What math do 2nd graders learn: Second Grade Math Online Lesson Plans

Second Grade Math Online Lesson Plans

View Our Lesson Demos

Time4Learning understands how important the choice of a second grade math curriculum is for families. Not only is second grade a time to review the foundational skills learned in first grade math, but it is a launchpad for multiplication and for understanding how numbers are used in everyday life.

The major math strands for second grade curriculum are number sense and operations, algebra, geometry and spatial sense, measurement, and data analysis and probability. Time4Learning teaches a comprehensive second grade math curriculum using fun, activities to build a solid math foundation.

What Math Should a Second Grader Know?

By the time they have finished first grade, students have begun to understand the relationships between numbers and have started to recognize mathematical patterns. Second graders become adept at one and two-digit addition and subtraction and have learned a variety of methods for solving mathematical problems.

Some of the key math concepts a second grader should know include:

• Read and write numerals to 100 and to count objects to 100 or more
• Addition and subtraction of two-digit numbers without regrouping, up to 100, using models and algorithms
• Explore number patterns on a hundred chart and with a calculator
• Combine shapes to form others shapes and find geometric shapes in real-life situations
• Learn and compare money values including the quarter (25 cents), half-dollar (50 cents), and dollar (100 cents)

The ideal math curriculum for second grade will continue to build on these skills and expand on to new ones while making learning fun and motivating them to continue to learn.

Second Grade Math Objectives

In second grade, students continue with more sophisticated approaches to addition and subtraction and begin understanding the patterns leading to multiplication. Simple fractions are also introduced this year. Geometric learning extends a student’s understanding of shapes and their parts.

Some of the key goals for second grade math include:

• Understanding the meaning, uses, and representations for numbers
• Computing addition and subtraction facts accurately
• Analyzing and interpreting data
• Using appropriate techniques, tools, units, and formulas in making measurements
• Investigating the properties and characteristics of two and three dimensional geometric shapes

Time4Learning’s Second Grade Math Scope & Sequence

Chapter 1: “Number Sense”

Lesson 1: Hundreds, Tens, & Ones –

3 Activities

Count and group objects into hundreds, tens, and ones. Identify a given number in expanded form. Identify the value of a given digit within a number up to the hundredths place.

Lesson 2: Write Numbers –

2 Activities

Read and write number words up to ninety-nine and match them to numerals.

Lesson 3: Compare Numbers –

7 Activities

Compare and order numbers using symbols such as <, =, and >. When given any number up to 1,000, identify one more than, one less than, 10 more than, 10 less than, 100 more than, and 100 less than.

Lesson 4: Ordinal Numbers –

2 Activities

Read and understand ordinal numbers 1st – 100th. Identify ordinal number words first – tenth by name.

Lesson 5: Equivalent Forms of Numbers –

2 Activities

Using diagrams, pictorial representations, and numerical expressions, represent equivalent forms of various numbers up to 1000.

Lesson 6: Skip Counting –

2 Activities

Count up to 1000 by fives, tens, twenty-fives, fifties, and hundreds using mental math and pictorial representations.

Lesson 7: Zero as a Placeholder –

2 Activities

Use zero as a placeholder and identify 10 tens as 100, 10 hundreds as 1000.

Lesson 8: Number Line and Rounding –

3 Activities

Locate numbers up to 1000 on a number line. Use a number line to round numbers to the nearest 10.

Lesson 9: Odd and Even Numbers –

4 Activities

Identify odd and even numbers.

Lesson 10: Sums and Differences: Even or Odd? –

2 Activities

Locate numbers up to 1000 on a number line. Use a number line to round numbers to the nearest 10.

Chapter Test: Number Sense

Chapter 2: “Fractions”

Lesson 1: Equal Parts of a Whole –

2 Activities

Identify, model, and record fractions that represent more than one equal part of a whole.

Lesson 2: Equal Parts of a Group –

2 Activities

Identify, model, and record equal parts of groups.

Lesson 3: More About Fractions –

3 Activities

Identify words for fractional parts such as halves, thirds, quarters, and eighths and fractions representing 1 whole.

Chapter Test: Fractions

Chapter 3: “Operations”

Lesson 1: Fact Families –

2 Activities

Solve addition and subtraction facts up to 18 by using inverse operations. Describe the related facts that make up a fact family.

Lesson 2: Grouping Property –

2 Activities

Use the Associative Property of Addition to solve addition problems involving three addends.

Lesson 3: Two-digit Addition –

2 Activities

Solve addition problems involving two-digit numbers with regrouping.

Lesson 4: Adding Whole Numbers –

5 Activities

Add single- and two-digit whole numbers.

Lesson 5: Two-digit Subtraction –

2 Activities

Solve subtraction problems involving two-digit numbers with regrouping.

