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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.
General Information
Student Resources
Original Student Tutorials
Help Ms. Griffin's class use pictographs to answer questions about the data they collected on their class's favorite ice cream flavors in this interactive student tutorial.
Type: Original Student Tutorial
Learn how to organize collected data about ice cream to create your own pictographs in this interactive student tutorial.
Type: Original Student Tutorial
Learn how to create numbers that are 100 less as you wrap up the place value party in this interactive tutorial.
This is part 1 in five-part series. Click below to view the other tutorials in the series.
Type: Original Student Tutorial
Find 100 less and 100 more than a given 3-digit number by helping Kaylin and Quinten keep track of the place value party game points in this interactive tutorial.
This is part 1 in five-part series. Click below to view the other tutorials in the series.
Type: Original Student Tutorial
Find 10 more and 10 less than 3-digit numbers with regrouping to help Kaylin and Quinten keep score at the place value party in this interactive tutorial.
This is part 1 in five-part series. Click below to view the other tutorials in the series.
Type: Original Student Tutorial
It's time for cake! Learn to partition cakes into thirds in this interactive student tutorial.
Type: Original Student Tutorial
Mr. Mahoney challenges students to solve 10 less and 10 more problems in a place value party planning adventure in this interactive tutorial.
This is part 1 in five-part series. Click below to view the other tutorials in the series.
Type: Original Student Tutorial
Learn to partition circular and rectangular pizzas into halves in this interactive tutorial.
Type: Original Student Tutorial
It's time for pie! Learn to partition circular pies into fourths in this interactive student tutorial.
Type: Original Student Tutorial
It's Thanksgiving and time for pie! Learn to partition rectangular pies into fourths in this interactive student tutorial.
Type: Original Student Tutorial
Learn to partition a rectangular chocolate bar into equally sized pieces by making rows and columns in this interactive tutorial.
Note: This tutorial extends beyond partitioning a rectangle into 4 equal sized shares and explores partitioning into higher numbers.
Type: Original Student Tutorial
Learn read and write numbers in expanded form with the dolphins in this interactive tutorial.
This is Part 2 in a two-part series. Click HERE to open Part 1.
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. Click HERE to open Part 2.
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 interactive 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
Explore the Base 10 place value system with 3-digit numbers in Bianca's Bubble Gum Factory with this interactive tutorial.
Type: Original Student Tutorial
Learn the value and characteristics of dollar bills when you meet with a bank teller in this interactive tutorial.
This is part 6 of 6. Click below to open the other tutorials in the series.
(Part 1) Let's Talk About Money
(Part 2) Let's Add Money: Using Similar Coins
(Part 3) Let's Add Money: Mixed Coins
(Part 4) Let's Add Money: Place Value
(Part 5) Let's Make a Dollar
Type: Original Student Tutorial
Find the value of 3-digit numbers which are 10 less with regrouping as Kaylin and Quinten keep score at a place value party in this interactive tutorial.
This is part 1 in five-part series. Click below to view the other tutorials in the series.
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
A printable hundreds chart featuring a 10x10 table numbered 1 to 100. (found on Illuminations website under "Trading for Quarters")
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.
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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 concrete approach to the solution. 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
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 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 critiquing the reasoning of others.
Type: Problem-Solving Task
This task asks students to explain how they know the list is complete. 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
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 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 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
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
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
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
Congratulations
