# Second Grade Math Text Book. Basic Level

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## Math textbook for first grade. Basic Level

### Check yourself! What did you learn in first grade?

Guess what feature connects the expressions.

Increase the value of each expression in the left column by 30, and the value of the expressions in the right column by 60. Write the correct equalities.

Write down the obtained results in descending order.

Name the digits that were used to represent these numbers.

What other digits do you know? Write them down.

Using these digits, write down 6 different two-digit numbers.

Find the rule by which the table is composed, and write down the correct equalities using the same rule.

Fill in the missing numbers so that the equations are correct.

Write down all two-digit numbers in which the digit in the tens place is 4.

According to what rule are the pairs of expressions composed?

1)8-6    2) 7-2    3)9-5

80 – 60      70 – 20      90 – 50

Compose pairs of expressions with different numbers using the same rule.

Arrange the numbers in ascending order: 72, 36, 54, 8, 0, 16, 20, 38.

Arrange the numbers in descending order: 32, 45, 27, 83, 0, 9 23.

Check yourself! Which values of the expressions do you remember?

One vase has 5 carnations, and the other has 2 more.

Mark each carnation with a cell and encircle as many cells in the notebook as there are carnations in the two vases.

According to what feature can you divide the constructor details into two groups so that one group has the same number of details as the other?

> or < ?

1)    1 dm 3 cm … 12 cm 2) 55 cm … 5 dm

24 cm … 4 dm 2 cm         6 dm … 61 cm

3 cm 5 mm … 30 mm         8 mm … 2 cm

1 dm 9 cm … 18 cm          50 mm … 4 cm

Write down the expressions using the table.

 First term 70 89 95 7 48 30 99 1 Second term 4 1 3 62 20 53 0 39

Find the values of the expressions.

There are 7 birch trees and 5 maple trees in the glade.

Represent the birch trees with one line segment and the maple trees with another line segment. Draw a line segment that represents the total number of trees in the glade.

8 strawberries were collected from one bush and 6 strawberries from another bush.

Represent 8 and 6 strawberries with line segments. Show on the diagram a line segment that represents the difference between the number of strawberries collected from one bush and the other.

Fill in the missing numbers and write the correct equalities.

Write the expressions using the table.

 Minuend 27 86 73 37 96 69 50 90 Subtrahend 7 6 3 20 90 9 1 1

Find the values of the expressions.

Perform operations with quantities.

1) 2 cm 3 mm + 7 mm 2) 2 cm 6 mm + 4 mm

2 cm 3 mm + 7 cm         2 cm 6 mm + 4 cm

3) 6 cm 8 mm – 3 mm 4) 8 cm 7 mm – 6 mm

6 cm 8 mm – 3 cm         8 cm 7 mm – 6 cm

Check the result.

The notebook is cheaper than the pen, but more expensive than the pencil. Which of the given items is more expensive? Represent the price of each item with a line segment, draw a diagram, and check your answer.

Examine the picture.

What is the weight of one bag of flour?

Find the values of the expressions.

Can you find the value of the second expression in each pair using the value of the first expression?

Express each of the numbers 84, 97, 63, 56, 13 as the sum of place value addends.

Select the squares on the picture.

Vova and Dima are the same height. Dima and Yuri are also the same height. Who is taller: Yuri or Vova?

Represent the height of each boy with a line segment, draw a diagram, and check your answer.

Find the difference between the numbers: 1) 85 and 30;

2) 96 and 60; 3) 78 and 2; 4) 59 and 7.

Write down the obtained result as the sum of the place-value sums.

Perform operations with quantities.

1) 4 cm 5 mm – 5 mm    2) 9 cm – 3 mm

3 cm 8 mm + 2 mm      8 cm – 3 cm

7 cm 7 mm – 4 mm      7 cm + 4 mm

6 cm 2 mm + 8 mm      1 cm + 5 mm

3) 5 cm 3 mm + 6 mm    4) 10 mm – 7 mm

1 dm – 3 cm 6 mm       1 dm – 3 cm

1 dm + 1 cm 5 mm       1 dm – 5 mm

2 dm – 2 cm 2 mm      1 cm – 3 mm

Check the obtained results.

Draw 5 broken lines, each 1 dm long, each consisting of two links.

An apple is heavier than a peach, and a plum is lighter than a peach. Which fruit is the heaviest?

Represent the mass of each fruit with a segment, draw a diagram and check your answer.