Lesson 6: Subtracting Whole Numbers –

6 Activities

Subtract single-digit numbers from single and two-digit numbers and two-digit numbers from two-digit numbers.

Lesson 7: Multiplication –

6 Activities

Identify multiplication as repeated addition. Multiply two one-digit numbers by 2, 3, and 5 using an array.

Lesson 8: Division –

2 Activities

Explain division as equal parts of a set. Divide a number up to 30 by 2, 3, or 5 using pictorial representations.

Lesson 9: Estimate Sums & Differences –

2 Activities

Estimate reasonable answers to addition and subtraction problems with sums to 100.

Chapter Test: Operations

Chapter 4: “Money”

Lesson 1: Identify Money –

3 Activities

Identify pennies, nickels, dimes, quarters, and half-dollars and their values. Count pennies, nickels, dimes, and quarters up to 50¢.

Lesson 2: Count Mixed Coins –

3 Activities

Count mixed collection of coins.

Lesson 3: Model Money Amounts –

3 Activities

Model the same amount in more than one way. Model an amount using the fewest coins.

Lesson 4: Add and Subtract Money –

3 Activities

Solve addition and subtraction problems involving money, with and without regrouping.

Chapter Test: Money

Chapter 5: “Patterns”

Lesson 1: Sort Objects –

3 Activities

Sort objects by attributes of shape, size, or color. Recognize and explain how patterns are made (e.g. repetition, transformation, or other changes to attribute).

Lesson 2: Venn Diagrams –

2 Activities

Sort objects using Venn diagram with one intersection.

Lesson 3: Pattern Rules –

2 Activities

Describe a given pattern and explain the pattern rule.

Lesson 4: Build Patterns –

2 Activities

Predict, extend, and create patterns that are pictorial or symbolic. Transfer patterns from one medium to another (e.g., change red, red, blue, green, red to 1,1,2,3,1).

Lesson 5: Compare Patterns –

2 Activities

Compare repeating and growing patterns and analyze how they are generated.

Lesson 6: Real World Patterns –

2 Activities

Identify patterns in the real world such as repeating, tessellating, and patchwork.

Lesson 7: Patterns on a Hundreds Chart –

2 Activities

Identify number patterns on a hundred chart.

Lesson 8: Number Patterns –

3 Activities

Predict and extend a linear pattern.

Chapter Test: Patterns

Chapter 6: “Algebra”

Lesson 1: Order Property –

2 Activities

Use the Commutative Property of Addition to solve problems. Check the sum by changing the addends. Solve two-digit equations with one unknown.

Lesson 2: Equalities and Inequalities –

2 Activities

Use pictorial representations and numbers to explore equalities and inequalities.

Lesson 3: Greater Than and Less Than –

2 Activities

Solve number sentences with equalities and inequalities using the symbols <, =, >.

Lesson 4: Two-digit Problems –

2 Activities

Using models, pictures, and algorithms, solve problems involving the addition and subtraction of two-digit numbers with and without regrouping.

Lesson 5: Real World Equations –

2 Activities

Solve real-world addition and subtraction equations with one unknown.

Lesson 6: Balance Equations –

2 Activities

Create models that explore the concept of an equation being balanced.

Chapter Test: Algebra

Chapter 7: “Geometry”

Lesson 1: Plane Shapes –

4 Activities

Describe and create plane shapes such as squares, rectangles, triangles, hexagons, trapezoid, and parallelograms.

Lesson 2: Solid Shapes –

4 Activities

Describe and create solids shapes such as cubes, rectangular prisms, spheres, cylinders, cones, and pyramids.

Lesson 3: Classify Shapes –

2 Activities

Describe, classify, and sort two- and three-dimensional shapes according to their attributes (sides, corners, faces, curves). Explain which attribute is being used for classification.

Lesson 4: Faces of Solids –

2 Activities

Identify plane shapes as faces of solid shapes.

Lesson 5: Similar and Congruent –

2 Activities

Identify similar and congruent two-dimensional objects.

Lesson 6: Parallel and Perpendicular –

2 Activities

Identify lines as parallel or perpendicular.

Lesson 7: Horizontal and Vertical Lines –

2 Activities

Identify lines as horizontal or vertical.

Chapter Test: Geometry

Chapter 8: “Positions”

Lesson 1: Position Words –

2 Activities

Identify, locate, and move objects according to positional words such as to the left, above, and behind.

Lesson 2: Directional Words –

2 Activities

Identify the location of objects according to two directions such as upper-right, upper-left, lower-right, and lower-left.

Lesson 3: Using a Map –

2 Activities

Locate objects on the first quadrant of a coordinate grid.

Lesson 4: Plot Numbers on Number Line –

2 Activities

Locate, plot, and identify known and unknown numbers on a number line from 0 to 50 by twos and from 1 to 100 by fives.

