## Course Standards

## General Course Information and Notes

### General Notes

In Grade 2, instructional time should focus on four critical areas: (1) extending understanding of base-ten notation; (2) building fluency with addition and subtraction; (3) using standard units of measure; and (4) describing and analyzing shapes.

1. Students extend their understanding of the base-ten system. This includes ideas of counting in fives, tens, and multiples of hundreds, tens, and ones, as well as number relationships involving these units, including comparing. Students understand multi-digit numbers (up to 1000) written in base-ten notation, recognizing that the digits in each place represent amounts of thousands, hundreds, tens, or ones (e.g., 853 is 8 hundreds + 5 tens + 3 ones).

2. Students use their understanding of addition to develop fluency with addition and subtraction within 100. They solve problems within 1000 by applying their understanding of models for addition and subtraction, and they develop, discuss, and use efficient, accurate, and generalizable methods to compute sums and differences of whole numbers in base-ten notation, using their understanding of place value and the properties of operations. They select and accurately apply methods that are appropriate for the context and the numbers involved to mentally calculate sums and differences for numbers with only tens or only hundreds.

3. Students recognize the need for standard units of measure (centimeter and inch) and they use rulers and other measurement tools with the understanding that linear measure involves an iteration of units. They recognize that the smaller the unit, the more iterations they need to cover a given length.

4. Students describe and analyze shapes by examining their sides and angles. Students investigate, describe, and reason about decomposing and combining shapes to make other shapes. Through building, drawing, and analyzing two- and three-dimensional shapes, students develop a foundation for understanding area, volume, congruence, similarity, and symmetry in later grades.

**English Language Development ELD Standards Special Notes Section:**

Teachers are required to provide listening, speaking, reading and writing instruction that allows English language learners (ELL) to communicate information, ideas and concepts for academic success in the content area of Mathematics. For the given level of English language proficiency and with visual, graphic, or interactive support, students will interact with grade level words, expressions, sentences and discourse to process or produce language necessary for academic success. The ELD standard should specify a relevant content area concept or topic of study chosen by curriculum developers and teachers which maximizes an ELL’s need for communication and social skills. To access an ELL supporting document which delineates performance definitions and descriptors, please click on the following link:

http://www.cpalms.org/uploads/docs/standards/eld/MA.pdf

**Florida Standards Implementation Guide Focus Section:**

The Mathematics Florida Standards Implementation Guide was created to support the teaching and learning of the Mathematics Florida Standards. The guide is compartmentalized into three components: focus, coherence, and rigor.Focus means narrowing the scope of content in each grade or course, so students achieve higher levels of understanding and experience math concepts more deeply. The Mathematics standards allow for the teaching and learning of mathematical concepts focused around major clusters at each grade level, enhanced by supporting and additional clusters. The major, supporting and additional clusters are identified, in relation to each grade or course. The cluster designations for this course are below.

**Major Clusters**

MAFS.2.OA.1 Represent and solve problems involving addition and subtraction.

MAFS.2.OA.2 Add and subtract within 20.

MAFS.2.NBT.1 Understand place value.

MAFS.2.NBT.2 Use place value understanding and properties of operations to add and subtract.

MAFS.2.MD.1 Measure and estimate lengths in standard units.

MAFS.2.MD.2 Relate addition and subtraction to length.

**Supporting Clusters**

MAFS.2.OA.3 Work with equal groups of objects to gain foundations for multiplication.

MAFS.2.MD.3 Work with time and money.

MAFS.2.MD.4 Represent and interpret data.

**Additional Clusters**

MAFS.2.G.1 Reason with shapes and their attributes.

**Note:** Clusters should not be sorted from major to supporting and then taught in that order. To do so would strip the coherence of the mathematical ideas and miss the opportunity to enhance the major work of the grade with the supporting and additional clusters.

### General Information

**Course Number:**5012040

**Course Path:**

**Abbreviated Title:**MATH GRADE TWO

**Course Length:**Year (Y)

**Course Attributes:**

- Class Size Core Required

**Course Type:**Core Academic Course

**Course Status:**Course Approved

**Grade Level(s):**2

## Educator Certifications

## Student Resources

## Original Student Tutorials

YOU and the DOLPHINS will be able to read and write numbers in expanded form by the end of this interactive tutorial. This is Part 2 of 2 tutorials.

Type: Original Student Tutorial

Learn to read and write numbers to 1000 using base-ten numerals with the dolphins!

This interactive tutorial is part 1 of a two-part series.

Type: Original Student Tutorial

Help Destinee use arrays and repeated addition to find how many donuts that she has in this interactive tutorial.