Find the pattern (rule) in the sequence of numbers.

1) 40, 50, 30, 40, 20,…

2) 4, 5, 3, 4, 2, …

3) 21, 24, 22, 25, 23,…

4) 41, 45, 42, 46, 43,…

5) 12, 22, 24, 34, 36,…

Continue each sequence, following the same pattern.

Find the rule by which the column of expressions is composed.

Write 4 more expressions in each column using the same rule.

Find the values of all expressions.

> or < ?

The pie was cut into 9 pieces. 4 pieces were eaten.

Mark each piece as a triangle and show how many pieces of the pie are left.

The weight of the loaf of bread and the pack of sugar is greater than the weight of the candy box and the loaf of bread. Which is lighter: the pack of sugar or the box of candy?

Mark the weight of each object as a segment, draw a diagram and check your answer.

Mark the candies as circles, the gingerbread cookies as squares, and show how many candies Olya has left.

> or < ?

+ or – ?

Write 3 expressions in which the minuend is a two-digit number, the subtrahend is a one-digit number, and the difference is 52.

Name the segment on the diagram that corresponds to the expression.

Write 6 inequalities with numbers that correspond to points A, K, and M on the number line.

Select the triangles in the picture.

Find the values of the expressions.

1)    9 — 2 – 6      2) 9-5-3

90 – 20 – 60       90 – 50 – 30

3)    8-6 + 4      4) 7-5 + 6

80 – 60 + 40       70 – 50 + 60

Can the value of the second expression be written in each pair using the value of the first expression?

Fill in the missing addends so that the equations are true.

The volleyball team has 11 players, including 5 substitutes.

Segment AK represents 11 players, and segment ME represents 5 players.

Select the diagram that corresponds to the text.

Explain what each segment represents on the diagram.

Write the sum of the numbers: 1) 48 and 30; 2) 54 and 20; 3) 17 and 70 — and find the values of the expressions.

Write the difference of the numbers: 1) 89 and 60; 2) 98 and 70; 3) 98 and 7 — and find the values of the expressions.

Find the values of the expressions.

Write down the results obtained in each column in ascending order.

Identify the segment on the diagram that corresponds to the expression.

Explain what each segment represents on the diagram.

+ or – ?

Find the pattern by which the series of numbers is composed and write down 4 more numbers in it.

1)    26,  46,  36,  56,  46…

2)    22,  25,  23,  26,  24…

3)    86,  66,  76,  56,  66…

4)    81,  84,  82,  85,  83…

By how much can the number 34 be increased so that only the digit in the units place changes?

•    Write down the answer as equations.

Identify the segment on the diagram that corresponds to the expression.

Find the values of the expressions.

How are the expressions in each column similar?

By how much should a segment with a length of 1 dm be reduced to obtain a segment with a length of 1 cm?

7 people got off the trolleybus at the stop, and 3 got on.

Mark each passenger with a circle and show how many fewer people are in the trolleybus now.

Using the table, write down the expressions and find their values.

 Minuend 63 37 73 59 36 95 87 Subtrahend 40 7 70 6 4 60 50

Two squirrels have 10 nuts. One squirrel has 2 more nuts than the other.

Label each nut with a circle and show on the picture how many nuts each squirrel has.

The amount of money paid for a pack of sugar, a can of peas, and a pack of cottage cheese is greater than the amount paid for a pack of cottage cheese, a carton of milk, and a can of peas. Which is more expensive: a carton of milk or a pack of sugar?

Label the price of each item with a line segment, draw a diagram, and check your answer.

Answer the questions using the diagram.

1)    How much longer is line segment ME than line segment KO?

2)    How much shorter is line segment KO than line segment AK?

How much can the number 97 be decreased so that only the digit in the units place changes in its representation?

On which pictures will the rays never intersect?

Find the values of the expressions.

By what criterion can numbers be divided into two groups?

1)    37, 54, 8, 61, 6, 0, 45, 23

2)    80, 90, 52, 40, 82, 30, 42

Name the characteristics that change in each subsequent figure.

Choose the figures that can continue the series using the same rule.

Compare the expressions without performing calculations.

Name the extra figure.

Using the table, write down the correct equalities.

Choose the quantities that can be compared: 5 mm, 20 kg, 7 cm, 12 kg, 6 dm.

Write the inequalities.

+ or -?