Chapter Test: Positions

Chapter 9: “Using Shapes”

Lesson 1: Slides, Flips, and Turns –

2 Activities

Identify and demonstrate slides, flips, and turns using pictures.

Lesson 2: Congruent Figures –

2 Activities

Recognize congruent figures under slides, flips, or turns.

Lesson 3: Reflections –

2 Activities

Match, predict, and identify the reflection of a two-dimensional shape.

Lesson 4: Line Symmetry –

2 Activities

Identify and create figures with line symmetry.

Lesson 5: Types of Line Symmetry –

2 Activities

Identify and create vertical and horizontal lines of symmetry.

Chapter Test: Using Shapes

Chapter 10: “Spatial Sense”

Lesson 1: Make Plane Shapes –

2 Activities

Separate or combine plane shapes to create new plane shapes.

Lesson 2: Perimeter and Area –

2 Activities

Explore perimeter and area of two-dimensional shapes.

Lesson 3: Find the Area –

6 Activities

Identify area as the number of squares it takes to cover a plane object.

Chapter Test: Spatial Sense

Chapter 11: “Time”

Lesson 1: Time to the Hour and Half-hour –

3 Activities

Tell time to the hour and half hour on analog and digital clocks.

Lesson 2: Time to Nearest Quarter-hour –

2 Activities

Tell time to the nearest quarter hour using digital and analog clocks by counting time in five-minute intervals.

Lesson 3: AM, PM, and Elapsed Time –

3 Activities

Describe time as A.M. or P.M., identify noon and midnight, and solve simple problems of elapsed time.

Lesson 4: Units of Time –

2 Activities

Identify relationships of time, such as seconds in a minute, minutes in an hour, days in a week, and months in a year.

Lesson 5: Months and Measuring Time –

3 Activities

Identify names of the months in order and their lengths and identify appropriate tools for measuring time.

Chapter Test: Time

Chapter 12: “Length”

Lesson 1: Measure with Non-standard Unit –

2 Activities

Measure and compare lengths using nonstandard units and describe lengths in terms of shorter and longer.

Lesson 2: Measure with Customary Units –

5 Activities

Recognize the need for a standard unit of measure and measure and estimate length to the nearest inch, foot, and yard.

Lesson 3: Tools and Units –

2 Activities

Estimate, compare, and measure distance in feet or miles and choose appropriate unit of measurement for various distances.

Lesson 4: Perimeter –

2 Activities

Explore perimeter of squares and rectangles by adding lengths of sides.

Lesson 5: Measure with Metric Units –

5 Activities

Recognize that the metric system is another system of measurement and measure length to the nearest centimeter or meter.

Chapter Test: Length

Chapter 13: “Weight”

Lesson 1: Sort by Weight –

2 Activities

Sort and classify objects according to their weight and describe objects in term of lighter, heavier, less than, and more than.

Lesson 2: Measure with Non-standard Unit –

2 Activities

Measure and compare weights using nonstandard units and recognize the need for a standard unit of measurement.

Lesson 3: Measure with Customary Units –

2 Activities

Estimate and measure weights in ounces, pounds, and tons and choose the most reasonable measurement of a specific item.

Lesson 4: Measure with Metric Units –

2 Activities

Recognize that the metric system is another system of measurement and measure weights to the nearest gram or kilogram.

Chapter Test: Weight

Chapter 14: “Capacity”

Lesson 1: Sort & Classify by Capacity –

2 Activities

Sort and classify containers according to their capacity. Describe capacity in terms of emptier, fuller, less than, and more than.

Lesson 2: Measure with Customary Units –

2 Activities

Measure and estimate capacity to the nearest cup, pint, quart, and gallon.

Lesson 3: Tools and Units –

2 Activities

Choose appropriate tool for measuring capacity.

Lesson 4: Measure with Metric Units –

2 Activities

Recognize that the metric system is another system of measurement. Measure capacity to using liters and milliliters.

Chapter Test: Capacity

Chapter 15: “Temperature

Lesson 1: Seasons and Temperatures –

2 Activities

Describe temperature of the seasons in terms of cool, cold, warm, and hot.

Lesson 2: Compare Fahrenheit & Celsius –

2 Activities

Compare Fahrenheit and Celsius thermometers.

Lesson 3: Measure Temperatures –

2 Activities

Read a Fahrenheit and Celsius thermometers to tell temperature to the nearest two degrees. Relate reasonable temperatures to the seasons.

Chapter Test: Temperature

Chapter 16: “Graphing”

Lesson 1: Tally Tables –

2 Activities

Create and interpret tally tables.

Lesson 2: Organize Data into Groups –

2 Activities

Collect, organize, and record data into 3 or more categories.