Type: Original Student Tutorial

Come tell time with Tomás in 5 minute intervals on a digital and analog clock in this interactive tutorial.

Type: Original Student Tutorial

Add and subtract within 100 to solve word problems involving lengths in the same units to fix the construction mix-up at a school in this interactive tutorial.

Type: Original Student Tutorial

Help Tyler balance equations by finding the unknown number in this interactive tutorial.

Type: Original Student Tutorial

Learn how to recognize and draw triangles, pentagons and hexagons using the shapes' attributes in this space-themed, interactive tutorial.

Type: Original Student Tutorial

Come explore even and odd numbers of objects and learn to determine if a group of objects has an even or odd number in this beach-themed, interactive tutorial.

Type: Original Student Tutorial

A 6 foot bug? No way! Learn how to estimate length using inches, feet and yards by using objects around you in this interactive tutorial.

Type: Original Student Tutorial

Learn how to compare three-digit numbers using place value models, number lines and place value charts in this online tutorial.

Type: Original Student Tutorial

Learn to use place value to solve subtraction problems within 100 in this interactive, basketball-themed tutorial.

Type: Original Student Tutorial

Learn different strategies for adding two-digit numbers and solve problems involving lengths as you complete this interactive tutorial.

Type: Original Student Tutorial

## Educational Games

Play the concentration game. Match the 2D shape to the correct name.

Type: Educational Game

Students are to guess two numbers based on their sum and difference: The sum of 2 numbers is 15 and their difference is 1. What are the 2 numbers?

Type: Educational Game

The students will be presented with two shapes and must estimate how many times the smaller will fit in the larger. They will be surprised at some of the results but will quickly learn and make adjustments.

Type: Educational Game

## Educational Software / Tools

This interactive Flash applet helps children learn grouping, tally marks, place value, addition, and subtraction. Students help the alien spaceship move cows into corrals by counting by 5s and 10s. They also can apply those grouping skills to practice adding and subtracting two-digit numbers with regrouping. Audio cues and prompts reinforce the user's actions and facilitate counting and the development of math language.

Type: Educational Software / Tool

This virtual manipulative can be used to picture whole number operations, addition, subtraction, multiplication and division, carried out on a number line.

Type: Educational Software / Tool

A printable hundreds chart featuring a 10x10 table numbered 1 to 100. (found on Illuminations website under "Trading for Quarters")

Type: Educational Software / Tool

This resource re-explains the concepts behind place value of numbers up to 1,000. It guides you through the place of numbers and uses simple terms and comparisons to describe the placement of numbers to students.

It could be set up for students on computers to go through, or project it for the class to follow along as you re-read about place value.

Type: Educational Software / Tool

## Problem-Solving Tasks

The purpose of this task is for students to see different ways of partitioning a figure into two or more equal shares, by which we mean decomposing the figure into "pieces" with equal area.

Type: Problem-Solving Task

This task is for assessment purposes, providing a context for indentifying different ways of representing half of an object, a rectangle in this case. The task may also be used for instructional purposes but if so the teacher may wish to introduce some other ways of showing one half of the rectangle, such as dividing along a diagonal (and shading in one piece) or dividing it into four equal pieces, shading in two pieces that only touch at a corner.

Type: Problem-Solving Task

The purpose of this task if for students to gain a better understanding of <,=,> with the help of number sentences.

Type: Problem-Solving Task

The purpose of this task is to help students understand composing and decomposing ones, tens, and hundreds. This task is meant to be used in an instructional setting and would only be appropriate to use if students actually have base-ten blocks on hand.

Type: Problem-Solving Task

The purpose of this task is for students to use currency to help better understand place value.

Type: Problem-Solving Task

The purpose of this task is for students to relate addition and subtraction problems to money and to situations and goals related to saving money. This task is an instructional task that brings many aspects of the mathematical work that second graders will be doing together with an opportunity to learn about financial literacy concepts.

Type: Problem-Solving Task

This task is specifically written so that students have opportunities to use different strategies to determine whether a set has an even or odd number of objects.

Type: Problem-Solving Task

This tasks uses school supplies in a problem to help students gain a better understanding of place value.

Type: Problem-Solving Task

Students who are struggling to build an understanding of the relationship between digit placement and the value of the number may still need concrete manipulatives such as grid paper and Base Ten Blocks. As a classroom extension, after students have worked independently or in small groups to solve the problem, the teacher can ask students to share their numbers, until all six possibilities are listed. Then, independently or as a whole group, students can order the six numbers from smallest to largest (or largest to smallest).

