## Course Standards

## General Course Information and Notes

### General Notes

This course supports students who need additional instruction in foundational mathematics skills as it relates to core instruction. Instruction will use explicit, systematic, and sequential approaches to mathematics instruction addressing all domains including number sense, algebraic thinking, geometry, measurement and statistical thinking. Teachers will use the listed standards that correspond to each students’ needs.

Effective instruction matches instruction to the need of the students in the group and provides multiple opportunities to practice the skill and receive feedback. The additional time allotted for this course is in addition to core instruction. The intervention includes materials and strategies designed to supplement core instruction.

**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 Language Arts. 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: https://cpalmsmediaprod.blob.core.windows.net/uploads/docs/standards/eld/la.pdf

### General Information

**Course Number:**5012005

**Course Path:**

**Abbreviated Title:**FDN SKILLS MATH K-2

**Course Length:**Multiple (M) - Course length can vary

**Course Attributes:**

- Class Size Core Required

**Course Status:**Course Approved

**Grade Level(s):**K,1,2

## Educator Certifications

## Student Resources

## Original Student Tutorials

Help Astronaut Archimedes teach the alien students to show numbers using place value and equations in this interactive tutorial.

Type: Original Student Tutorial

Learn how to order and compare numbers from least to greatest using number lines and place value with the students in Mr. Rivera’s class in this interactive tutorial.

This is Part 3 of 3 in the tutorial series. Click below to open parts 1 and 3.

- Part 1: Number Lines
- Part 2: Using Number Lines or Order Numbers
- Part 3: Comparing Statements

Type: Original Student Tutorial

Help Amari, Sonia, and their friends compose and decompose 2-digit numbers in equivalent ways to compete in a base ten block building contest with this interactive tutorial.

This is part 3 of 3. Click below to view the other tutorials in this series.

Type: Original Student Tutorial

Explore ways to break apart 2-digit numbers into tens and ones to help Amari and Sonia build base ten block towers in this interactive tutorial.

This is part 2 of 3. Click below to view the other tutorials in this series.

Type: Original Student Tutorial

Help Amari and Sonia build base-ten block towers using their knowledge of 2-digit place value in this interactive tutorial.

This is part 1 of 3. Click below to view the other tutorials in this series.

Type: Original Student Tutorial

Learn about the American flag by identifying colors and shapes and sorting parts of flag designs into groups in this interactive S.T.E.M. and civics integrated tutorial.

This is part 1 of 2-part series, click HERE to view part 2.

Type: Original Student Tutorial

Learn how to order to compare numbers using >, <, and = symbols with Mr. Rivera’s class as they build and test racing cars in this interactive tutorial.

This is Part 3 of 3 in the tutorial series. Click below to open parts 1 and 2.

Type: Original Student Tutorial

Learn how to plot numbers on number lines using data from race cars in this interactive tutorial.

This is part 1 of 3 in a series of tutorials on plotting and comparing numbers. Click below to open the other tutorials in the series.

- Part 2 (Coming soon)
- Part 3 (Coming soon)

Type: Original Student Tutorial

Astronaut Archimedes launches into space to teach the outside world all about place value and expanded form in this interactive tutorial.

Type: Original Student Tutorial

Join Juliana for her 8th birthday party! Learn to solve addition problems within 20 using objects and creating drawings in this interactive student tutorial.

Type: Original Student Tutorial

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 how to recognize and write the number 5 and count up to 5 objects using 10 frames and number lines as you help Lucy the dog plan a party in this interactive tutorial.

Type: Original Student Tutorial

Help Lucy the dog recognize and write number 4. She will also learn to count up to 4 objects using a ten frame and number line in this interactive tutorial.

Type: Original Student Tutorial

Learn to partition circular and rectangular pizzas into halves in this interactive tutorial.

Type: Original Student Tutorial

Count on beginning at any number within 11-20 in this playground-themed, interactive tutorial.

This is part 2 in a two-part series. Click to open Part 1, **Hopscotch Counting On: 1-10**.

Type: Original Student Tutorial

Count on beginning at any number within 1-10 in this interactive tutorial.

Type: Original Student Tutorial

Help Lucy and Izzy learn to recognize and write the number 2. In this interactive tutorial, you'll also count two objects and use a 10 frame and a number line.