Lesson 3: Organize Data into Graphs –

2 Activities

Organizes data into simple graphs such as pictographs and bar graphs.

Lesson 4: Transfer Data to Graphs –

2 Activities

Transfer data from a chart of two or three categories to a bar or picture graph.

Chapter Test: Graphing

Chapter 17: “Using Data”

Lesson 1: Compare Data –

2 Activities

Identify and interpret information such as range, mode, and median from a graph or chart.

Lesson 2: Make Predictions –

2 Activities

Interpret data to make predictions about events or situations.

Chapter Test: Using Data

Chapter 18: “Probability”

Lesson 1: Certain and Impossible –

2 Activities

Identify whether an event is certain, possible, or impossible.

Lesson 2: Most Likely and Least Likely –

2 Activities

Identify the likelihood of a mathematical event as less likely, likely, or more likely to occur.

Lesson 3: Predictions Based on Data –

2 Activities

Make predictions based on data from activities of chance such as coin flips and spinners.

Chapter Test: Probability

Why Choose Time4Learning Second Grade Math Homeschool Curriculum

Time4Learning’s award-winning program is flexible and easy to use as a second grade core homeschool curriculum or for supplemental enrichment. Our program offers families an affordable and engaging way to help students gain the core mathematics skills they need in second grade, and prepare them for third grade math.

Math Skills for 2nd Grade, What Your Child Will Learn

• Math Tips
• Education
• 2nd

In second grade math, children begin to work with larger numbers and develop a stronger understanding of place value. Students also learn everyday skills like telling time, working with money, and measuring. 

We parents can help our children succeed in second grade math by finding out more about what they’re going to learn. Over the year, your child will learn how to: 

1. Count within 1,000 

Second graders learn to read and write numbers to 1,000. They practice skip counting by 5s, 10s, and 100s as they notice patterns among numbers. 

At home: Create opportunities for reading and writing three-digit numbers. For example, have your child read the numbers on nutritional labels.
You can also ask your child to verbally skip count by 10s or 100s. Begin by starting at 10 or 100, then challenge your second grader to skip count on from other numbers, such as 60 or 204. 

2.  Understand place value in three-digit numbers

As kids learn to count within 1,000, they’ll be looking at three-digit numbers more closely. By looking at patterns in numbers, kids start to understand place value.

At home: Help your child by asking how many ones, tens and hundreds are in three-digit numbers. 

3. Compare three-digit numbers

After learning about place value and counting within 1,000, second graders will be able to compare three-digit numbers. They will be able to use their knowledge of place value to look at two numbers and tell which one is more or less than the other. Kids will learn how to use the symbols <,>, and = to compare three-digit numbers. 

At home: Help your child practice comparison skills by asking questions like “Which is bigger: 943 or 783?” Push your child’s thinking by asking why one number is bigger than another.

4. Add and subtract within 1,000

In second grade, kids get used to adding and subtracting numbers within 100. They solve one-step and two-step word problems, such as “Timmy had 39 toy cars. He got 12 more, then gave 18 away. How many cars does Timmy have left?”

After working to add and subtract within 100, kids will use their knowledge of three-digit numbers to practice adding and subtracting within 1,000. 

At home: make up some word problems like the one above, using your child’s favorite toys or foods.

5. Measurement

Second graders develop their understanding of measurement by estimating lengths and measuring using different units. They compare lengths, similar to the comparison work they do with numbers, and use addition and subtraction to find out how much longer or shorter objects are. 

At home: Give your child a ruler and ask them to measure three different objects in the house. Then have your child put the objects in order from shortest to longest and explain how much longer or shorter each object is than the other ones.  

6. Telling time to the nearest five minutes

In first grade, students were introduced to telling time. Now second graders are able to extend their understanding to tell time to the nearest five minutes. Kids will also be able to tell the difference between AM and PM. 

At home, have your child practice telling time to the nearest five minutes – remind them to use AM and PM!

7. Word problems involving money

Second graders will solve lots of word problems involving addition and subtraction, including money problems. 

At home: Give your child a pile of coins and the job to count the total value. Or play “store” and have your child practice buying objects for different amounts of money, then figuring out how many cents are left. 

8. Picture and bar graphs

In second grade, your child will learn to use picture and bar graphs with up to four categories.

Challenge your child to take surveys at home and represent the data that is collected on a graph.  

Have a wonderful time digging into second grade math! 

Found this useful? Check out our grade by grade math guides from Kindergarten to 5th grade

Written by Lily Jones, Lily Jones loves all things learning. She has been a kindergarten & first grade teacher, instructional coach, curriculum developer, and teacher trainer. She loves to look at the world with curiosity and inspire people of all ages to love learning. She lives in California with her husband, two kids, and a little dog. 