Type: Problem-Solving Task

This task acts as a bridge between understanding place value and using strategies based on place value for addition and subtraction. Within the classroom context, this activity can be differentiated using numbers that are either simpler or more difficult to manipulate across tens and hundreds.

Type: Problem-Solving Task

This task serves as a bridge between understanding place-value and using strategies based on place-value structure for addition. Place-value notation leaves a lot of information implicit. The way that the numbers are represented in this task makes this information explicit, which can help students transition to adding standard base-ten numerals.

Type: Problem-Solving Task

The purpose of this task is for students to compare two options for a prize where the value of one is given $2 at a time, giving them an opportunity to "work with equal groups of objects to gain foundations for multiplication." This context also provides students with an introduction to the concept of delayed gratification, or resisting an immediate reward and waiting for a later reward, while working with money.

Type: Problem-Solving Task

The purpose of this task is to represent and solve problems involving addition and subtraction with the help of a bar diagram.

Type: Problem-Solving Task

The point of this task is to emphasize the grouping structure of the base-ten number system, and in particular the crucial fact that 10 tens make 1 hundred. Second graders should have been given opportunities to work with objects and pictures that represent the grouping structure of the base-ten number system, which would help prepare them for doing this task.

Type: Problem-Solving Task

The purpose of this task is for students to relate addition and subtraction problems to money and to situations and goals related to saving money. This task has students adding two 2-digit numbers that require regrouping and the solution shows a more concrete approach than the solution approach shown in 2.OA, NBT Saving Money 2. This problem can be adjusted based on where students are in their understanding of addition involving two digit numbers.

Type: Problem-Solving Task

Students who work on this task will benefit in seeing that given a quantity, there is often more than one way to represent it, which is a precursor to understanding the concept of equivalent expressions. This particular question also lays a foundation for students to understand the commutative property of multiplication in third grade. This task would be much more valuable if included in an appropriate place in an instructional sequence than as an isolated task.

Type: Problem-Solving Task

The purpose of this task is for students to gain a better understanding of 3-digit numbers and their place value.

Type: Problem-Solving Task

The language in this task is above the reading level of many second grade students, so it is best for the teacher to explain the task to the students verbally. After students have drawn and measured their ten line segments, it might be more useful for the class to discuss part (b) as a whole group. It is a good idea to have the students use color to help them keep track of the connection between a line that they have drawn and the corresponding data point on the graph.

Type: Problem-Solving Task

The purpose of this task is to introduce students to the characteristics of money in a financial literacy sense as well as to solve problems involving money.

Type: Problem-Solving Task

Students determine the number of hundreds, tens and ones that are necessary to write equations when some digits are provided. Student must, in some cases, decompose hundreds to tens and tens to ones. The order of the summands does not always correspond to the place value, making these problems less routine than they might seem at first glance.

Type: Problem-Solving Task

This task requires students to compare numbers that are identified by word names and not just digits. The order of the numbers described in words are intentionally placed in a different order than their base-ten counterparts so that students need to think carefully about the value of the numbers. Some students might need to write the equivalent numeral as an intermediate step to solving the problem.

Type: Problem-Solving Task

This is an instructional task related to deepening place-value concepts. The important piece of knowledge upon which students need to draw is that 10 tens is 1 hundred. So each sheet contains 100 stamps. If students do not recall this fact readily, one way to review it is to have them draw a strip of ten stamps on graph paper (so they don't have to draw all the individual stamps) and then draw ten strips that are side-by-side to represent a sheet and ask how many stamps there are in one sheet.

Type: Problem-Solving Task

The purpose of the task is to allow children an opportunity to subtract a three-digit number including a zero that requires regrouping. The solutions show how students can solve this problem before they have learned the traditional algorithm.

Type: Problem-Solving Task

It is important that students be asked to explain well beyond saying something like "She should choose the 8 because it is the biggest." They should be asked to think through the other possibilities and then draw on their ability to compare three digit numbers (as developed in 2.NBT.4) to complete the task. In the second part, students are presented with an incorrect statement supported by a correct one. It is worth pausing to ask students to carefully sort this through, since attending to reasoning that is partially true and partially false lends itself to the SMP.3: Constructing viable arguments and critiquing the reasoning of others.

Type: Problem-Solving Task

This task asks students to explain how they know the list is complete, it aligns with Standard for Mathematical Practice 3 Construct viable arguments and critique the reasoning of others. A systematic approach to listing the solutions is not required to meet the standard, but it's a nice way for students to explain how they found all the possible ways to make 124 using base-ten blocks

Type: Problem-Solving Task

The purpose of this task is to address the concept of opportunity cost through a real world context involving money. In economics, resources are limited, but our wants are unlimited. Therefore, choices must be made. Every choice involves a cost.

