# Kid number line: Intro to the Number Line Math Video for Kids

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## Number line addition: a quick refresher

If you have a child of kindergarten age, it won’t be long before they’re introduced to the math concept of addition.

To start with, they’ll explore how numbers can be joined together to make other numbers, with lots of hands-on practice using things like counters and blocks.

Before long, they’ll move on to other strategies and methods for adding.

One of those is adding numbers using a number line.

This post will show you how to add using a number line and give you some pointers for how to help your child too.

So without further ado, let’s get going. First of all, some basics…

What is a number line?

Well, the name pretty much says it all. It’s a line (usually horizontal) with numbers marked on at evenly spaced intervals. If your child is just starting out with math, it’s likely they’ll start with a number line up to 10, like so:

Here you can see that the numbers increase by 1 if you follow them to the right.

If you follow the numbers to the left, they decrease by 1, down to 0.

Before you get started adding numbers, it’s worth just taking time to look at the number line together with your child so they can see how it works.

Before too long your child will be both adding and subtracting on a number line, so it’s crucial they know which direction to move in for each operation.

Ask them: “As we go along the number line, what is happening to the numbers? Are they getting bigger or smaller?”.

You can also ask a few questions to get them thinking too, such as:

• What’s the smallest number on the number line?
• Whats the biggest number on the line?
• Can you point to the number 7 on the number line? (or the number 10 or 3 or whatever. .)
• Can you find your age on the number line?

When your child is familiar with the number line and what it does, it’s time to move on to adding numbers.

How to do addition using a number line

The easiest way to show you how to add on a number line is by using some examples.

Example 1

For our first example, let’s say we want to find the answer to 4 + 3.

We’ll start by finding the number 4 on the number line.

To do this, we start at the number 4, and hop along the number line 3 times to the right.

We land at the number 7, so this tells us that 4 + 3 = 7.

Important!

The important thing to note here is that you count the hops along the number line. (This is why you will often see number lines being explained with help of things like frogs, kangaroos or indeed anything that jumps – it helps children remember to count the hops along the number line when adding and subtracting). Sometimes, children will try to count the number they start on as ‘one’. Don’t! Only count the hops.

Example 2:

Let’s look at another example, say 6 + 4.

If we want to find the answer to 6 + 4, we first need to find 6 on the number line.

Then, to add 4, we will hop 4 times to the right and see where we land.

We land on the number 10 so that tells us that 6 + 4 = 10.

One thing that’s great to show your child when adding numbers is that the order of the two addends (the numbers you’re adding together) doesn’t matter. When it comes addition, the order of the numbers can be swapped around.

Let me show you:

Let’s take 5 + 4 as an example

If we start at the number 5 and hop 4 times along the number line, we reach the number 9.

This tells us that 5 + 4 = 9.

Let’s now swap the order of the addends around. This time, instead of 5 + 4, we will calculate 4 + 5.

We will start at the number 4 and hop 5 times along the number line. We still land on the number 9.

This shows us that 5 + 4 and 4 + 5 both equal 9.

The order of the 4 and 5 can be swapped around and yet the answer is still the same.

How to add three 1-digit numbers using a number line

The method is exactly the same, there is just one extra number to add.

Let’s look at an example, say 3 + 6 + 2.

For this example, we’ll be using a number line that goes up to 15.

Let’s start by finding the number 3 on the number line.

Next, we’ll add 6 by hopping along the number line to the right 6 times. This lands us at 9.

We have one more number to add: 2. Let’s hop 2 more times to the right, starting at 9.

And we land at the number 11.

So this tells us that 3 + 6 + 2 = 11.

And remember, just as before, the numbers can be added in any order.

The three numbers ( 3, 6 and 2) can be added in any order and your answer will still be 11.

### So there we have it! A quick how-to for adding numbers using a number line. I hope you found it helpful.

If you liked this post or want to save it for later, why not pin it? Thanks for your help!

More kindergarten math posts from Math, Kids and Chaos:

• What are number bonds?
• The best math games for practising early math skills
• What are ten frames?

## Hopping On the Number Line Book by Nancy Allen

Hopping On the Number Line Book by Nancy Allen | Epic

Hopping On The Number Line Represents Addition And Subtraction Using A Number Line.

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## Draw lines — lesson summary — Corporation Russian textbook (Drofa-Ventana publishing house)

Development of lessons (lesson notes)

Line of teaching materials by M. I. Bashmakov. Mathematics (1-4)

Mathematics

This lesson plan is part of the Classwork Service*

Attention! The administration of the site rosuchebnik.ru is not responsible for the content of methodological developments, as well as for the compliance of the development with the Federal State Educational Standard.

Purpose of the lesson

Acquaintance with the concepts of «straight line», «curve», «intersecting lines», «non-intersecting» and elements of research activity.