54 … 5 … 2 = 57

68 … 2 … 40 … = 26

74 … 30 … 5 = 49

17 … 20 … 6 = 31

27 … 40 … 6 … = 61

By how much does each of the numbers: 9, 2, 3, 5, 6, 4, 7, – need to be increased to obtain the number 10?

Write the equations.

Read the numbers: 58, 36, 44, 57.

By how much can each number be increased so that only the units digit changes in its representation?

Choose from the numbers 97, 39, 68, 19, 86, 69 those that you will not be able to complete the previous task with.

Guess what criterion Misha divided the numbers 29, 28, 47, 79, 78, 27, 48, 26, 76 into 3 groups, and Masha – into 4 groups.

What is the largest number that needs to be added to the number 16 so that only the units digit changes in its representation?

Write the answer in the form of an equation.

What single-digit number needs to be added to each of the numbers: 47, 58, 76, 89, – in order to get a two-digit number, where the units digit is O?

Find the values of the expressions.

If you have difficulties, use models of tens and units.

Is the statement that the values of the expressions in each pair are the same correct?

Compare the expressions in the column. How are they similar? How are they different?

Can you find the values of all the expressions without using models of units and tens?

Using the figure, explain what the equations represent.

Choose the expressions that correspond to the figure and find their values.

Draw a line segment with a length of: 1) 3 cm; 2) 7 cm;

3)    8 cm.

How much should the length of each segment be increased to obtain a segment of length 1 dm?

What are the similarities and differences in the notation in each pair?

1)    3 dm 4 cm + 6 cm 2) 2 dm 8 cm + 2 cm 3 dm 4 cm + 6 dm 2 dm 8 cm + 2 dm

3)    6 dm 7 cm + 3 cm 4) 5 dm 9 cm + 1 cm 6 dm 7 cm + 3 dm 5 dm 9 cm + 1 dm

Find the sum of the lengths of the segments.

Find the difference between the lengths of the segments.

1)    1 dm – 8 cm          2) 1 dm – 3 cm

3)    1 dm – 5 cm          4) 1 dm – 7 cm

5)    1 dm – 1 cm          6) 1 dm – 2 cm

Identify the segment on the diagram that corresponds to the expression.

Write the expression that corresponds to the picture. What are the similarities in all the expressions?

Find the values of the expressions using the diagram.

Find the values of the expressions using the models of tens and units.

What are the similarities in all the expressions?

Is the statement that the values of the expressions in each pair are the same true?

Read the numbers: 27, 38, 46, 79, 30, 19, 51, 40.

How much can you decrease each number so that only the units digit changes?

Write down the numbers that you couldn’t complete this task with.

Write down 3 more two-digit numbers that you won’t be able to complete this task with.

What are the similarities in the expressions?

20 – 2      80 – 8      30-3

50 – 5      70 – 7      90-9

60-6    40-410-1

Select the expression that corresponds to the picture.

Find the values of all the expressions.

How many centimeters do you need to increase each measurement to obtain 5 dm?

1)    4 dm 4 cm 2) 4 dm 2 cm 3) 4 dm 7 cm

4 dm 8 cm      4 dm 6 cm      4 dm 9 cm

A broken line consists of three segments. The length of the first segment is 3 cm, the length of the second segment is 8 mm. Find the length of the third segment if the length of the broken line is 4 cm.

Perform operations with measurements.

1)    30 cm – 4 cm       2) 40 cm – 7 cm

3)    60 cm – 6 cm       4) 50 cm – 9 cm

5)    60 cm – 8 cm       6) 90 cm – 5 cm

7)    20 cm – 1 cm       8) 80 cm – 3 cm

Insert the missing numbers so that the equations are correct.

1) 37 + 3 = 4…          2) 32 + 8 = 4…

54 + 6 = 6…            29 + 1 – 3…

3)    56 + 4 = 6…         4) 63 + 7 = 7…

78 + 2 = 8…            45 + 5 = 5…

What are the similarities between all the equations?

Write 3 expressions in which the minuend is equal to the number 40, and the subtrahend is a single-digit number.

Find the values of the expressions.

<, >, or = ?

1)    30 cm – 3 cm … 2 dm 6 cm

2)    50 cm – 7 cm … 46 cm

3)    13 cm + 6 cm … 2 dm

4)    2 dm 6 cm + 4 cm … 3 dm

In one box there are 35 candies, in the other – 28.

Explain what each segment represents on the diagram.