This is part 2 in a multi-part series. Click below to open the other tutorials.

Type: Original Student Tutorial

Help Lucy and Izzy explore the numbers 0 and 1 using writing, ten frames and number lines 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 how many quarters, nickels, dimes and pennies are needed to make a dollar with this interactive tutorial.

This is part 5 of 5. 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**

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

Use place value and a tens and ones chart to add pennies, nickels, dimes, quarters in this interactive tutorial.

This is part 4 of 5. 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 5) Let's Make a Dollar!**

Type: Original Student Tutorial

Learn to add a combination of coins, such as quarters, dimes, nickels, and pennies using a number line, skip counting, and a hundred chart in this interactive tutorial.

This interactive tutorial is part 3 of 5. 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 4) Let's Add Money: Place Value****(Part 5) Let's Make a Dollar!**

Type: Original Student Tutorial

Learn how to wash your hands and count to 20 in this interactive tutorial.

Type: Original Student Tutorial

Learn how to add the same type of coins together using skip counting and a number line in this interactive student tutorial.

This is part 2 of 5. Click below to open the other tutorials in the series.

**(Part 1) Let's Talk About Money****(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

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

Learn to sort and identify two-dimensional and three-dimensional shapes in this carnival-themed 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

Practice sorting, counting, and comparing by visiting the Sorting Sweet Shop in this candy-themed, interactive tutorial.

Type: Original Student Tutorial

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

Type: Original Student Tutorial

Help Kolby learn to identify coins by their characteristics and values in this interactive tutorial.

This is part 1 of 5. Click below to open the other tutorials in the series.

- (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

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

Type: Original Student Tutorial

Relative positions include up and down, top and bottom, over, on, and under, and above and below. Learn different types of up and down positions to rescue eight chicks in this farm-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

Help Farmer Betsy! You'll use multiple strategies to make a ten and write equations in this interactive tutorial.

Type: Original Student Tutorial

Learn about the defining attributes of trapezoids in this interactive tutorial series about shapes.

Click below to learn about other shapes.

Note: This tutorial uses the definition of trapezoid that includes exactly one pair of parallel sides.

Type: Original Student Tutorial

Help find clues to identify rectangles and squares and their defining attributes in this interactive tutorial.

Type: Original Student Tutorial

Learn the attributes, or characteristics, of a circle in this interactive tutorial.

Type: Original Student Tutorial

Identify and name rectangles and squares based on their defining attributes, even if they have different sizes or positions. Join King Geo and his scout, Quad, as they search for rectangles and squares in this interactive tutorial.

This is part of a series on the defining attributes of shapes. Click the links below.

**"The Search for Shapes: Tracking Triangles"**- The Search for Shapes: Recognizing Rectangles and Squares"

Type: Original Student Tutorial

Explore strategies to add or subtract ten from a two-digit number in this interactive tutorial.

Type: Original Student Tutorial

Help find hexagons based on their defining attributes for King Geo in this interactive tutorial. Learn what makes a hexagon a hexagon.

This is part of a series on the defining attributes of shapes. Click the links below.

**"The Search for Shapes: Tracking Triangles"****"The Search for Shapes: Recognizing Rectangles and Squares"**- "The Search for Shapes: Exploring Hexagons"

Type: Original Student Tutorial

Track down triangles based on their defining attributes for King Geo in this interactive tutorial. Learn what makes a triangle a triangle.

This is part of a series on the defining attributes of shapes. Click the links below.

- "The Search for Shapes: Tracking Triangles"
**The Search for Shapes: Recognizing Rectangles and Squares"**

Type: Original Student Tutorial

Change the order of the numbers in an addition sentence and use the counting on strategy to become quicker at your math facts in this 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 about the defining attributes of hexagons in this interactive tutorial series about shapes.

Click below to learn about other shapes.

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 about the defining attributes of triangles in this interactive tutorial series about shapes.

Click below to learn about other shapes.

Type: Original Student Tutorial

Learn how to tell whether an equation is true or false based on what you know about the equal sign as you complete this interactive tutorial.

Type: Original Student Tutorial

Practice counting on by ones from a given number zero through twenty, as you help Miranda and Jacob 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 how to organize data in three categories as well as represent and interpret the data in this interactive tutorial.