About Komodo – Komodo is a fun and effective way to boost K-5 math skills. Designed for 5 to 11-year-olds to use in the home, Komodo uses a little and often approach to learning math (15 minutes, three to five times per week) that fits into the busy family routine. Komodo helps users develop fluency and confidence in math – without keeping them at the screen for long.

Find out more about Komodo and how it helps thousands of children each year do better at maths – you can even try Komodo for free.  

Back to School – 5 Tips to Help you Ease Back into the Routine

Here are some steps you can take to ease children back from full vacation mode so that the first week of school doesn’t knock you sideways.

Mindset – The Path to Mastery

People who have a growth mindset believe that they always have the potential to learn and improve. They are more motivated to persevere with difficult tasks, to take risks and to learn from failure.

Mathematics Grade 2 – what topics should a child learn?

After the child goes to school, parents have many new experiences: was he well prepared for learning, will he be able to find a common language with teachers and classmates, will he succeed in school? In particular, mom and dad really want the kid to study well and be able to master the entire school curriculum by the end of the year. If the first grade is essentially a consolidation of the skills of the preparatory class, then the second year of school is new topics and subjects, therefore, more efforts need to be made both in writing, reading, and in mathematics.

The main task of a second-grader is to master the multiplication table by the end of the year or be fully prepared for its study. To do this, the student must master addition and subtraction, be able to count with the transition through a dozen within a hundred. Indeed, before moving on to a new level – multiplication, it is necessary to learn the commutative, associative and distributive laws of mathematics. Many schools allow children to gradually and independently study them during the summer holidays, when they move from second grade to third.

Mathematics second grade – main topics

What topics are covered in mathematics in the second grade? Basically, the guys study geometric shapes and their properties, solve simple problems, study units of measurement, get acquainted with the basic laws of mathematics, learn to add and subtract units and tens, try to apply mental counting techniques in life.

Of course, the final stage of the second class is the multiplication table. To be ready for its study, the child needs to consolidate the material already covered well. If the multiplication table was set for the summer, then there is an opportunity to go through all the topics again during the holidays in free mode.

Well-prepared students who have successfully completed the first grade are easier to bear the burden of the second grade, because they already have a certain base. Therefore, do not neglect the preparation of your son or daughter for school even before he went to study.

Multiplication and division

A well-learned multiplication table is a very important skill that is necessary in order to successfully master mathematics, and later algebra and geometry. After all, the program of middle and high school is based, among other things, on the ability to multiply and divide. If you do not learn multiplication in the second grade, then the backlog like a snowball will only increase. It is very important to explain to the child that the key to understanding mathematics is to consistently and efficiently master all the topics that flow one into another.

Parents should help their child learn the multiplication table and bring the process of tabular multiplication and division to automaticity. It will be useful to learn about some tricks of this process. There are four stages, each of which must be completed successfully to consolidate this skill:

• The child must understand the principle and sequence of actions. There is a memorization of terms and concepts.
• The student memorizes the algorithm of actions in order to try to independently perform calculations.
• Gaining experience in using a skill. This is an important stage during which you should not rush.
• The final stage, during which the multiplication table is gradually brought to automatism with increasing speed.

Mathematics simulator Grade 2 – learning in the game

Despite the fact that the second grader is no longer a small child, but a schoolboy, he is also attracted by interesting activities in the form of games. It is important to make learning, including memorizing the multiplication table, exciting and unusual. The AMAKids Intelligence Development Academy offers students to use the convenient Amamatika platform, where they will find 12 games for tabular multiplication and division, as well as 10 useful games for extra-table. Thanks to these activities, children will be able to easily master this topic. Over time, the skill of tabular multiplication will be brought to automaticity, and the child will accurately understand his actions during calculations. Also, the counting speed will be very high.

Mathematics simulator for the second grade will help not only to learn and consolidate the skill of tabular multiplication, but will also allow developing attention, perseverance, logic and other important abilities of students. In addition, the platform offers other mathematical directions.

Selecting a 2nd grade math program

After finishing the second grade, it is very important to consolidate the acquired skills. A great assistant in this will be a mathematical simulator. Amamatika will allow you to repeat the material covered, as well as increase the level of knowledge.

The platform offers a separate multiplication table program where students can bring multiplication and division to automatism. You can work out each topic separately, using interdisciplinary connections. After fixing the multiplication table, you should move on to solving problems and examples using an already developed skill. Studying on the Amamatika course will allow children to study with pleasure and interest.

How to captivate a child with mathematics. Advises Ludmila Peterson

Mathematics “according to Peterson” is widely known not only in Russia. In December 2018, Lyudmila Georgievna’s textbook for elementary and basic schools successfully passed all the necessary examinations and, at the numerous requests of teachers and parents, returned to the federal list again. At the beginning of the school year, we asked her to tell us how to help a child with mathematics, how to get adults interested in it, and why it is important for children to feel their success.