Insert the missing numbers so that the equations are correct.

Insert the missing numbers so that the equations are correct.

Vova has 70 stamps, and Misha has 8 stamps more.

Which segment on the diagram represents Vova’s stamps? Which segment represents Misha’s stamps?

Name the segment that represents how many more stamps Misha has than Vova.

Construct a segment that represents the total number of stamps the boys have together.

What do the expressions in the column have in common?

Find the values of all the expressions.

> or < ?

Can you write inequalities without calculating the values of the expressions?

•    In one train car there are 28 passengers, and in another there are 6 passengers more.

Construct a segment that represents the total number of passengers in the two train cars.

•    Write five expressions in which the minuend is equal to the number 90, and the subtrahend is a single-digit number.

Find their values.

• Find the values of the expressions.

. >, < or =?

1) 9 cm … 5 dm              2) 25 cm … 4 dm

1 dm 7 cm … 18 cm       2 dm … 17 cm

8 dm … 80 cm              4 dm … 38 cm

5 dm … 52 cm              40 dm … 40 cm

70 cm … 7 dm               9 cm … 9 dm

• Create correct numerical equations using the numbers 10, 7, 19, 17, 16, 6, 9.

• Borya, Vova, and Kolya are brothers. Borya is older than Vova but younger than Kolya. Name the oldest, middle, and youngest brothers. Represent the age of each brother with a segment, draw a diagram, and check your answer.

• How are the expressions in each pair similar and different?

 1) 4 cm 5 mm + 3 cm 4 cm 5 mm + 3 mm 3) 5 cm 3 mm – 2 mm 5 cm 3 mm – 2 cm 2) 7 cm 2 mm + 2 mm 7 cm 2 mm + 2 cm 4) 6 dm 8 cm — 5 cm 6 dm 8 cm – 5 dm

Perform addition and subtraction of quantities.

Write all the results in ascending order.

Increase each quantity: 1) by 1 dm;

2) by 1 cm; 3) by 1 mm.

By how much do you need to reduce each quantity to get 2 cm?

. Borya, Kolya, and Lena took prize places in a math olympiad. Lena didn’t take first place, and Borya didn’t take first or second place. What place did each person take?

Draw the same table.

 Names Places Borya Kolya Lena 1st — — 2nd — 3rd +

Guess what is indicated in the table by the + and – signs.

• Using the picture, write down 4 equations.

• Using the numbers 7, 8, 9, write down nine two-digit numbers. (Digits in the number can be repeated.)

. Choose expressions whose values you can calculate, and write down equations.

•    Write down three sums of two single-digit numbers, whose values are equal to a two-digit number.

What equations did you get?

•    Choose expressions whose values are greater than 10.

Measure the length of segment AK.

By how much should the length of segment AK be increased to obtain a segment of length 12 cm?

• How many circles need to be added to the triangle to make 1 ten?

Complete the blue circles with red ones to make ten.

Explain what the expressions mean.

1)8 + 2 + 3         2) 8 + 5

• Which picture corresponds to each expression?

What does each number in the expressions written below the picture mean?

Find the values of the expressions in each pair.

. Write down the expression that corresponds to the picture on the number line.

Using the number line, find the values of the expressions.

How are the pictures similar and how are they different?

Find the values of the expressions.

1)6 + 5   2) 9 + 2   3)8 + 3   4) 7 + 4

•    There are 8 caramel candies and 3 chocolate candies in the New Year’s gift.

Mark each candy with a circle and show how many candies are there in total.

•    What has changed?

Write down the answer as an equation.

> On one tree there are 7 crows, and on the other tree there are 4 more crows.

Mark each bird with a triangle and show how many crows are there on the other tree.

> Compare the expressions in a pair. How are they similar? How are they different?

Find the values of all expressions.

•    The book has 98 pages. Katya has read 24 pages.

Draw a diagram that corresponds to the given text.

, Write an expression that corresponds to the picture on the number line.

What do all the expressions have in common?

Write each expression as a sum of two single-digit numbers and find its value.

. The length of the red ribbon is 65 cm, and the blue one is 15 cm longer.

Explain what each segment represents on the diagram.

. Is the statement true that the values of the expressions in the columns are the same?

•    Write the number 11 as a sum of two single-digit numbers.

# Try to remember!

• Write the sum of the lengths of each pair of segments.

•    Draw a line segment AK with a length of 1 dm 1 cm.

