Silviase/jgov_v1.4_full_ann huggingface dataset:
mathematical activities:

a. Activities to find situations in everyday life where integers are used.

b. Activities to find properties and rules of the multiplication by constructing and observing multiplication tables.

c. Activities to estimate the length and volume of objects in everyday life and measure them by using units.

d. Activities to draw and make squares, rectangles, and right triangles and tessellate them on a plane.

e. Activities to express and explain the mutual relationships between addition and subtraction by using figures, diagrams and algebraic expressions.

[Terms and Symbols]

unit, straight line, right angle, vertex, side, face, ×, >, <

3. Handling the Content

(1) As for the content (1) in “A. Numbers and Calculations,” the number 10,000 should be dealt with.

(2) As for the content (2) in "A. Numbers and Calculations," and (1) in "D. Mathematical Relations," symbols such as ( ) and □ can be used when necessary.

(3) As for the content (2)-c in "A. Numbers and Calculations," commutative law and associative law should be dealt with.

(4) As for the content (3)-b in "A. Numbers and Calculations," the way in which the product increases when the multiplier increases by 1 and commutative law should be dealt with.

## [Grade 3]

### 1. Objectives

(1) To help pupils use addition and subtraction appropriately, to help them deepen their understanding of multiplication and use the calculation appropriately. To help them understand the meaning of division, explore ways of the calculation, and use the calculation. Furthermore, to help them understand the meaning and the representations of decimal numbers and fractions.

(2) To help pupils understand the units and measurements of length, weight and time.
(3) To help pupils understand geometrical figures such as isosceles triangles and equilateral triangles by paying attention to the elements that compose the geometrical figures.

(4) To help pupils represent numbers and quantities as well as their relations by using words, numbers, algebraic expressions, figures, diagrams, tables, and graphs, and interpret such representations.

### 2. Content

A. Numbers and Calculations

(1) To help pupils deepen their understanding of the representations of integers, and extend their ability to use the numbers.

a. To get to know the unit of ten-thousands (man in Japanese).

b. To get to know numbers that are 10 or 100 times as many or 1/10 of another number, and the representations of the numbers.

c. To deepen their understanding of relative size of numbers.

(2) To help pupils add and subtract accurately, and extend their ability to use the calculations appropriately.

a. To explore ways of addition and subtraction of 3- and 4-digit numbers and to understand that those calculations are based on basic calculations of 2-digit numbers and so on. To understand the way of calculations using algorithms in column forms.

b. To add and subtract accurately, and to use the calculations appropriately.

c. To explore properties of addition and subtraction and to make use of the properties in order to explore ways to calculate or check the results.

(3) To help pupils deepen their understanding of multiplication, multiply accurately, and extend their ability to use the calculation appropriately.

a. To explore ways of multiplication of 2- or 3-digit numbers and 1- or 2-digit numbers and understand that those calculations are based on basic multiplication of 1-digit numbers. To understand the way of calculation using algorithms in column forms.

b. To multiply accurately, and to use the calculation appropriately.

To explore properties of multiplication and to make use of the properties in order to explore ways to calculate or check the results.
(4) To help pupils understand the meaning of division, and use the calculation.

a. To get to know situations where division is used. Also, to get to know remainders.

b. To understand the relationships between division and multiplication and between division and subtraction.

c. To divide accurately when both the divisors and the quotients are 1-digit numbers.

d. To explore ways of division in simple cases when the divisors are 1-digit numbers and the quotients are 2-digit numbers.

(5) To help pupils understand the meaning and the representations of decimal numbers.

a. To use decimal numbers in expressing size of fractional part. To get to know the representations of decimal numbers to the tenth place.

b. To understand the meaning of addition and subtraction of decimal numbers through the tenths place. To explore ways of the calculations and do the calculations through the tenths place.

(6) To help pupils understand the meaning and the representations of fractions.

a. To use fractions in expressing size of fractional parts or quantities obtained as a result of equal partitioning. To get to know the representations of fractions.

b. To get know that a fraction can be represented as a collection of unit fractions.

c. To understand the meaning of addition and subtraction of fractions in simple cases, and to explore ways of the calculations.