How to get a child interested in mathematics if teaching at school is mediocre?

First, let’s make a reservation that “mediocre teaching” is a very conditional term. All parents and teachers have a different idea of ​​what it should be. But in general, I understand what you mean: let’s say a child comes from school with dull eyes, and at the very word “mathematics” he develops a persistent disgust.

Let’s try to understand why children cannot be torn away, for example, from computers, in contrast to the study of mathematics. What attracts them so much in computer games? It seems to me that several factors are at work:

• they are not forced to play;
• do not scold in case of failure;
• children understand the goal (to score a goal, overcome an obstacle), it is significant for them, and they achieve it themselves;
• they are interested in content, design;
• achievements are necessarily recorded (points, levels), which feeds the feeling of victory;
• the results of the game are significant for peers, and thus the child’s need for recognition is satisfied.

This set of factors sufficiently provides the mechanism of motivation “necessary” – “want” – “can”. To interest a child in mathematics, you can act by analogy.

Ludmila Peterson

1. The main thing is not to force, but to inspire

The desire to engage in any business arises only in an atmosphere of mutual respect, trust and goodwill. Without close relationships with children, parents can do little to help them other than buying food, clothes, and stationery.

It is very important to understand what exactly makes a child unwilling to study. This requires a calm, nonjudgmental conversation. The child must be sure that you are asking him not to evaluate or give instruction, but to help him cope with what is not working yet.

Give him a chance to talk. Think together about the reasons why math has become an unloved subject. It is always easier to attribute everything to “mediocre teaching” or to something else external that does not require work on oneself. But this will not help solve the problem, rather the opposite. To inspire a child to work on himself, you need to sincerely believe in him and not get tired of repeating that he will succeed.

2. Do not scold your child for mistakes and poor grades

This does not mean remaining indifferent to its results. On the contrary, an adequate reaction of parents to failure is empathy and complicity: “Let’s figure out what has not worked out so far.” It is not notation that helps to move forward, but awareness of one’s problems.

Each child develops at an individual pace, so it is not the result that matters, but the dynamics relative to oneself.

Any effort is already a small victory. A job well done is one more step. It turned out that it didn’t work before – the next

It is very important to notice and fix any forward movement, even the smallest one. Then the child will feel that he is not accused, his parents are on the same side with him, they are his friends and support.

3. Help to achieve the goal

The child’s awareness of what is not yet achieved will help lead him to a new goal. In studies, it is always to find out what he “does not know” yet, to learn what he “does not know” yet. That is why it is so important to understand what specifically causes difficulties. Let me give you an example of an introductory dialogue. Suppose he says that he understands nothing about mathematics.

— Nothing at all? Let’s look through the textbook, notebook.

— Are you able to do such tasks? What about those?

When examining a textbook together with a child, you need to show the simplest tasks first, then the more difficult ones. And so on until the really incomprehensible comes across. Next, we need to think together how to carry out such tasks.

— Excellent! You figured out what you need to learn (goal). Now let’s think about how this can be done?

It is important to let the child speak out, to listen to his options, to suggest the possibilities that he did not name. There may be many of them. For example, approach a teacher, ask a friend or older sister, figure it out from a textbook on your own or with you.

The main thing is to outline an action plan and bring it to a successful result. Let the child believe in himself, be sure to pay attention to what happened: “That’s cool, but you said you don’t know how!”

4. Maintain interest

Of course, it is useful to involve a child of any age and any level of training in solving game and non-standard tasks. It’s always better to start small. Throw up a problem that he will definitely cope with, and then another one, more difficult.

Now on the Internet you can find a huge number of interesting tasks of any complexity, not limited, of course, only to our textbook. For example, the wonderful books by Y. Perelman “Entertaining Mathematics”, “Funny Problems”, “Quick Counting”, “Live Mathematics”; B. Kordemsky “Mathematical ingenuity”; A. Kalinina, E. Katz, A. Tilipman “Mathematics is in your hands”, cartoon problems from TED and many others.

Don’t rush, don’t chuckle if he gives a wrong answer. Admire his achievements: “Wow, but I didn’t guess! Great!”

If a child’s eyes light up when he talks about a problem that he could solve, then he is ready to set higher goals – first participation, and then victory in various mathematical Olympiads. Now, in addition to the All-Russian Olympiad for schoolchildren, there are many, full-time and online. The main thing is to make sure that interest does not disappear, and that the level and pace are feasible for him.

5. Notice and fix the situation of success

A child will always strive only for what he succeeds. We all, like water for life, need a situation of success. The teacher Vasily Sukhomlinsky wrote: “The child draws moral strength to overcome his weaknesses in his successes.”