Choose pairs of segments, the lengths of which add up to the length of segment AK.

Create a plan for completing the task.

β Masha and Misha have 11 rubles.

Choose from the list the items they can buy with this money.

1.    Eraser 3 rubles.

2.    Bookmark 6 rubles.

3.    Pen 8 rubles.

4.    Pencil 5 rubles.

5.    Pastry 5 rubles.

6.    Ice cream 7 rubles.

7.    Ruler 4 rubles.

8.    Bun 6 rubles.

. Identify the segment on the diagram that corresponds to the expression.

. Write the equation that corresponds to the picture.

. Choose the expression that corresponds to the picture and find its value.

i Write the expression that corresponds to the picture on the number line.

What has changed?

Write the answer using two equalities.

. Choose pairs of expressions that have the same value.

. By what characteristic were the figures divided into two groups?

Choose expressions that correspond to the picture and explain what each number means in them.

•    Find the values of the expressions.

1)7 + 2       2) 8 + 3       3)9 + 2

6 + 4          6 + 3           2 + 6

Using each obtained equation, create two others applying the rule:

## If you subtract one addend from the sum, you will get the other addend.

• Using the picture, write down 4 correct equations.

•    Create valid equations using the numbers 7, 9, 6, 5, 4, 2, 11, 3.

How many equations did you get?

•    By what rule is the number sequence written?

1)    9, 8, 11, 10, 13, …

2)    9, 11, 10, 12, 11, …

Continue the sequence using the same rule.

•    Using the pictures, find the values of the expressions.

•    By what characteristic were the figures divided into two groups?

Choose expressions that correspond to the picture and explain what each number means in them.

. Choose pairs of expressions whose values are the same.

• Draw a segment AK with a length of 1 dm 2 cm. Choose pairs of segments whose lengths add up to the length of segment AK.

Describe the plan for completing the task.

. Using the picture, write down 4 equations.

What is the mass of the dog? What is the mass of the cat?

•    Write the number 12 as the sum of two single-digit numbers.

# Try to remember!

. Lena has 12 notebooks. 7 of them are squared, the rest are lined.

Explain what each segment represents in the diagram.

• Write the equation that corresponds to the drawing on the number line.

•    One box contains 12 ice cream bricks, and the other contains 8.

Explain what each segment represents in the diagram.                                 .

What is the mass of the watermelon?

Find the values of the expressions.

Using each obtained equation, create two others by applying the rules:

## If you add the subtrahend to the difference, you get the minuend.

Find the values of the expressions.

. Create correct equations using the numbers:

1)    12, 9, 3, 7, 4, 8, 11

2)    11, 5, 4, 2, 9, 7, 12

How many equations did you come up with?

. Write a series of numbers from 1 to 11.

Find the sum of the numbers connected by a line.

What do all the equations have in common?

Check if this rule holds true when writing a series of numbers: 1) from 1 to 12; 2) from 1 to 13.

. Choose the drawing that corresponds to each expression and find its value.

• Choose pairs of expressions that have the same values.

•    Write the equality that corresponds to the picture on the number line.

>, < or =?

• Insert the missing numbers to make correct equalities.

Guess what the numerical expression under the picture represents.

Find the values of these expressions.

Insert the missing numbers to make the equalities correct.

•    Write the number 13 as the sum of two single-digit numbers.

# Try to remember!

Draw a segment AK with a length of 1 dm 3 cm. Construct the difference of lengths.

Describe the plan for completing the task.

‘. Write the equalities using the table.

 First term 9 7 6 9 5 8 9 Second term 2 5 7 4 6 5 3
 Minuend 12 12 13 11 13 13 12 Subtrahend 8 3 8 6 4 7 5

Find the values of the expressions.

Construct the sum of the lengths of the segments.

Describe the plan for completing the task.

• In the garden there are 9 apple trees and 4 more pear trees. Circle each tree and show how many pear trees are in the garden.

. + or -?

<, > or =?

Guess which number is missing.

• Explain what each number means in the expression below the picture.

Using the picture, write 4 equations.

» Answer the questions without performing calculations.

1) What single-digit numbers can be added to 8 to get a number that is greater than 10?

2) What single-digit numbers can be subtracted from 13 to get a number that is less than 10?

• Using the pictures, find the values of the expressions: 8 + 6; 9 + 5; 7 + 7.

What are the similarities between the written equations?

Draw a line segment AK that is 1 decimeter and 4 centimeters long.

