# Mathematics - Grade One   (#5012030)

## 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.

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

Florida Standards Implementation Guide Focus Section:

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

Major Clusters

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

MAFS.1.OA.2 Understand and apply properties of operations and the relationship between addition and subtraction.

MAFS.1.OA.3 Add and subtract within 20.

MAFS.1.OA.4 Work with addition and subtraction equations.

MAFS.1.NBT.1 Extend the counting sequence.

MAFS.1.NBT.2 Understand place value.

MAFS.1.NBT.3 Use place value understanding and properties of operations to add and subtract.

MAFS.1.MD.1 Measure lengths indirectly and by iterating length units.

Supporting Clusters

MAFS.1.MD.3 Represent and interpret data.

MAFS.1.MD.2 Work with time and money.

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

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

### General Information

Course Number: 5012030
Course Path:
Course Length: Year (Y)
Course Attributes:
• Class Size Core Required
Course Status: Course Approved

## Educator Certifications

One of these educator certification options is required to teach this course.

## Student Resources

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

## Original Student Tutorials

Exploring Equations in Space:

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

Type: Original Student Tutorial

Race Car Competition - Part 2 Using Number Lines to Order Numbers:

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.

Type: Original Student Tutorial

Block Building Blast - Part 3:

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.

Part 1

Part 2

Part 3

Type: Original Student Tutorial

Block Building Blast - Part 2:

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.

Part 1

Part 2

Part 3

Type: Original Student Tutorial

Block Building Blast - Part 1:

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.

Part 1

Part 2

Part 3

Type: Original Student Tutorial

Race Car Competition - Part 3 Comparing Statements:

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

Race Car Competition - Part 1 Number Lines:

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

Exploring Expanded Form in Space:

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

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

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

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

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

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

Ten More, Ten Less:

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

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

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

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

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

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

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

Addition Word Problems Around the Zoo - Part 1:

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

Subtraction Word Problems Around the Zoo - Part 2:

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

Word Problems Around the Zoo - Part 3:

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

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

## 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

## Presentation/Slideshow

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

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).

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."

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.

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.

How Long:

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

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.

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.

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.

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.

At the Park:

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

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."

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.

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 by helping them explicitly attend to the meaning of mathematical notation and carefully analyze whether it is being used correctly.

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.

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.

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.

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.

## Tutorials

Adding 5 + 3 + 6:

Learn how to add 5 + 3 + 6.

Type: Tutorial

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

Type: Tutorial

Place Value Example with 25:

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

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

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

## Video/Audio/Animation

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

## Virtual Manipulatives

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

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

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

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.
MAFS.1
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. Note: Students should apply the principle of transitivity of measurement to make indirect comparisons, but they need not use this technical term.
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.