At the same time, success is not directly related to grades. For example, you can get an A for writing off work. There is nothing to rejoice. And you can, with effort, reach the top three – this is a real victory! Her formula: “difficulty – effort in overcoming it – success. ” The greater the effort, the happier the victory.

Adults often praise a child only for grades. It seems to me that it is much more important to observe his efforts, dynamics, achievement of goals and share the joy of victories with him.

6. Make victories meaningful family events

The need for recognition and respect from others is one of the basic needs of any person. Recognition gives rise to self-confidence, the desire to achieve a result that is significant for others.

That is why the family’s attention to success is so important. Tell your grandparents about your child’s victories. Remember and rejoice during a family dinner or on a walk. By doing this, you will not only support the desire to do mathematics, but also help your child develop self-respect.

These simple rules are just some model that does no harm to follow. Of course, it is important that mathematics be interesting to the parent himself: the more useful it will be, the more he is passionate about it. After all, you can hardly be carried away by something that you yourself are not interested in.

What should adults do who did not like mathematics at school, but now they understand that they missed something important? Where to begin?

Now there are more and more such adults. Recently, I came across a book by Nelly Litvak, professor of mathematics at the University of Twente in Holland, in collaboration with Alla Kechedzhan, “Mathematics for Hopeless Humanities”, which was born as a response to this request from adults. The authors, having learned how many readers the book has, created a Facebook group for them called “Mathematics – Great and Terrible”. Now it has tens of thousands of members and is constantly growing.

Nelly Litvak and Alla Kechedzhan’s book “Mathematics for Hopeless Humanities” was published by AST in 2019

This is just one example, but many other excellent books can be recommended. For example, “The Great Novel about Mathematics. The history of the world through the prism of mathematics” Mikael Lone. This book is part of the “Pleasure of Science” series and helps to understand how interesting and exciting mathematics is. The author tells about the history of this science from antiquity to the present day and about what it will become in tens, hundreds of years.

Mikael Lone’s book “The Great Romance of Mathematics. The history of the world through the prism of mathematics” was published by the publishing house “Bombora” in 2017

There are also many fascinating videos and films of various genres that inspire the study of mathematics. For example, the videos “We and Math”, “Nature in Numbers”, the films “The Great Secret of Mathematics”, “Proof”, “Good Will Hunting”, “Sensual Math”, “X + Y”, “Professor’s Favorite Equation”, ” The Man Who Knew Infinity”, “Secret Sign”, “Sofya Kovalevskaya”, “Twenty One”, “The Big Short Game”, “Stephen Hawking’s Universe”, “Infinity”, “Agora”, “Pi”, “Math and the Devil ”,“ I.Q. ”,“ Mind Games ”.

There are many lectures and comprehensive math courses for adults on the Internet, including free ones. In a couple of hours, everyone can build their own trajectory of mathematical development. The best scenario is to study it together with children, discover new mathematical concepts and formulas with them, solve interesting problems, joke and enjoy success. And the main thing is to communicate with them and do a common thing, for which parents often do not have enough time today and what children need so much.

In 2019year, your benefits returned to the federal list of textbooks. What has changed for you since that moment and what are your plans for the new academic year?

The return of the textbooks to the FPU, no doubt, removed the gigantic problem that prevented the work of thousands of schools and kindergartens. Not only because teachers can use textbooks again without any problems. The main thing is that justice has been restored in relation to brilliant teachers who have prepared more than one generation of successful and talented children over the years.

As always, we have a lot of plans. For all teachers working on our continuous mathematics course “Learning to Learn”, there will be free monthly online consultations for all classes.

Methodological webinar by Lyudmila Peterson

In September, we are planning to launch the Smart Solver project. This is an online educational platform where children and parents can not only find ready-made solutions to the tasks of our course, but also independently understand the causes of difficulties associated with solving certain problems.

We continue the work of the Federal Innovation Platform and the All-Russian Research Project, which today brings together more than four thousand leaders in their regions. This year, the All-Russian project became international. Within these platforms, we develop and test new directions for solving problems that concern everyone today: how to systematically and effectively form the ability to learn, how to measure and evaluate meta-subject results of education, how to transfer schools with so-called low learning outcomes for children, the system of Olympiad training in mathematics from 1st to 9thth class. We are looking for answers to these and other questions: we create educational programs and technologies, test them in schools and kindergartens.

Lyudmila Peterson with participants at the IMS Quality Mark “Learning to Learn” award ceremony in 2018 th class, one of our young projects. We help each child find their own answer to the question “Why should I learn math?”.

Each student in our “Children’s Academy” undergoes a comprehensive monitoring of aptitudes, according to the results of which our specialists, together with the child himself and his parents, draw up an individual route of his education. Classes at the “Children’s Academy” are more like exciting quests, where everyone can move at their own pace along the chosen route.