Choose pairs of line segments whose lengths add up to the length of line segment AK.

• Is the statement true that the values of the expressions in each pair are the same?

<, > or =?

• In the garage there are 14 cars. In the morning, 9 cars left the garage.

Circle each car and show how many cars left the garage and how many cars are left.

Using line segments, draw a diagram that corresponds to the text.

• In the bus, there were 14 schoolchildren. 4 girls and 2 boys got off at the bus stop. Circle each student and show how many fewer children there are in the bus.

• What is the weight of the watermelon? What is the weight of the melon?

. > or

1) 14 mm … 1 cm 2 mm

2) 28 cm … 2 cm 8 mm

3) 1 cm 2 mm … 10 mm

4) 54 mm … 6 cm

5) 3 dm 5 cm … 3 dm 8 mm

6) 81 mm … 8 cm

. Insert the missing numbers to make the equations correct.

•    Grandma made 9 cabbage pies and 4 fewer meat pies. Circle each pie and show how many pies Grandma made in total.

•    Write the correct equations using the numbers 12, 13, 14, 7, 5, 8, 9.

How many equations have you written?

. Insert the missing numbers to make the equations correct.

•    Write the number 14 as the sum of two single-digit numbers.

# Try to remember!

•    Create correct equations using the numbers 9, 5, 6, 7, 8, 14.

•    Choose pairs of numbers from the given series whose sum is 13 and write correct equations.

Find the values of the expressions.

•    Masha and Misha have a total of 15 candies. How many candies can Masha have and how many can Misha have?

Circle each candy and show the possible answers in the picture.

•    First, 8 train cars were detached from the train, then another 7.

Circle each car and show how many train cars were detached in total.

Choose the equations that correspond to the picture and explain what they represent.

Insert the missing numbers to make the equations correct.

Write the number 15 as the sum of two single-digit numbers.

# Try to remember!

How are the expressions similar? How are they different?

Find the values of the expressions.

How are the equations you obtained similar?

• Write the equations using the table.

 Subtrahend 15 15 15 15 15 15 Subtrahend 5 6 7 8 9 10
 First term 10 9 8 7 6 7 5 Second term 5 4 6 5 9 6 7

“Find the pattern in the sequence of numbers.”

1) 11,  8,  12,  9,  13,…

2) 13,  9,  12,  8,  11,…

3) 15,  8,  13,  6,  11,…

Write 5 more numbers following the same pattern.

“Find the values of the expressions.”

• Choose pairs of expressions that have the same values.

“From the numbers 20, 16, 14, 21, 13, 32, 15, choose those that can be written as the sum of two single-digit numbers.”

“Find the pattern in the following sequence and write 5 more numbers.”

1)    5, 9, 6, 10, 7, …

2)    9, 6, 11, 8, 13, …

3)    8, 6, 10, 8, 12, …

4)    7, 9, 6, 8, 5, …

• Choose pairs of line segments whose sum of lengths is 15 cm.

.. Misha and Masha together ate 11 cakes. Indicate each cake with a circle and show how many cakes the boy ate and how many the girl ate, if she ate 3 cakes more than Misha.

“Fill in the missing numbers to make the equations true.”

“Misha found 9 mushrooms and Masha found 2 fewer.”

Indicate each mushroom with a square and show how many mushrooms the children found.

“. The first number is 30, and the second number is 6 less. Explain what the segments AM and MK represent on the diagram, if the segment EO represents the second number.”

“Fill in the missing numbers to make the equations true.”

“. How are the pictures on the left similar? How are the pictures on the right similar?”

“Choose the expression that corresponds to each picture.”

Using the pictures, write the equations.

“. Draw a polyline with a length of 1 dm 6 cm using two line segments, so that the length of one segment is equal to: 1) 1 dm; 2) 9 cm; 3) 8 cm.”

“. Write the equations using the table.”

 Subtrahend 9 8 6 8 7 8 8 Minuend 15 14 12 13 15 11 16

• Choose the image that corresponds to the pair of expressions.

# Try to remember!

•    What single-digit numbers can be subtracted from 16 to get a number less than 10?

• Fill in the missing single-digit numbers to make the equations correct.

. The weight of a rooster is 3 kg less than the weight of a goose, and 2 kg more than the weight of a hen. Explain what segments АМ, МЕ, ЕД, АО, МК represent on the diagram, if the weight of the rooster is represented by segment АК.