Type: Original Student Tutorial

Be a hero and partition circles and rectangles into four equal shares. Describe equal shares using the words "fourths" and "quarters" in this interactive tutorial.

Type: Original Student Tutorial

Learn to combine simple shapes to compose larger shapes with Robbie the Robot in this interactive tutorial.

Type: Original Student Tutorial

Learn to tell time to the hour on an analog clock and a digital clock as you complete this interactive tutorial.

Type: Original Student Tutorial

Help Gabriella and Olivia count groups of objects from 0 to 5 in this interactive tutorial.

Type: Original Student Tutorial

Help Becca identify and build shapes that you see in the world around you as you complete this interactive 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

Learn how to count to 120 and fill in the missing number on a chart to 120 in this interactive tutorial.

Type: Original Student Tutorial

Help the heroes separate circles and rectangles into equal shares and describe the equal shares as "halves" or "half of" as you complete this interactive tutorial.

Type: Original Student Tutorial

Learn how to identify the similarities and differences in the number of sides of two-dimensional shapes in this interactive tutorial.

Type: Original Student Tutorial

Join Thomas and count to twenty by ones in this interactive tutorial.

Type: Original Student Tutorial

Explore the zoo and learn how to order and compare objects by length and height in this interactive tutorial.

Type: Original Student Tutorial

Learn to count to ten by ones with 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

Help Mario and Gretchen model and write equations for addition word problems, in this interactive tutorial.

This is part 1 in a 3-part series. Click below to explore the other tutorials in the series.

Part 1: Addition Word Problems Around the Zoo (this one)

Part 2: Subtraction Word Problems Around the Zoo

Part 3: Word Problems Around the Zoo

Type: Original Student Tutorial

Help Mario and Gretchen model and write equations for subtraction word problems in this interactive tutorial.

This is part 2 in a 3-part series. Click below to explore the other tutorials in the series.

Part 1: Addition Word Problems Around the Zoo

Part 2: Subtraction Word Problems Around the Zoo (this one)

Part 3: Word Problems Around the Zoo

Type: Original Student Tutorial

Help Gretchen and Mario differentiate between addition and subtraction word problems during their field trip to the zoo in this interactive tutorial.

This is part 3 in a 3-part series. Click below to explore the other tutorials in the series.

Part 1: Addition Word Problems Around the Zoo

Part 2: Subtraction Word Problems Around the Zoo

Part 3: Word Problems Around the Zoo (this one)

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

Count along with George by popping bubbles from his bath. You can pop the bubbles by counting out loud with George if your computer has a microphone. If your computer does not have a microphone, you can click on the bubbles to count!

Type: Educational Game

Score points by sorting 2D and 3D shapes into the correct basket as they fly by. Lose points if you answer incorrectly.

Type: Educational Game

Help Froggy jump to the other side of the pond! Start with Froggy's number and click the lily-pad with the next higher number.

Type: Educational Game

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

Type: Educational Game

Fly high in a hot air balloon and catch the jet stream to go faster! Use addition to add hot air, and see if you can win against other students!

This is a single level basic version. Teachers can register for additional levels for practicing subtraction, multipiication and division.

Type: Educational Game

Dive deep with this fun subtraction facts game. Correctly answer the math facts and capture pictures of sea creatures! Choose to focus on one fact family or practice them all!

Type: Educational Game

Help George figure out which color hat is the most popular by grabbing hats from people's heads at the airport.

Type: Educational Game

Flowers are popping up everywhere! Help George keep track of how many there are by counting with him.

Type: Educational Game

Help George search for hidden numerals, number words, and animals in this hide-and-seek game.

Type: Educational Game

Help George catch bugs with a net to find which group has more.

Type: Educational Game

Count along as Allie counts up to 20 objects in a counting book for George.

Type: Educational Game

Help George make museum displays by picking the number of items that need be added to make 10.

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

This is an educational game in which the student manipulates sticky buns to estimate and measure baking pans. The site features a kid's voice that walks the student through math explanations, game directions, and tips for estimating and measuring objects.

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

## Presentation/Slideshows

"What Time Is It?" is a slideshow story that illustrates the activities in a student's day.

Type: Presentation/Slideshow

In this lessons students will use this accessible, easy-to-read book that shows objects up to ten. It can be downloaded and used with PowerPoint, Impress, or Flash. It can be used on the Intellikeys keyboard with a custom overlay, or even used with 1-3 switches.