Children work in groups of different ages – they play, experiment, build mathematical models, solve design problems in teams. For each group, the lesson is assembled with the help of a special “constructor” that takes into account the age, interests, and characteristics of the children of this group. Thus, we implement the ideas of personalized learning (including within the framework of online education).

Lyudmila Peterson with participants at the IMC Quality Mark “Learning to Learn” award ceremony in 2018

Last time you said that education should result not only in knowledge, but also in the development of certain qualities in children. Can we say that modern education is moving in this direction?

Yes, this is the key question. From his decision, in my opinion, the competitiveness of the school in the future will depend. More and more parents are waiting for their children to be interested in learning, so that their faith in their own strengths grows, experience of personal and collective victories accumulates, so that they are ready for self-development and consciously choose their path – along with the acquisition of new knowledge. All this is achieved by the meta-subject results of education, the skills of the 21st century.

This requires new teaching methods. However, in practice, educators often prefer to simply explain topics to children. The reason is clear. Any structure, achieving efficiency, focuses on the result for which it reports. In our case, these are mainly administrative tests, the average score of the VPR, the OGE and the Unified State Examination. These results are achieved to some extent by habitual training.

Why should teachers change something? After all, explaining the material to children is much easier than leading them to discover it on their own

A real transition to a new school requires new measures of educational outcomes. Now many people are engaged in this area, including us, both in theoretical research and applied development within the framework of the over-subject course “The World of Activity”.

Already today there are different options for criteria and monitoring of meta-subject skills, but so far they are all in the testing stage. There is still a lot of work ahead to refine and improve them.

How significant is the USE in this sense? Or is it just about knowledge?

The exam, like any exam, of course, is not only about knowledge, but also about diligence, responsibility, the ability to build a strategy for one’s preparation, cope with excitement, focus and much more. However, the final result of the USE, from my point of view, does not provide sufficient information about the quality of education.

What was the initial level of the child and what is the dynamics of his growth? What can he do on his own – without tutors and mentors? Does he know how to work in a team? What are his interests and hobbies? How stress-resistant is he if something goes wrong? What are his goals and plans and how does he set and describe them?

The answers to these and many other questions, it seems to me, are no less important for evaluating the results than the score received on the USE. Moreover, it is these questions that will primarily be of interest to future employers of our graduates.

Therefore, it is obvious to me that the USE will change and be supplemented over time in order to meet the requirements of our life.

You have been doing mathematics for many years, and you don’t seem to get bored at all. Tell us why it might be of interest to everyone?

The most precise definition of mathematics was given, in my opinion, by the great Henri Poincaré: “Mathematics is the art of calling different things by the same name.” This definition combines the essence of the mathematical language – a generalized description of the patterns of the surrounding world – and the magic and beauty that mathematical laws carry. Albert Einstein was always surprised and admired by how easily and clearly mathematics describes the Universe.

Let’s take a simple series of numbers: 1, 1, 2, 3, 5, 8, 13, 21, 34, 55… In it, each number, starting from the third, is equal to the sum of the previous two. This sequence was built by Leonardo Fibonacci over seven centuries ago. And it turned out that it is these numbers that, as a rule, express the number of petals on flowers. How can it be?

But that’s not all. The sequence of Fibonacci numbers can be visually depicted using a spiral. We will unexpectedly find this form in nature on completely unrelated objects: snail spirals, Galaxy spirals, spirals on a cut of a head of cabbage, in a sunflower inflorescence, whirlwinds and cyclones have the same form.

Fibonacci sequence

Why is that? Why is the ratio of numbers in the golden ratio, which simultaneously describes the proportions of the human body, and the arrangement of leaves on the stem of a flower, and the rules of harmony in painting, architecture, design, which are already more than 4000 years old, all this is directly related to the ratio of neighboring numbers of the Fibonacci series? Is it really possible not to be surprised?

For me, the beauty of mathematics is associated primarily with the depth and universality of its laws

If, for example, we randomly select 1000 people and plot their distribution by height, then we get a Gaussian curve, where the top point of the graph will correspond to the average height in the group. The more people in the sample, the more aesthetically perfect the line will be. The famous English scientist Francis Galton said: “If the ancient Greeks knew the Gaussian law of normal distribution, they would have deified it.”

Mathematics is a living, developing science. Today, of course, it does not describe all the phenomena of the world, and this means that amazing mathematical discoveries await us ahead. We want children to master this science as part of culture, so the main task is to help them see mathematics in its development, to feel the beauty and depth of its laws.

To do this, it is important to create an environment in which children can make discoveries for themselves – face the unknown, experience inspiration, put forward their ideas, experience victories and failures, be surprised and admire the logic of mathematics and the beauty of mathematical laws. We see our task in creating pedagogical tools for this – technologies, methods, new content of mathematical education.