Foundational Skills in Mathematics K-2   (#5012005)

Version for Academic Year:

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

Student Resources

Vetted resources students can use to learn the concepts and skills in this course.

Original Student Tutorials

Hopscotch Counting On: 11-20:

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

Hopscotch Counting On: 1-10:

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

Type: Original Student Tutorial

We Have 2 Bones! Recognizing and Writing Number 2:

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

Where Is My Bone? Recognizing and Writing Numbers 0 and 1:

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

Partitioning Circular Pies: Fourths:

It's time for pie! Learn to partition circular pies into fourths in this interactive student tutorial. 

Type: Original Student Tutorial

Partitioning Rectangular Pies: Fourths:

It's Thanksgiving and time for pie! Learn to partition rectangular pies into fourths in this interactive student tutorial.

Type: Original Student Tutorial

Chocolate Partitioning!:

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

Can You Teach A Dolphin Math? - Part 2:

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

Let's Make A Dollar:

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.

Type: Original Student Tutorial

Can You Teach A Dolphin Math? - Part 1:

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

Let's Add Money: Place Value (Part 4):

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.

Type: Original Student Tutorial

Let’s Add Money: Mixed Coins (Part 3):

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.

Type: Original Student Tutorial

Washing Hands: Counting to 20:

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

Type: Original Student Tutorial

Let’s Add Money: Using Similar Coins (Part 2):

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.

Type: Original Student Tutorial

Destinee Dragon’s Donut Troubles: Arrays:

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

Type: Original Student Tutorial

Telling Time with Tomás:

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

Type: Original Student Tutorial

Sorting Shapes:

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

Type: Original Student Tutorial

Construction Measurement Mix-Up:

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

Sweet Sorting:

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

Type: Original Student Tutorial

Balancing Act:

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

Type: Original Student Tutorial

Let's Talk About Money (Part 1):

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.

Type: Original Student Tutorial

Shapes in Space:

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

Type: Original Student Tutorial

Farm Baby Rescue Part 1: Up and Down Positions:

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

Beach Buddies: Even or Odd? :

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

Ten on the Farm:

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

Type: Original Student Tutorial

Shape Sleuths: Trapezoids:

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

Shape Sleuths: Rectangles and Squares:

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

Type: Original Student Tutorial

Circus Fun: The Search for Circles:

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

Type: Original Student Tutorial

The Search for Shapes: Recognizing Rectangles and Squares:

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.

Type: Original Student Tutorial

Ten More, Ten Less:

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

Type: Original Student Tutorial

The Search for Shapes: Exploring Hexagons:

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.

Type: Original Student Tutorial

The Search for Shapes: Tracking Triangles:

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"

Type: Original Student Tutorial

Addition Switcheroo :

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

Big Brown Bug: Estimating Measurements!:

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

Shape Sleuths: Hexagons:

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

Tale of the Tallest Skyscraper:

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

Shape Sleuths: Triangles:

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

Teams with the Same Amount:

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

Counting on by Ones When Given Any Number From 0 through 20:

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

Subtraction with Stanley:

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

Type: Original Student Tutorial

What's the Weather?:

Learn how to organize data in three categories as well as represent and interpret the data in this interactive tutorial.

Type: Original Student Tutorial

Equal Shares Heroes Find Fourths:

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

The Shape Factory with Robbie the Robot:

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

Type: Original Student Tutorial

Hickory Dickory Dock:

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

Count a Group of 0 to 5 Objects:

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

Type: Original Student Tutorial

Building Shapes With Becca:

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

 

Type: Original Student Tutorial

Racing Riley Adds Lengths:

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

Type: Original Student Tutorial

Filling in a 120 Chart!:

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

Equal Shares Heroes:

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

Briana's Shape Playground:

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

Counting by Ones:

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

Type: Original Student Tutorial

Zoo School:

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

Type: Original Student Tutorial

I Can Count... By Ones to Ten:

Learn to count to ten by ones with this interactive tutorial.

Type: Original Student Tutorial

Educational Games

Curious George - Blast Off!:

Help George count backwards to launch a rocket.

Type: Educational Game

Curious George - Bubble Pop:

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

Is it 2D or 3D?:

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

Lily-pad Jumper:

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

Match the 2D Shape:

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

Type: Educational Game

Jetstream Riders:A high flying Addition 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

Underwater Subtraction:

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

Curious George - Hat Grab:

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

Type: Educational Game

Curious George - Flower Garden:

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

Type: Educational Game

Curious George - Hide and Seek:

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

Type: Educational Game

Curious George - Bug Catcher:

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

Type: Educational Game

Curious George - Count with George and Allie:

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

Type: Educational Game

Curious George, Museum of Tens:

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

Type: Educational Game

Practicing Logic with addition and subtraction:

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

Estimation of Length, Area, and Volume:

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

Estimate and Measure - Sticky Math!:

