Word (.docx)
Acrobat (.pdf)
Create CMAP
Course Standards
General Course Information and Notes
General Notes
In Grade 1, instructional time should focus on four critical areas: (1) developing understanding of addition, subtraction, and strategies for addition and subtraction within 20; (2) developing understanding of whole number relationships and place value, including grouping in tens and ones; (3) developing understanding of linear measurement and measuring lengths as iterating length units; and (4) reasoning about attributes of, and composing and decomposing geometric shapes.1. Students develop strategies for adding and subtracting whole numbers based on their prior work with small numbers. They use a variety of models, including discrete objects and length-based models (e.g., cubes connected to form lengths), to model add-to, take-from, put-together, take-apart, and compare situations to develop meaning for the operations of addition and subtraction, and to develop strategies to solve arithmetic problems with these operations. Students understand connections between counting and addition and subtraction (e.g., adding two is the same as counting on two). They use properties of addition to add whole numbers and to create and use increasingly sophisticated strategies based on these properties (e.g., “making tens”) to solve addition and subtraction problems within 20. By comparing a variety of solution strategies, children build their understanding of the relationship between addition and subtraction.
2. Students develop, discuss, and use efficient, accurate, and generalizable methods to add within 100 and subtract multiples of 10. They compare whole numbers (at least to 100) to develop understanding of and solve problems involving their relative sizes. They think of whole numbers between 10 and 100 in terms of tens and ones (especially recognizing the numbers 11 to 19 as composed of a ten and some ones). Through activities that build number sense, they understand the order of the counting numbers and their relative magnitudes.
3. Students develop an understanding of the meaning and processes of measurement, including underlying concepts such as iterating (the mental activity of building up the length of an object with equal-sized units) and the transitivity principle for indirect measurement.
4. Students compose and decompose plane or solid figures (e.g., put two triangles together to make a quadrilateral) and build understanding of part-whole relationships as well as the properties of the original and composite shapes. As they combine shapes, they recognize them from different perspectives and orientations, describe their geometric attributes, and determine how they are alike and different, to develop the background for measurement and for initial understandings of properties such as congruence and symmetry.
General Information
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 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
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
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 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 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 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
Explore strategies to add or subtract ten from a two-digit number in this interactive tutorial.
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
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 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
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 tell time to the hour on an analog clock and a digital clock 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
Explore the zoo and learn how to order and compare objects by length and height in this interactive tutorial.
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
Educational Games
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
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/Slideshow
"What Time Is It?" is a slideshow story that illustrates the activities in a student's day.
Type: Presentation/Slideshow
Problem-Solving Tasks
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
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
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 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
Tutorials
In this tutorial, you will learn to see 25 as 2 tens and 5 ones.
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 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
Video/Audio/Animation
Choose the correct amount of candy to package in the box. The truck will deliver the correctly filled packages.
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
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 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 students to draw geometric shapes and then decompose and recompose them into other shapes, using slides, turns, and flips to cut and move pieces around.
Type: Virtual Manipulative
In this activity, students can create and view a histogram using existing data sets or original data entered. Students can adjust the interval size using a slider bar, and they can also adjust the other scales on the graph. This activity allows students to explore histograms as a way to represent data as well as the concepts of mean, standard deviation, and scale. This activity includes supplemental materials, including background information about the topics covered, a description of how to use the application, and exploration questions for use with the java applet.
Type: Virtual Manipulative
Congratulations
