Title:  10 for the Win!Grade: Kindergarten Overall Goal: To have students be able to count by multiples of 10 and comprehend the idea of a sequence of steps involved in a process.  StandardsLearning ObjectiveAssessment5d Students understand how automation works and use algorithmic thinking to develop a sequence of steps to create and test automated solutions. K.NS.1: Count to at least 100 by ones and tens and count on by one from any number.Students will be able to program the beebots to go the correct distance. Students will be able to count to 100 by tens.The students will have to use the beebots to move forward the correct amount of steps. The students will have the squares the beebot travels represent sets of 10.  Key Terms & Definitions: Sequence- certain order in which steps flowSkip counting- skipping numbers while counting, counting by multiples Number line- line which shows number in order, often marked at intervalsProgram- provide machine with coded instructions to perform task  Lesson Introduction (Hook, Grabber): 10 Students will paint hands and stamp them on paper! Each set of hands will represent a set of 10. We will do this all the way up to 100. This paper will be hung in the front of the classroom as a reminder of multiples of 10. Lesson Main:After hanging up our poster with the hands displaying multiples of 10, the teacher would count with the class by 10’s all the way up to 100, while referring to the poster so they can follow along.We will also pass out a number line to the students that highlights 10’s so they have a reference if they struggle.We will make a number line and write multiples of 10 along the side. We will measure out the space between numbers so that it is equal to the length the Beebot travels for each time the button is pushed. For example, if the student wanted to get to 30, they would have to know that you count up by saying “10, 20,30” and they would need to press the forward button on the Beebot 3 times. Each press of the button is a multiple of 10. For this activity, the teacher will break up the students into small groups and they will work together. They will draw a card which will have a multiple of 10 on it ranging from 10-100. The students will have to decide how many 10’s it takes to count up to that number, as well as how many times they will need to program the Beebot to reach the answer on the number line.   Lesson Ending:For the lesson ending, we will regroup as a class and talk about how we felt the Beebot activity went. Then we will count together by 10’s up to 100 again to reiterate what we have been learning. Lastly, we will pass out a worksheet to the students which we have included a link to under our resources, and have them complete it individually. This will give us an idea of the students understanding of this concept and can be used for our assessment.  Assessment Rubric: GreatAveragePoorIndicatorDescriptionDescriptionDescriptionHand Cut-outsStudent participated in the tracing and cutting out of hands.Student partially participated in the tracing and cutting out of hands.Student failed to participate in the tracing and cutting out of hands.Beebot activityStudent was able to successfully move the Beebot to correct answer.Student was able to move the Beebot, but not to the correct answer.Student was unable to move the Beebot and was unable to correctly answer.WorksheetStudent was able to correctly fill out the entire worksheet.Student was able to fill out 70% of the worksheet.Student was unable to fill out at least 70% of the worksheet.  Resources / Artifacts: Number line for students https://www.helpingwithmath.com/printables/others/lin0301number11.htmWebsite which has handprint idea on it https://www.theclassroomkey.com/2016/02/big-list-skip-counting-activities.htmlLesson assessment used in the lesson ending https://www.pinterest.com/pin/287597126178910688  Differentiation:       Differentiation for ability levelsIf a student really struggled with math skills, we could place them in a group with stronger math students. We could also offer an alternative activity for the Beebot timeline where we made the timeline go up by smaller multiples. For the worksheet, they could receive a longer amount of time to work on it and have directions read to them/receive help as needed.        Differentiation for access & resourcesIf the school had limited resources and did not have access to these robots, they could use other tools like toy cars or something they could use to roll to the spots on the timeline. The game could be altered to fit a large variety of resources. The worksheet we used was found online but a similar version could be created by the teacher. Anticipated Difficulties: Some students might struggle with the concept of skip counting. It may be hard at first for them to remember the multiples of 10. Hopefully by making a poster and providing them with their own number line for reference, this will eliminate some potential difficulties the students may have. 

This task gives students the opportunity to analyze two number lines in order to identify the one that correctly shows an improper fraction. Students then communicate their understanding by describing the reasoning they used to determine their answer was correct. It is aligned to evidence statement 3.C.6-1

In this seminar you will learn about the absolute value of numbers. You will learn how taking the absolute value affects both positive and negative numbers. You will use the techniques learned in this seminar to verify solutions to various other types of problems involving absolute value as you move forward. When looking at absolute value, you will identify how it can change a solution and the compare the difference that it makes in equations when there are multiple negative signs.StandardsCC.2.1.HS.F.2Apply properties of rational and irrational numbers to solve real world or mathematical problemsLearning TargetI can find the absolute value of a given number or numbers.Habits of MindPersistingCritical Thinking SkillAnalyze/evaluateAcademic/Concept VocabularyAbsolute valueNegativeNumber linePositive  

Adult Learners will review the previous lesson, measuring with a thermometer, to continue their application in horizontal number lines. Learners will use the number line to increase their understanding of integer values as well as apply their understanding to solving real world problems.