Lesson Objectives

To form ideas about straight lines and curves, intersecting and non-intersecting lines.

To form skills to recognize lines in drawings.

Strengthen the ability to draw curves and straight lines.

To contribute to the formation of the ability to use a drawing tool — a ruler.

To consolidate ideas about the number series, comparison, increase and decrease of numbers.

To develop observation, logical thinking, spatial representations of students.

Contribute to the development of mathematical speech of students.

Activities

Distinguishing between straight and curved lines in a drawing; intersecting and non-intersecting lines.

Defines the number of line intersection points.

Draw straight lines using a ruler.

Establishing a correspondence between the line image and its name.

Keywords

Straight line, curved line, intersecting lines, non-intersecting lines, ruler.

Lesson plan

No. Stage name Methodological comment
1 1. Motivation for learning activities The task is aimed at updating the concept of «straight line». Students look at the lines in the drawing and mark only the straight lines. You can suggest calling the rest of the lines — curves.
2 2. Actualization of basic knowledge The task contributes to the actualization of the concept of «curved line» and reinforces the ability to distinguish between images of straight and curved lines. Students distribute straight and curved lines into the corresponding cells of the table.
3 3. Statement of educational problem and goal-setting Work with assignment No. 1 of the textbook. Using the concepts of «straight line», «curve», «intersecting lines», «non-intersecting». Students look at a painting by Wassily Kandinsky, reminiscent of a child’s drawing. You can ask the children what they see in a color drawing (ships, waves, lightning, the moon), what state the artist wanted to convey (waves at sea), what lines he used. Then work is carried out with the concept of «intersecting lines» on the assignment. Students answer the questions on the picture on the right.
The task contributes to the formation of ideas about intersecting and non-intersecting lines. Students choose images of intersecting lines among the proposed drawings, the lines on which have or do not have intersection points. You can propose to determine the number of lines in each figure, characterize the lines (straight or curved) and name how many intersection points they have (if any).
4 4. Discovery of new knowledge Work with task No. 2 of the textbook. The task is aimed at developing the ability to determine the points through which straight lines pass, training in drawing lines along a ruler. A blue line passes through points 2 and 3, a green line passes through points 1 and 3.
Students determine how many intersecting lines are shown in the figure, and note the number of intersection points.
5 5. Primary fastening Work with task No. 3 of the textbook. When introducing the concept of “curve”, children need to be explained that a curve is a smooth line without kinks.
Students mark among the proposed images a line that is not a curve. Please note that this line has breaks, so it does not apply to curved lines.
6 6. Independent work with self-examination Students establish a correspondence between the image of lines and their names (straight lines and curves).
7 7. Summary of the lesson Students choose among the proposed drawings the option where a straight line and a curved line are shown that intersect. They must explain their choice: in one figure, a straight line and a curve do not intersect, in another, two straight lines intersect, in a third, two curved lines intersect.

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## Content-methodical lines of the course of mathematics «Learning to learn» for grades 5−6 authors G.V. Dorofeeva, L.G. Peterson

• Introductory consultation
• Didactic system of the activity method of teaching “School 2000…”
• Content-methodical lines of the mathematics course «Learning to learn» for grades 5-6
• Implementation levels of technology activity method

• Monthly consultations

### mathematics course «Learning to learn» for grades 5-6

authors G. V. Dorofeeva, L.G. Peterson

### Number line

The number line is built on the basis of counting objects (set elements) and measuring quantities. The concepts of set and magnitude lead students from different sides to the concept of a number: on the one hand, a natural number, and on the other, a positive real number. This reflects the dual nature of number, and in a deeper aspect, the dual nature of the infinite systems with which mathematics deals: discrete, countable infinity and continual infinity. The measurement of magnitudes connects natural numbers with real ones, therefore, the number line receives its further development in the transition from elementary school to the middle school as an infinitely precise process of measuring magnitudes.

In elementary school, within the numerical line, students learn the meaning of the concept of a natural number and zero, the principles of writing and comparing non-negative integers, the meaning and properties of arithmetic operations, the relationship between them, methods of oral and written calculations, estimates, evaluations and verification of the results of arithmetic operations , dependencies between their components and results, ways to find unknown components. On the other hand, they get acquainted with various quantities and the general principle of their measurement, learn to perform actions with the values ​​\u200b\u200bof quantities (named numbers).

The use of the activity method of teaching made it possible not only to preserve in full the content of the traditional elementary school mathematics curriculum, but also to enrich it, taking into account the sensitive periods of children’s development. So, in the 3rd grade, they study with interest numbering and actions with non-negative integers within 12 digits, in the 4th grade — fractions, addition and subtraction of fractions with the same denominators, mixed numbers, that is, topics that were traditionally studied in the 5th grade, but children were not interested.