Type: Presentation/Slideshow

## 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 instructional task is for students to help students understand the meaning of the equal sign and to use it appropriately. The idea is that students should be comparing the number of circles in each of the rectangles and to write an equation that reflects the fact there are an equal number in each of the boxes (when this is the case).

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

These problems explicitly describe one-to-one correspondences without using comparison language. Such problems are easier for students to solve than problems that use comparison language such as "How many more?" or "How many fewer."

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 purpose of this task is to give students an opportunity to compose and decompose polygons to make rectangles. This is a challenging problem for first graders and it would be inappropriate to use it as an assessment.

Type: Problem-Solving Task

The purpose of this task is for students to measure something that interests them (namely themselves) by laying multiple copies of a shorter object that represents the length unit end to end. This task provides students an opportunity to discuss the need to be careful when measuring as it is very likely that some of them will get incorrect comparisons of their leg length with their partner's leg length.

Type: Problem-Solving Task

The purpose of this task is to help students learn how to take measurements.

Type: Problem-Solving Task

The purpose of this task is to give students an opportunity to compare numbers less than 100 to benchmark numbers. Even though a number line is not explicitly given in the task, it is useful for students to list the numbers in the order they would appear on the number line; this allows them to focus on the relative ordering without worrying about the exact placement on the number line.

Type: Problem-Solving Task

This instructional task asks students to consider all the decompositions of a number into two addends. Because first grade students may have trouble reading this task even thought they are intellectual capable of working on this problem, it will help if the teacher reads the prompt to the students and then has them work together in pairs or small groups.

Type: Problem-Solving Task

This task represents the Put Together/Take Apart with both addends unknown context for addition and subtraction. Once a student finds one correct answer, he/she can be encouraged to find another. Ask the student to use objects, pictures, or equations to represent each answer.

Type: Problem-Solving Task

Students may use either addition or subtraction to solve these types of word problems, with addition related to the action of putting together and subtraction related to the action of taking apart. Depending on how students think about these word problems, either is appropriate for the "addend unknown" problems. Seeing it both ways emphasizes the relationship between addition and subtraction.

Type: Problem-Solving Task

This task includes three different problem types using the "Add To" context with a discrete quantity.

Type: Problem-Solving Task

This task asks students to solve addition and subtraction equations with different structures so that they are able to see the connections between addition and subtraction more easily. Examples should be presented with the the sum or difference on either side of the equal sign in order to dispel the notion that = means "compute."

Type: Problem-Solving Task

Students benefit from encountering one problem type limited to small numbers and to develop strategies for that type of problem before encountering mixed sets of problems and larger numbers that distract the student from the problem itself. Over time they will be able to distinguish between types of problems in mixed sets and apply the appropriate strategy to solve each.

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 help broaden and deepen students' understanding of the equals sign and equality. This task helps students attend to precision by helping them explicitly attend to the meaning of mathematical notation and carefully analyze whether it is being used correctly.

Type: Problem-Solving Task

The purpose of this task is for students to gain a better understanding of measurements with the example being the growth of a pet snake.

Type: Problem-Solving Task

This task could be used for either instructional or assessment purposes, depending on where students are in their understanding of addition and how the teacher supports them. The solution shown is very terse; students' solution strategies are likely to be much more varied.

Type: Problem-Solving Task

These task types represent the Take From contexts for addition and subtraction. This task includes the three different problem types using the Take From context: result unknown, change unknown, and start unknown. Students need experience and practice with all three types.

Type: Problem-Solving Task

The purpose of this task is to give students an opportunity to compose and decompose squares. This is a challenging problem for first graders and it would be inappropriate to use it as an assessment. However, if presented as a brainteaser it can be useful for giving the students practice in recognizing squares and stimulate interest as students compete to try to find the most squares.

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 video tutorial from Khan Academy, called, "Measuring a golden statue", we see an example of how to solve a problem in which we measure an object with same-size length units that span it with no gaps or overlaps.

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, you will learn to see 25 as 2 tens and 5 ones.

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 tutorial, you will learn how to add 7 + 6 using a number line and objects to count.

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

In this tutorial video from Khan Academy, explore adding two-digits numbers with base ten blocks and connect this to the standard algorithm. The examples do not include regrouping.