(7) To help pupils get to know the representations of numbers on soroban (Japanese abacus) and do simple addition and subtraction by using soroban.

a. To get to know the representations of numbers on soroban.

b. To get to know ways of addition and subtraction.

### B. Quantities and Measurements

(1) To help pupils deepen their understanding of length, and to help them understand the meaning of units and measurements of weight, and measure the weight.
a. To get to know the unit of length (kilometer [km]).

b. To get to know the units of weight (gram [g] and kilogram [kg]).

(2) To help pupils estimate length and weight and measure them by selecting appropriate units and instruments according to their purposes.

(3) To help pupils understand time.

a. To get to know seconds.

b. To determine clock time and elapsed time which are necessary in their daily lives.

C. Geometrical Figures

(1) Through activities such as observing and composing geometrical figures, to help pupils pay attention to the elements that compose geometrical figures and understand geometrical figures.

a. To get to know isosceles triangles and equilateral triangles.

b. To get to know angles.

c. To get to know circles and spheres. Also, to get to know the center, radius and diameter of such figures.

D. Mathematical Relations

(1) To help pupils represent situations where divisions are used, by using algebraic expressions, and interpret these expressions.

(2) To help pupils understand algebraic expressions that represent the relationships between numbers/quantities and use these expressions.

a. To represent the relationships between numbers/quantities in algebraic expressions, and to make connections between algebraic expressions and diagrams.

b. To represent numbers and quantities by using □, to represent the relationships between numbers/quantities in algebraic expressions, and to explore the expressions by substituting numbers for the □.

(3) To help pupils organize and classify data, and represent them clearly by using tables and graphs, and interpret these representations.

a. To get to know how to interpret and draw bar graphs.

[Mathematical Activities]

(1) The content listed in “A. Numbers and Calculations,” “B. Quantities and Measurements,” “C. Geometrical Figures” and “D. Mathematical Relations” should be taught through, for example, the following mathematical activities:
a. Activities to explore and explain the meaning and ways of calculating integers, decimal numbers and fractions by using concrete objects, words, numbers, algebraic expressions, figures and diagrams.

b. Activities to express decimal numbers and fractions by using concrete objects, figures, diagrams and number lines and to compare sizes.

c. Activities to investigate the relationships among the units within each quantity such as length, volume, and weight.

d. Activities to construct isosceles triangles and equilateral triangles using a ruler and a pair of compasses.

e. Activities to organize data from perspectives, such as dates, locations, and to represent the data in tables.

[Terms and Symbols]

sign of equality, sign of inequality, decimal point, tenth place, number line, denominator, numerator, ÷

3. Handling the Content

(1) As for the content (1) in “A. Numbers and Calculations,” the number 100 million should be dealt with.

(2) As for the content (2) and (3) in “A. Numbers and Calculations,” consideration should be given to enable pupils to do simple mental calculations.

(3) As for the content (2)-c in “A. Numbers and Calculations,” commutative law and associative law should be dealt with.

(4) As for the content (3) in “A. Numbers and Calculations,” the calculations in cases where either the multiplier or the multiplicand is 0 should be dealt with.

(5) As for the content (3)-c in “A. Numbers and Calculations,” commutative law, associative law and distributive law should be dealt with.

(6) As for the content (5) and (6) in “A. Numbers and Calculations,” the decimal numbers 0.1 and the fraction 1/10 and so on should be dealt with by using number lines with each other.

(7) As for the content (1)-b in “B. Quantities and Measurements,” the unit of “ton”[t] should be touched upon.

## [Grade 4]

1. Objectives
(1) To help pupils deepen their understanding of division and use the calculation appropriately. To help them deepen their understanding of the meaning and the representations of decimal numbers and fractions, understand the meaning of addition and subtraction of decimal numbers and fractions, explore ways of addition and subtraction, and use them. Moreover, to help them understand round numbers and use them according to their purposes.

(2) To help pupils understand the units and measurements of area, determine the area of geometrical figures, and understand the unit and measurements of angle.

(3) To help pupils understand plane figures, such as parallelograms and rhombuses, and solid figures, such as rectangular parallelepiped, by paying attention to the elements that compose the geometric figures and the relationships of those elements.

(4) To help pupils represent numbers and quantities as well as their relations by using words, numbers, algebraic expressions, figures, diagrams, tables, and graphs, and investigate such representations.