In grade 5, the number line continues with the study of ordinary and decimal fractions, and in grade 6 — rational numbers. In conclusion, children’s knowledge of numbers is systematized, children get acquainted with the history of the development of the concept of number and with the method of expanding numerical sets. The problem of the insufficiency of the studied numbers for measuring quantities (for example, the length of the diagonal of a square with side 1) is posed.

The number line, having its own tasks and specifics, nevertheless, is closely intertwined with all other content-methodological lines of the course. So, when constructing algorithms for actions on numbers and studying their properties, various graphical models are used. Actively included in the educational process as an object of study and as a means of teaching such concepts as a set (at first — a «bag», a group of objects), a part and a whole, an operation and an algorithm, which then become the basis for the formation of strong computational skills and learning in children their solution of equations and word problems.

### Algebraic line

The development of the algebraic line is inextricably linked with the numerical one, in many ways complements it and provides a better understanding and assimilation of the material being studied, and also increases the level of generalization of knowledge acquired by children. Students, starting from grade 1, write down expressions and properties of numbers using alphabetic symbols, which helps them structure the material being studied, identify similarities and differences, and analogies of objects. For example, when solving equations, from the fact that A + X \u003d B it follows that X \u003d B — A (for sets), and from the fact that a + x \u003d b it follows that x \u003d b — a (for quantities). In both cases, the decision is justified by the fact that we are looking for an unknown part, so we subtract the other part from the whole.

As a rule, the recording of the general properties of operations on sets and quantities overtakes the corresponding skills of students in performing similar operations on numbers. This makes it possible to create a general framework for each of these operations, which then, as new classes of numbers are introduced, operations on numbers and the properties of these operations fit. This gives a theoretically generalized method of orientation in the doctrines of sets, magnitudes, and numbers, which then makes it possible to solve vast classes of specific problems.

In grades 5-6, students move up to the next level by learning to use letter notations to prove general statements. This allows them to carry out a logical proof of the properties and signs of divisibility, the properties of proportions, etc. Thus, high-quality preparation of children for the study of program material in algebra in grades 7–9 is ensured.

### Geometric line

When studying geometric line in elementary school, students get acquainted with such geometric shapes as a square, rectangle, triangle, circle, the simplest spatial images: cube, parallelepiped, cylinder, pyramid, ball, cone, as well as more abstract concepts point, straight and curved line, ray, segment and polyline, angle and polygon, area and border, circle and circle, etc., which are used to solve a variety of practical problems. For example, segment diagrams serve as graphical models of word problems, circles are used to build pie charts, etc.

Cutting figures into parts and composing new figures from the resulting parts, drawing figures, gluing models according to their scans develops spatial representations of children, imagination, speech, combinatorial abilities and at the same time forms practical skills in working with basic measuring and drawing tools (ruler, square, compass, protractor).

The stock of geometric ideas and skills that students have accumulated by grades 3-4 allows them to set a new, much deeper and more exciting goal: the study and discovery of the properties of geometric shapes. With the help of constructions and measurements, they reveal various geometric patterns (for example, the property of the angles of a triangle, the properties of adjacent and vertical angles, inscribed and central angles, etc.), which they formulate as an assumption, a hypothesis.

This work continues in grades 5-6: students explore and discover various properties of a triangle and a rectangle, a parallelogram and a trapezoid, a circle and a circle, etc. At the same time, not only flat, but also spatial figures are considered — a ball, a sphere, cylinder, cone, pyramid, polyhedra. This helps them, on the one hand, to discover the beauty of geometric facts, and on the other hand, to realize the need for their logical substantiation, proof, which prepares them to study the systematic course of geometry in 7–9classes. E.S. Smirnova “Geometric line in mathematics textbooks for grades 5–6 G.V. Dorofeeva, L.G. Peterson» .

### Functional line

Functional line is built around the concept of the functional dependence of quantities, which is an intermediate model between reality and the general concept of a function, and thus serves as a source of the concept of functions in the upper grades. Students observe the interconnected change of various quantities, get acquainted with the concept of a variable quantity, and by grade 4 gain significant experience in fixing dependencies between quantities using tables, diagrams, graphs (movements) and simple formulas. So, students build and use formulas for solving practical problems: area of ​​a rectangle S = a • b, volume of a rectangular parallelepiped V = a • b • c, path s = = v • t, ​​cost C = a • x, work A = w • t, etc. When studying various dependencies, children identify and fix their general properties in mathematical language, which creates the basis for building a general concept of a function in high school, understanding the expediency of its introduction and practical significance.

### Call appearance

Quite serious attention is paid in the course to the development of the logic line in the study of arithmetic, algebraic and geometric questions of the program. All tasks of the course of mathematics «Learning to learn» require students to perform logical operations (analysis, synthesis, comparison, generalization, analogy, classification), contribute to the development of cognitive processes: imagination, memory, speech, logical thinking.