Write the equations using the table.

 First addend 9 8 7 3 6 4 6 7 Second addend 5 7 4 9 6 8 8 7

. Name two-digit numbers that can be written as the sum of two identical single-digit numbers.

ORDER OF OPERATIONS IN EXPRESSIONS. BRACKETS. THE COMBINING PROPERTY OF ADDITION

. How are the expressions in each pair similar and different?

1)8-3 + 4     2) 9-6-1

8 – (3 + 4)           9 – (6 – 1)

I noticed that in each pair, the numbers and operations are the same.

And I noticed the difference. The second expression has parentheses, which the first expression doesn’t have.

Signs ( ) are called parentheses. They indicate which action should be performed before others.

1) 8 – (3 + 4)                 2) 9 – (6 – 1)

If there are no parentheses in the expression, the actions are performed in order from left to right.

1) 8 – 3 + 4        2) 9-6-1

The expression 8 – (3 + 4) is read as: “Subtract the sum of three and four from eight”.

1        2

The expression 8 – 3 + 4 is read as: “Add four to the difference between eight and three”.

• Arrange the order of operations in the expression 18 – (6 – 4) and read it.

Subtract the difference between six and four from eighteen.

Can this expression be read differently?

• Arrange the order of operations in the expression 18-6-4 and read it.

Subtract four from the difference between eighteen and six.

Subtract six from eighteen, and then subtract four.

•    Who is right: Misha or Masha?

•    Define the order of operations and read the expressions in each pair.

Calculate the values of the expressions in each pair.

In which pairs are the values of the expressions the same, and in which pairs are they different?

• Find the rule by which the columns of expressions are constructed.

Create columns using the same rule for the expressions:

1)    18 + 30 + 40

2)    40 + 8 + 50

3)    12 + 3 + 20

Calculate the values of all the expressions.

What did you notice?

## You can replace two adjacent addends with the value of their sum.

This is the distributive property of addition.

(10 + 5) + 3 = 10 + (5 + 3)

You can use the distributive property of addition when calculating the values of expressions.

. Which expression in each pair will you use to calculate the result?

• Show with parentheses which two addends you will replace with the value of their sum in order to find the value of each expression.

. Compare the texts in each pair. Which text can be called a problem and which one cannot?

Masha found 7 little foxes, and Misha found 3 more.

Masha found 7 little foxes, and Misha found 5. How many foxes did Misha and Masha find in total?

In class, there are 12 girls and the same number of boys. How many students are there in total?

How many more stamps does Petya have than Ira?

There are 3 cucumbers on one plate, and 4 on the other. How many tomatoes are there on both plates?

There are 3 cucumbers on one plate, and 4 on the other. How many cucumbers are there on both plates?

There are 9 mushrooms in one basket, and 3 mushrooms less in the other. How many mushrooms are there in both baskets?

There are 9 mushrooms in one basket. How many mushrooms are there in both baskets?

## The problem consists of a condition and a question, which are connected in meaning.

• Think about what arithmetic operations need to be performed to answer the question of each problem.

In class, there are 10 girls and 20 boys. How many students are there in total?

Petya has 12 stamps, and Ira has 9. How many more stamps does Petya have than Ira?

In the first problem, you need to combine the girls and boys together and perform addition of the numbers 10 and 20.

In the second problem, you need to subtract the number of stamps that Ira has from the number of stamps that Petya has, and perform subtraction of the numbers 12 and 9.

The solution of the problems can be presented as follows:

Problem 1.

10 + 20 = 30 (students) Answer: 30 students.

Problem 2.

12 – 9 = 3 (stamps) Answer: 3 stamps.

• Compare the texts of the problems. How are they similar? How are they different?

There are 7 apple trees near the house and 3 cherry trees. How many fruit trees are there near the house?

There are 7 apple trees, 3 cherry trees, and 2 birch trees near the house. How many fruit trees are there near the house? Is it true that the solutions of these problems are the same?

Choose questions that you can answer using the conditions of both problems.

1) How many more apple trees are there than cherry trees? 2) How many trees are there near the house in total?

3) How many fir trees are there near the house?

• How are the texts of the problems similar? How are they different?

There are 7 chamomiles and violets in the bouquet. How many flowers are there in the bouquet?

There are 7 chamomiles and 6 violets in the bouquet. How many flowers are there in the bouquet?