Type: Problem-Solving Task

This task is intended to assess adding of four numbers as given in the standard while still being placed in a problem-solving context. As written this task is instructional; due to the random aspect regarding when the correct route is found, it is not appropriate for assessment. This puzzle works well as a physical re-enactment, with paper plates marking the islands and strings with papers attached for the tolls.

Type: Problem-Solving Task

## Tutorials

In this tutorial, you will learn more about what the equals sign means and how to balance equations.

Type: Tutorial

Demonstrates how to tell time on unlabeled analog clocks to the nearest five minutes.

Type: Tutorial

Tell time on a labeled analog clock to the nearest five minutes.

Type: Tutorial

In this tutorial you will learn how to solve a word problem by creating a chart and adding the same number many times.

Type: Tutorial

This Khan Academy tutorial, called, "sports on a die" explains the pitfalls of relying on key words in a word problem. Students solve a problem by writing a missing addend addition equation and solve with the standard algorithm for subtracting two digit numbers.

Type: Tutorial

In this tutorial video from Khan Academy, called "Using crayons", explore subtracting within 100 using the standard algorithm, as well as a bar diagram.

Type: Tutorial

In this video tutorial from Khan Academy called "losing tennis balls", explore solving a two-step subtraction word problem using the standard algorithm.

Type: Tutorial

In this tutorial video from Khan Academy, called "Fence posts for horses", explore adding a two digit number to a two digit number using the standard algorithm

Type: Tutorial

In this video tutorial from Khan Academy, explore using a number line solve word problems involving more than two numbers.

Type: Tutorial

In this tutorial video from Khan Academy, a subtraction problem is solved which contains two numbers each with two-digits. The video demonstrates subtraction with regrouping using the standard algorithm, as well as a method using expanded form.

Type: Tutorial

In this video tutorial from Khan Academy, explore subtracting two-digit numbers by using the standard algorithm. This video does not include regrouping.

Type: Tutorial

This tutorial for student audiences will assist learners with a further understanding of how to add two three-digit numbers together by drawing out base ten blocks based on the digits in each place. The tutorial supports student learning with visuals of using base ten blocks on place value charts to add two 3-digit addends.

Type: Tutorial

This tutorial for student audiences will assist learners with a further understanding of how to identify triangles by finding shapes with 3 straight sides that meet at 3 corners. The tutorial supports student learning with visual representations to help identify various shaped and sized triangles, including non-examples.

Type: Tutorial

You can watch a video that demonstrates how to convert numbers into words. Then, you can practice this skill by answering multiple choice questions.

Type: Tutorial

Students will view a video that uses place model values up to 1000, to teach the concept of how to convert numbers into words. After viewing the video students have an opportunity to practice this skill and receive immediate feedback on their responses.

Type: Tutorial

This tutorial for student audiences will assist learners with a further understanding of how to identify cubes by finding solid shapes with 6 square faces. The tutorial supports student learning with visual representations to help identify cubes, including non-examples.

Type: Tutorial

This combination of illustrations and narration defines convex as well as concave polygons and describes the features of various polygons. Examples of polygons shown include triangles and quadrilaterals of various types, including some that are convex and some that are concave, and even one that has a hole in it. Narration or read-along text describes the shapes for the user. Copyright 2005 Eisenhower National Clearinghouse

Type: Tutorial

## Virtual Manipulatives

This drag and drop Venn diagram simulation gives students the opportunity to solve a mathematical problem based on number properties using a range of different Venn diagrams. There are five different levels involving a range of multiples and simply odds and evens. The three core layouts cover simple separate sets, two intersecting sets, and a three way intersecting Venn Diagram. The odds and evens layout is limited to two intersecting sets, of course.

Type: Virtual Manipulative

This virtual manipulative is intended to introduce users to the idea of visual representation of data by means of a bar chart. This manipulative is also useful for letting the students categorize collections of familiar objects, (shoes, dry food items, coins etc.) separate them into sub-categories, and describe.

Type: Virtual Manipulative

This virtual manipulative will help the students to develop some familiarity with the currency, both coins and bills. Three different features of the manipulative will provide practice to the students:

- Make a dollar gives students practice in the equivalence of different sets of coins.
- How much money asks the student to total the value of the displayed bills and coins.
- Pay exact amount could be used to model either payment or giving change.

Type: Virtual Manipulative

This virtual manipulative will allow the students to form different kinds of patterns. Learners will be able to describe parts in relation to a whole group. They will also be able to distinguish between characteristics of shapes.