In this module, students reconnect with and deepen their understanding of statistics and probability concepts first introduced in Grades 6, 7, and 8. Students develop a set of tools for understanding and interpreting variability in data, and begin to make more informed decisions from data. They work with data distributions of various shapes, centers, and spreads. Students build on their experience with bivariate quantitative data from Grade 8. This module sets the stage for more extensive work with sampling and inference in later grades.

Find the rest of the EngageNY Mathematics resources at https://archive.org/details/engageny-mathematics.

In this interactive activity adapted from Anneberg Learner’s Teaching Math Grades 3–5, compare fractions on number lines to determine which class of students wins bubble-gum-blowing contests.

This lesson focuses on comparing and ordering fractions in ways that encourage deeper understanding of’ ‘number sense’ by supporting learners to consider different techniques to order and compare fractions with different numerators and denominators. The three techniques covered in this lesson are those used to compare fractions with like numerators or denominators, unlike numerators or denominators and by comparing to a 1/2 benchmark. Emphasis are placed on the two latter techniques. Activities and practice exercises involve real-world problems including sales discounts, cooking measurements and school score reports.

Explore fractions while you help yourself to 1/3 of a chocolate cake and wash it down with 1/2 a glass of orange juice! Create your own fractions using fun interactive objects. Match shapes and numbers to earn stars in the fractions games. Challenge yourself on any level you like. Try to collect lots of stars!

"Shadows are corrupting the land. Restore the balance of nature by exploring place value. Gate guides students in: lowering intimidation about large numbers and
decimals, understanding the meaning of place value, and realizing that the same mathematical concepts that apply to the ""easy"" integers apply to every order of magnitude."

In this 35-day Grade 3 module, students extend and deepen second grade practice with "equal shares" to understanding fractions as equal partitions of a whole. Their knowledge becomes more formal as they work with area models and the number line.

Find the rest of the EngageNY Mathematics resources at https://archive.org/details/engageny-mathematics.

Build equivalent fractions with different denominators. Match shapes and numbers to earn stars in the game. Challenge yourself on any level you like. Try to collect lots of stars!

In this Cyberchase video segment, the CyberSquad locates the Cyberchase Council by using negative numbers.

Equations and Inequalities

Type of Unit: Concept

Prior Knowledge

Students should be able to:

Add, subtract, multiply, and divide with whole numbers, fractions, and decimals.
Use the symbols <, >, and =.
Evaluate expressions for specific values of their variables.
Identify when two expressions are equivalent.
Simplify expressions using the distributive property and by combining like terms.
Use ratio and rate reasoning to solve real-world problems.
Order rational numbers.
Represent rational numbers on a number line.

Lesson Flow

In the exploratory lesson, students use a balance scale to find a counterfeit coin that weighs less than the genuine coins. Then continuing with a balance scale, students write mathematical equations and inequalities, identify numbers that are, or are not, solutions to an equation or an inequality, and learn how to use the addition and multiplication properties of equality to solve equations. Students then learn how to use equations to solve word problems, including word problems that can be solved by writing a proportion. Finally, students connect inequalities and their graphs to real-world situations.

Lesson OverviewStudents solve a classic puzzle about finding a counterfeit coin. The puzzle introduces students to the idea of a scale being balanced when the weight of the objects on both sides is the same and the scale being unbalanced when the objects on one side do not weigh the same as the objects on the other side.Key ConceptsThe concept of an inequality statement can be modeled using an unbalanced scale. The context—weighing a set of coins in order to identify the one coin that weighs less than the others—allows students to manipulate the weight on either side of the scale. In doing so, they are focused on the relationship between two weights—two quantities—and whether or not they are equal.Goals and Learning ObjectivesExplore a balance scale as a model for an equation or an inequality.Introduce formal meanings of equality and inequality.