Type: Tutorial

In this tutorial video from Khan Academy, explore how making a ten can help to make thinking about addition easier. This video includes an example of adding a one-digit number to a two-digit number by decomposing the one-digit number.

Type: Tutorial

In this video tutorial from Khan Academy, explore the connection between place value and subtraction. This video explains how to solve a subtraction problem with numbers less than one hundred using base ten blocks.

Type: Tutorial

Learn how to subtract 4 from 46 by thinking about place value.

Type: Tutorial

Learn how to add 23 + 30 by thinking about place value.

Type: Tutorial

In this tutorial video from Khan Academy, a word problem is solved with unit cubes, as well as with a missing addend addition equation and a subtraction equation.

Type: Tutorial

In this tutorial video from Khan Academy, explore place value relationships with tens and ones within 20.

Type: Tutorial

Using a ten-frame as a model, you will learn how to use equations to join two addends, one addend unknown, to make 10.

Type: Tutorial

Using a five-frame as a model, you will learn how to use equations to join two addends, to make 5.

Type: Tutorial

In this tutorial video from Khan Academy, place value patterns are explored in "teen" numbers.

Type: Tutorial

In this tutorial, you will learn how to solve a result unknown word problems: 10 - 2 = ?.

Type: Tutorial

In this tutorial, you will learn to find the unknown change in an equation with a sum of 10: 3 + ? = 10.

Type: Tutorial

In this tutorial, you will learn to use symbols to record an unknown whole number in a subtraction equation relating to three whole numbers.

Type: Tutorial

In this tutorial, you will learn to use symbols to record an unknown whole number in an addition equation relating to three whole numbers.

Type: Tutorial

In this video on using a chart to count numbers 0 to 99, you will start to see patterns in the numbers in each row and the numbers in each column.

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

## Video/Audio/Animations

Choose the correct amount of candy to package in the box. The truck will deliver the correctly filled packages.

Type: Video/Audio/Animation

What does 100 look like? Sound like? Feel like? In this video from Teacher's Domain, Curious George helps students explore the many ways to measure 100 things.

Type: Video/Audio/Animation

## Virtual Manipulatives

This interesting game will help the learners to test their memory and the clock skills. The learners will have to match the time on the two cards which they will flip during the game. Each match will include a digital clock and one analog clock.

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

This interactive Flash applet supports the exploration of numbers to 100 by simulating a 100-bead string. A teacher or child can move all or some beads to the left or right to add and subtract. The controls allow users to move beads individually or 10 at a time to model different counting and calculation strategies. Users can hide or show the numbers represented by the beads. This applet lends itself well to use on an interactive white board. A PDF guide to this collection of teaching applets is cataloged separately.

Type: Virtual Manipulative

This tool helps students better understand that equality is a relationship and not an operational command to "find the answer." The applet features a pan balance that allows the student to input each half of an equation in the pans, which responds to the numerical expression's value by raising, lowering or balancing.

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 you to create patches and more complex figures using the provided 2-dimensional geometric shapes.

Type: Virtual Manipulative

This applet contains four games (How Many?, Build, Fill, and Add) that utilize a frame with five slots for students to place objects, which helps students develop counting and addition skills.

Type: Virtual Manipulative

This applet contains four games (How Many?, Build, Fill, and Add) that utilize a frame with ten slots for students to place objects, which helps students develop counting and addition skills.

Type: Virtual Manipulative

This is an interactive game where students are prompted to distinguish between a longer or shorter object. The tool increases in difficulty as the student progresses.

Type: Virtual Manipulative

This applet asks students to save as many octopuses as possible before the timer runs out. A number of how many they can net is displayed in the top right, and they will use the mouse to net that amount into the tank before releasing them for the next round. When the timer is up, another screen comes up with the number of octopuses saved represented in rows of ten. Finally, students will be asked to input on a number line how many they successfully saved.

Type: Virtual Manipulative

This site features an interactive game to help students develop number sense and fluency with addition and subtraction facts to 10. Okta the octopus hides some bubbles under a shell, and then either adds more bubbles or takes some away. Students have to determine how many bubbles are left under the shell. The number of bubbles Okta works with can be set to a desired number or the student can select random draw. This allows for focus with a preferred number if desired by the teacher or student.

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

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