problems and symbolic recordings of those models can be used to justify solutions and strategies.
Diverse Learning Needs:
Essential Skills:
Learning Objectives:
M.2.14.1: Explain addition and subtraction problems using concrete objects, pictures.
M.2.14.2: Use multiple strategies to add and subtract including counting on, counting back and using doubles.
M.2.14.3: Recall single-digit subtraction facts.
M.2.14.4: Recall single-digit addition facts.
M.2.14.5: Represent addition and subtraction with objects, fingers, mental images, drawings, sounds (e.g., claps), acting out situations, verbal explanations, expressions, or equations.

Prior Knowledge Skills:
  • Match numerals to objects or drawings.
  • Identify numerals 1 to 10.
  • Count from 0 to 10.
  • Add and subtract numbers within 20 using objects, pictures and fingers.
  • Take a smaller set out of a larger set.
  • Combine two sets to make a larger set up to twenty.
  • Count items in a set up to twenty.
  • Establish one-to-one correspondence between numbers and objects.
  • Understand one less than a number 2 through 20.
  • Understand one more than a number 1 through 20.
  • Understand positional terms with equal signs.
Tags: addition, hundreds, ones, operations, place value, strategy, subtraction, tens, threedigit, within 1000
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There are six lessons in this topic.

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Author: Hannah Bradley