In elementary school, as part of the study of the logical line, students master the mathematical language, learn to read mathematical text, use mathematical terms to describe the phenomena of the world around them. In the process of calculations, solving problems, equations, geometric constructions, they check the truth of statements, build their judgments in mathematical language and justify them based on an agreed method of action (standard). Already in the 3rd grade, students get acquainted with the language of sets, various types of statements (private, general, about existence), with complex statements with the unions “and” and “or”, gain experience in proving and refuting them.

On this basis, in grades 5-6, the logical line unfolds into a chain of interrelated questions: mathematical language — statements — proof — methods of proof — definitions — equivalent sentences — negation — logical consequence — theorem, etc. Thus, students get the opportunity to fully prepare for the study of mathematics in high school and for solving various life problems of a logical nature.

### Data analysis line

Data analysis line purposefully forms students’ information literacy, the ability to independently obtain information — from observations, reference books, encyclopedias, Internet sources, conversations; work with the information received: analyze, systematize and present in the form of diagrams, tables, abstracts, diagrams and graphs; draw conclusions; identify patterns and significant features; carry out the classification; carry out a systematic search of options; build and execute algorithms.

Already in elementary school, students get acquainted with the tree of possibilities, with different types of programs: linear, branched, cyclic. The systematic construction and use of algorithms to justify their actions and self-check the results helps to more successfully study many traditionally difficult issues of the program (for example, the order of actions in expressions, actions with multi-digit numbers, etc. ).

In grades 5–6, this work continues, and information skills are formed both in the classroom and in extracurricular project activities, circle work, when creating your own information objects: presentations, collections of tasks and examples, wall newspapers and information sheets, etc. . During this activity, students master the basics of computer literacy and computer skills necessary for schooling and modern life.

### Simulation line

Within the framework of the line of modeling (line of text problems), students master all types of mathematical activities, realize the practical significance of mathematical knowledge, they form universal learning activities, develop thinking, imagination, speech.

The knowledge acquired by children in the study of various sections of the course finds practical application in solving word problems. In elementary school, students get acquainted with the solution of simple and compound text problems on the meaning of arithmetic operations, difference and multiple comparisons (containing the relations “more by . .., in …”, “less by …, in …”), on the dependence of values ​​of the form a = bc (path, speed, time; cost, price, quantity of goods; work, productivity, work time, etc.). A feature of the course is that after systematically working out a small number of basic types of tasks, students are offered a wide range of various structures consisting of basic elements, but containing some novelty, which develops their ability to act in a non-standard situation.

The system for selecting and arranging problems creates an opportunity to compare them, identify similarities and differences, and relationships between them (mutually inverse problems, problems with the same mathematical model, etc.). Particular attention is paid to teaching independent analysis of text problems. Students identify the quantities referred to in the problem, establish relationships between them, make condition models using diagrams and tables, draw up and implement a solution plan, justifying each step. They learn to give a complete answer to the question of the problem, find various ways to solve them and choose the most rational ones, independently compose tasks according to a given model (expression, scheme, table), while using the language and tools that are accepted in high school.

The modeling line is constructed in such a way as to, on the one hand, ensure that students learn the learned methods of action in all other lines, and on the other hand, create conditions for their systematization, and on this basis reveal the role and significance of mathematics in the development of culture. This is facilitated by specially developed methods, as well as the literal notation of expressions for problems and the properties of operations on numbers, which already in elementary school make it possible to identify the commonality of text problems with outwardly different plots, but a single mathematical content. So, in the 3rd grade, students identify four types of simple tasks, the methods for solving which are well known to them: 1) a + b = c; 2) a • b = c; 3) difference comparison; 4) multiple comparison. At the same time, tasks for finding the part and the whole (1) are modeled using graphical diagrams, tasks for the relationship of quantities of the form a • b = c (2) — using tables, and tasks for difference and multiple comparison — using the rules, respectively, of difference and multiple comparison, finding a larger number by a smaller one and a difference (multiple), finding a smaller number by a larger one and a difference (multiple). And the solution of any compound problem is presented as a program of actions, each operation in which is the solution of one of these four types of simple problems well mastered by students.

Mastering the general methods of constructing a plan for solving compound problems (analytical, synthetic, analytical-synthetic) «puts things in order» in the thinking of children and thereby reduces the time for their study. In the free time, children get acquainted with new types of tasks — tasks for fractions (three types) and for the simultaneous uniform movement of two objects (four types), they form an idea of ​​\u200b\u200bpercentage, which creates a solid basis for the successful mastering of these traditionally difficult sections of the program 5 –6 classes, and in general, for mastering the general method of mathematical modeling.

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