There are 7 chamomiles and the same number of violets in the bouquet. How many flowers are there in the bouquet?

Which problem can you solve? Which one can’t you solve? Why?

Which questions can you answer by performing the operation: 7-6 = 1 (flowers)?

What does the number 6 represent in this equation?

• Can these texts be called problems and can their solutions be written?

1) How many paws do two dogs have?

2) How many wheels do two cars have?

3) How many tails do five dogs have?

4) How many legs do three chickens have?

5)    How many wheels do two bicycles have?

6)    How many humps do four camels have?

, Compare the texts of the problems. How are they similar? How are they different?

A freight train has 36 cars. The first and second cars were detached at the station. How many cars are left in the train? A freight train has 36 cars. The thirty-sixth and thirty-fifth cars were detached at the station. How many cars are left in the train?

Misha wrote the solution to both problems like this:

1)    1 + 1 = 2 (c.)

2)    36 – 2 – 34 (c.) Answer: 34 cars.

Write the solution to the problem.

A freight train has 38 cars. 3 cars were detached from it at the station. How many cars are left in the train?

. Using the numbers 3, 2, 4, 5, write different two-digit numbers without repeating the same digit in the number. Check your answer by filling in the table.

 unit tens 3 2 4 5 3 2 4 42 5 55

. Compare the texts of the problems. How are they similar? How are they different?

Misha made 15 flags, and Kolya made 5 flags less. How many flags did Kolya make?

Misha made 15 flags, and Kolya made 5 flags more. How many flags did Kolya make?

Write the solution to each problem

. Check yourself! Write down only the values of the expressions that you remember.

•    Compare the texts of the problems. How are they similar? How are they different?

10 buckets of water were taken from a barrel. How many buckets of water are left in the barrel?

There are 40 buckets of water in the barrel. How many buckets of water are left in the barrel?

Complete the condition of each problem and answer its question.

. > or <?

1) 87 … 78       2) 63 … 36       3) 17 … 71

54 … 45          24 … 42         98 … 89

Masha and Katya were shooting with a bow. Who won after three attempts?

Can you answer the question of the problem without performing arithmetic operations?

Formulate questions to the given condition that require you to perform arithmetic operations to answer them.

Kolya has 38 stamps. Misha has 8 stamps less. How many more stamps does Kolya have than Misha?

Do you need to perform an arithmetic operation to answer the problem?

Create questions based on the given information that you can answer by performing arithmetic operations.

What question did Masha ask if she wrote the solution to the problem as follows:

Problem.

38-8-30 (stamps)

What question did Misha ask if he wrote the solution to the problem as follows:

Problem.

1)    38 – 8 = 30 (stamps)

2)    38 + 30 – 68 (stamps) Answer: 68 stamps.

Write the solution to the problem.

Kolya has 30 stamps. Misha has 2 more stamps. How many stamps do Kolya and Misha have together?

, Figure out the rule used to select the 3 numbers.

Fill in the missing numbers using the same rule and write the correct equations.

Write the equations using the table.

. Compare the problem texts. How are they similar? How are they different?

9 families moved out of one old house into new houses, and 4 families moved out of another. How many families decreased the population of the old houses?

9 families moved out of one old house into new houses, and 4 families moved out of another. How many families in total moved to the new houses?

Write the solution to each problem.

“Choose pairs of numbers that add up to 38 and write the correct equations.”

34,    40, 20, 5, 18, 32, 35, 4, 7, 6.

• Anton’s step length is longer than Petya’s, but shorter than Vova’s. Whose step length is shorter: Petya’s or Vova’s?

Can this text be considered a problem?

Yes, it can. It has a condition and a question related to the condition. But you don’t need to perform arithmetic operations to answer the question in the problem.

Select the diagram that corresponds to the condition and answer the question in the problem.

. Based on what criteria can the expressions be divided into two groups?

54+6   37+3   69+1   62+6

78+2   26+2   34+5   75+5

Find the value of each expression.

. What do the expressions in the column have in common?

•    By what characteristic can the expressions be divided into two groups?

Find the value of each expression.

In the box there are 4 more pencils than in the pencil case. How many fewer pencils are in the pencil case than in the box? How many pencils are in the box?

Which question of the problem can be answered without performing arithmetic operations? Which question cannot be answered? Why?

•    Write equalities using the table.

 First addend 74 83 67 41 56 32 Second addend 5 6 2 8 3 7

What do the obtained equalities have in common?