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

Grouping and Grazing:

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

Hundreds Chart:

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

Type: Educational Software / Tool

My Place:

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

Presentation/Slideshows

What Time Is It? - Tarheel Reader Powerpoint Story:

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

Type: Presentation/Slideshow

Counting- A World of Numbers :

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

Which Pictures Represent One Half?:

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

Representing Half of a Rectangle:

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

Equality Number Sentences:

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

Comparisons 2:

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

Type: Problem-Solving Task

Three composing/decomposing problems:

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

Ten $10s make $100:

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

Type: Problem-Solving Task

Saving Money 2:

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

Red and Blue Tiles:

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

Finding a Chair:

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

Boxes and Cartons of Pencils:

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

Type: Problem-Solving Task

Digits 2-5-7:

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

One, Ten, and One Hundred More and Less:

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

Regrouping:

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

Delayed Gratification:

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

A Pencil and a Sticker:

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

Overlapping Rectangles:

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

Measure Me!:

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

How Long:

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

Type: Problem-Solving Task

Ordering Numbers:

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

Daisies in vases:

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

Boys and Girls, Variation 2:

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

Boys and Girls, Variation 1:

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

At the Park:

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

Type: Problem-Solving Task

Find the Missing Number:

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

Maria’s Marbles:

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

Party Favors:

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

Saving Money 1:

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

Counting Dots in Arrays:

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

Ordering 3-digit numbers:

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 Longest Walk:

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

Visiting the Arcade:

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

Bundling and Unbundling:

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

Comparisons 1:

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

Counting Stamps:

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

How Many Days Until Summer Vacation?:

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

Largest Number Game:

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

Making 124:

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

Valid Equalities?:

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 (as in Standard for Mathematical Practice 6) 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 Pet Snake:

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

School Supplies:

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

Sharing Markers:

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

Counting Squares:

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

Susan's Choice:

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

Toll Bridge Puzzle:

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

Understanding the Meaning of the Equal Sign:

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

Type: Tutorial

Adding 5 + 3 + 6:

Learn how to add 5 + 3 + 6.

Type: Tutorial

Adding 8 + 7:

Learn how to add 8 + 7 by making a group of ten.

Type: Tutorial

Telling Time Examples #2:

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

Type: Tutorial

Telling Time Examples #1:

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

Type: Tutorial

Measuring Length With No Gaps or Overlaps:

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

Repeated Addition Example:

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

Solving word problems within 100:

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

Place Value Example with 25:

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

Type: Tutorial

Subtracting within 100 using the standard algorithm:

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

Adding 7 + 6 Using a Number Line and Objects to Count:

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

Type: Tutorial

Solving a word problem using the standard algorithm for subtraction:

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

Adding two-digit numbers using the standard algorithm:

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

Adding and subtracting on number line word problems:

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

Type: Tutorial

Subtracting with regrouping:

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

Subtracting two-digit numbers without regrouping:

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

Adding two-digit numbers without regrouping:

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

Adding by getting to group of 10 first:

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

Understanding place value when subtracting tens:

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

Understanding place value while subtracting ones:

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

Type: Tutorial

Understanding place value while adding tens:

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

Type: Tutorial

Exercising gorillas:

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

Monkeys for a party:

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

Type: Tutorial

Making Ten on a Ten Frame and Using Equations and Symbols:

Type: Tutorial

Making Five on a Five Frame and Using Equations and Symbols:

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

Type: Tutorial

Teens as sums with 10:

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

Type: Tutorial

Result Unknown - Subtraction Word Problem Within 10:

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

Type: Tutorial

Change Unknown - 3 + ? = 10:

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

Type: Tutorial

Subtraction - Using Equations and Symbols to Find an Unknown:

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

Addition - Using Equations and Symbols to Find an Unknown:

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

Number Patterns on a 0-99 Chart:

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

Converting Numbers Into Words - Word Problems:

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

Converting Numbers Into Words:

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

Polygon Gallery:

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

Candy Shipping:

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

Type: Video/Audio/Animation

100's Day:

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

Sorting Numbers with a Venn Diagram:

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

Time Memory:

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

Addition to 20:


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

Polygon Sort:

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

Number Sense-Place Value:

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

Data Grapher:

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

Counting on and back:

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

Pan Balance - Numbers:

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

Shape Tool:

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

Patch Tool:

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

Type: Virtual Manipulative

Five Frame :

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

Ten Frame:

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

Animal Legs (multiply using repeated addition):

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

Type: Virtual Manipulative

Groups of Dogs (multiplication):

Students use arrays to understand the meaning of multiplication.

Type: Virtual Manipulative

Long or Short?:

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

Okta's Rescue (Counting Success):

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

How Many Are Under The Shell?:

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

Shape Cutter:

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

Histogram:

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

Parent Resources

Vetted resources caregivers can use to help students learn the concepts and skills in this course.