Lesson OverviewStudents represent inequalities on a number line, find at least one value that makes the inequality true, and write the inequality using words.SWD:When calling on students, be sure to call on ELLs and to encourage them to actively participate. Understand that their pace might be slower or they might be shy or more reluctant to volunteer due to their weaker command of the language.SWD:Thinking aloud is one strategy for making learning visible. When teachers think aloud, they are externalizing their internal thought processes. Doing so may provide students with insights into mathematical thinking and ways of tackling problems. It also helps to model accurate mathematical language.Key ConceptsInequalities, like equations, have solutions. An arrow on the number line—pointing to the right for greater values and to the left for lesser values—can be used to show that there are infinitely many solutions to an inequality.The solutions to x < a are represented on the number line by an arrow pointing to the left from an open circle at a.Example: x < 2The solutions to x > a are represented on the number line with an arrow pointing to the right from an open circle at a.Example: x > 2The solutions to x ≤ a are represented on the number line with an arrow pointing to the left from a closed circle at a.Example: x ≤ 2The solutions to x ≥ a are represented on the number line with an arrow pointing to the right from a closed circle at a.Example: x ≥ 2Goals and Learning ObjectivesRepresent an inequality on a number line and using words.Understand that inequalities have infinitely many solutions.

Getting Started

Type of Unit: Introduction

Prior Knowledge

Students should be able to:

Solve and write numerical equations for whole number addition, subtraction, multiplication, and division problems.
Use parentheses to evaluate numerical expressions.
Identify and use the properties of operations.

Lesson Flow

In this unit, students are introduced to the rituals and routines that build a successful classroom math community and they are introduced to the basic features of the digital course that they will use throughout the year.

An introductory card sort activity matches students with their partner for the week. Then over the course of the week, students learn about the lesson routines: Opening, Work Time, Ways of Thinking, Apply the Learning, Summary of the Math, and Reflection. Students learn how to present their work to the class, the importance of taking responsibility for their own learning, and how to effectively participate in the classroom math community.

Students then work on Gallery problems to further explore the program’s technology resources and tools and learn how to organize their work.

The mathematical work of the unit focuses on numerical expressions, including card sort activities in which students identify equivalent expressions and match an expression card to a word card that describes its meaning. Students use the properties of operations to identify equivalent expressions and to find unknown values in equations.

Gallery OverviewAllow students who have a clear understanding of the content thus far in the unit to work on Gallery problems of their choosing. You can then use this time to provide additional help to students who need review of the unit's concepts or to assist students who may have fallen behind on work.Gallery DescriptionRepresent a Math ProblemStudents explore the number line tool and the double number line tool. They use the number line tool to solve a problem about the weights of a cheetah and a fisher cat.Research ExpressionsStudents learn the difference between numerical expressions and variable expressions. They watch video tutorials, review worked examples, use the Glossary, and explore other resources.Fish TankStudents create diagrams and use text and images as they solve a problem about the size of a fish tank.

Rational Numbers

Type of Unit: Concept

Prior Knowledge

Students should be able to:

Solve problems with positive rational numbers.
Plot positive rational numbers on a number line.
Understand the equal sign.
Use the greater than and less than symbols with positive numbers (not variables) and understand their relative positions on a number line.
Recognize the first quadrant of the coordinate plane.

Lesson Flow

The first part of this unit builds on the prerequisite skills needed to develop the concept of negative numbers, the opposites of numbers, and absolute value. The unit starts with a real-world application that uses negative numbers so that students understand the need for them. The unit then introduces the idea of the opposite of a number and its absolute value and compares the difference in the definitions. The number line and positions of numbers on the number line is at the heart of the unit, including comparing positions with less than or greater than symbols.

The second part of the unit deals with the coordinate plane and extends student knowledge to all four quadrants. Students graph geometric figures on the coordinate plane and do initial calculations of distances that are a straight line. Students conclude the unit by investigating the reflections of figures across the x- and y-axes on the coordinate plane.

Students watch a video showing the highest and lowest locations on each of the continents. Then they create a diagram (a number line) for a book titled The World’s Highest and Lowest Locations. Students show four of the highest elevations and four of the lowest elevations in the world on their diagrams.Key ConceptsA complete number line has both positive numbers (to the right of 0) and negative numbers (to the left of 0).Negative numbers are written with a minus sign—for example, –12, which is pronounced “negative 12.”Positive numbers can be written with a plus sign for emphasis, such as +12, but a number without a sign, such as 12, is always interpreted as positive.Every number except 0 is either positive or negative. The number 0 is neither positive nor negative.Goals and Learning ObjectivesCreate a number line to show elevations that are both above and below sea level.