Type: Virtual Manipulative

This extremely versatile manipulative can be used by learners of different grades. At early grades, this manipulative will help the students recognize, name, build, draw, and compare two-dimensional shapes. As they progress students can classify and understand relationships among types of two-dimensional objects using their defining properties. The application computes perimeter and area allowing students to explore patterns as dimensions change.

Type: Virtual Manipulative

With this virtual manipulative, you can represent place value in base 10 to 100. Students place a chip in the "100" box, and click to exchange a "100" chip for 10 tens, and 1 ten for ten ones.

Type: Virtual Manipulative

This game provides learners with an opportunity to perform addition of single addends to 20. This tool encourages decomposition of numbers, as multiple addends will give them a larger score. The learners should be motivated to obtain a higher score.

Type: Virtual Manipulative

This interactive Java applet helps users develop place value concepts involving addition of numbers with 1, 2, 3, or 4 digits. The virtual blocks are manipulated to model regrouping in order to solve addition problems posed by the applet. Users also may create and solve their own problems with whole numbers or up to 3 decimal places. The default of base 10 may be changed to any of the bases 2, 3, 4, or 5.

Type: Virtual Manipulative

This versatile interactive applet helps students learn to skip count, practice multiplication facts, and discover number patterns. Users select the number to count by and the starting number. In Practice mode the user clicks on the respective numbers in order. In Show mode the applet displays all numbers in the chosen counting sequence immediately. In Animate mode numbers in the counting sequence are highlighted in order one at a time.

Type: Virtual Manipulative

With this interactive applet students can develop their understanding of place value and the relative position and magnitude of numbers in the base-10 number system. Users drag given numbers to their position on a number line, zooming in and out to increase precision. They can select from six levels of difficulty (Tens, Hundreds, Thousands, Millions, Billions, Decimals) and from 1 to 3 dots. There are three modes: Explore, Practice, Test.

Type: Virtual Manipulative

This interactive Flash activity asks the user to sort shapes into a 2 by 2 chart, known as a Carroll Diagram, based on their properties. Properties used to sort include "quadrilateral" or "not quadrilateral" and "regular polygon" or "not regular polygon."

Type: Virtual Manipulative

Hacker has given you a challenge. He will run his number machine to create a number. Then you will get three numbers between one and nine. The challenge is to make a number that is larger than the one on Hacker's machine. Be careful though--Hacker will give you numbers that can't be bigger than his!

Type: Virtual Manipulative

Students use this interactive tool to explore the connections between data sets and their representations in charts and graphs. Enter data in a table (1 to 6 columns, unlimited rows), and preview or print bar graphs, line graphs, pie charts, and pictographs. Students can select which set(s) of data to display in each graph, and compare the effects of different representations of the same data. Instructions and exploration questions are provided using the expandable "+" signs above the tool.

Type: Virtual Manipulative

A versatile tool that can be used to illustrate the operations of addition, subtraction, multiplication, and division.

Type: Virtual Manipulative

This virtual manipulative provides base blocks that consist of individual "units," "longs," "flats," and "blocks" (ten of each set for base 10). They can be used to show place value for numbers and to increase understanding of addition and subtraction. Also allows for representation of decimal numbers.

Type: Virtual Manipulative

This virtual manipulative allows you to create, color, enlarge, shrink, rotate, reflect, slice, and glue geometric shapes, such as: squares, triangles, rhombi, trapezoids and hexagons.

Type: Virtual Manipulative

Students use repeated addition as a strategy to solve multiplication story problems.

Type: Virtual Manipulative

Students use arrays to understand the meaning of multiplication.

Type: Virtual Manipulative

This virtual manipulative allows students to draw geometric shapes and then decompose and recompose them into other shapes, using slides, turns, and flips to cut and move pieces around.

Type: Virtual Manipulative

Diffy is a virtual manipulative that allows students to practice their subtraction facts with whole numbers, integers, fractions, decimals, or money. It is a puzzle of sorts with four black numbers placed at the corners of a black square. The first goal is to fill in the four blanks in the blue circles in the middle of each side of the black square.

Type: Virtual Manipulative

In this activity, students can create and view a histogram using existing data sets or original data entered. Students can adjust the interval size using a slider bar, and they can also adjust the other scales on the graph. This activity allows students to explore histograms as a way to represent data as well as the concepts of mean, standard deviation, and scale. This activity includes supplemental materials, including background information about the topics covered, a description of how to use the application, and exploration questions for use with the java applet.

Type: Virtual Manipulative

Section:Grades PreK to 12 Education Courses >Grade Group:Grades PreK to 5 Education Courses >Subject:Mathematics >SubSubject:General Mathematics >