### 2. Content

A. Numbers and Calculations

(1) To help pupils deepen their understanding that integers are represented by the decimal positional numeration system.

a. To understand units such as hundred million (oku in Japanese) and trillion (cho in Japanese), and to summarize the decimal positional numeration system.

(2) To help pupils understand round numbers and use them according to their purposes.

a. To get to know cases where the use of round numbers is appropriate.

b. To get to know the rounding to the nearest integer.

c. To estimate the results of four rules of calculation according to one's purpose.

(3) To help pupils deepen their understanding of division of integers, divide accurately, and extend their ability to use the calculation appropriately.

a. To explore ways of division in the cases where the divisor is a 1-digit or 2-digit number and the dividend is a 2-digit or 3-digit
number, and to understand that these calculations are based on the basic calculations. Also, to understand the way of calculation using algorithms in column forms.

b. To divide accurately, and to use the calculation appropriately.

c. To investigate the relationships between dividend, divisor, quotient and remainder and to put them in the following formula:

$$ \left(dividend\right)=\left(divisor\right)\times\left(quotient\right)+\left(remainder\right) $$

d. To explore properties of division and to make use of the properties in order to explore ways to calculate or check the results.

(4) To help pupils consolidate the ability to calculate integers and extend their ability to use the calculations.

(5) To help pupils deepen their understanding of decimal numbers as well as their understanding of addition and subtraction of decimal numbers, and to help them understand the meaning of multiplication and division in decimal numbers, and use the calculations.

a. To get to know the fact that decimal numbers are represented in the same manner as integers, and to deepen their understanding of the relative size of numbers.

b. To explore ways of addition and subtraction of decimal numbers and to do the calculations.

c. To explore ways of multiplication and division of decimal numbers in cases where multipliers and divisors are integers, and to do the calculations.

(6) To help pupils deepen their understanding of fractions, and to help them understand the meaning of addition and subtraction of fractions with the same denominators, and use the calculations.

a. To pay attention to the fact that there are fractions that are the same in size in simple cases.

b. To explore ways of addition and subtraction of fractions with the same denominators, and to do the calculations.

(7) To help pupils add and subtract using soroban (Japanese abacus).

B. Quantities and Measurements

(1) To help pupils understand the meaning of units and measurements of area, and determine the area by calculation.

a. To get to know the units of area (square centimeter $ [cm^{2}] $ , square meter $ [m^{2}] $ , square kilometer $ [km^{2}] $ ).
b. To explore ways to determine the area of squares and rectangles.

(2) To help pupils understand the meaning of unit and measurements of angle, and measure angles.

a. To regard the size of an angle as the amount of turn.

b. To get to know the unit of angle measurement (degree [°]).

C. Geometrical Figures

(1) Through activities such as observing and composing geometrical figures, to help pupils pay attention to the elements that compose geometrical figures as well as their positional relationships, and deepen their understanding of geometrical figures.

a. To understand the relationships such as parallelism and perpendicularity of straight lines.

b. To get to know parallelograms, rhombuses and trapezoids.

(2) Through activities such as observing and composing geometrical figures, to help pupils understand solid geometrical figures.

a. To get to know cubes and rectangular parallelepiped.

b. To understand such relationships as parallelism and perpendicularity of straight lines and planes in connection with rectangular parallelepiped.

(3) To help pupils understand how to represent the position of an object.

D. Mathematical Relations

(1) To help pupils represent and explore the relationships between two numbers/quantities as they vary simultaneously.

a. To represent how the numbers/quantities vary on a broken-line graph and to interpret the features of their variation.

(2) To help pupils understand the algebraic expressions that represent the relationships between numbers/quantities, and use these expressions.

a. To understand algebraic expressions that contain some of the four basic operations and parentheses (), and to calculate them accurately.

b. To understand the idea of formulas and to use them.

c. To represent numbers and quantities by using □ and △, to represent the relationships between numbers/quantities in algebraic expressions, and to explore the expressions by substituting numbers for the □ and △.
(3) To help pupils deepen their understanding of the properties of the four basic operations.

a. To summarize the properties of commutative, associative, and distributive laws.

(4) To help pupils gather and organize data according to their purposes, and represent them clearly by using tables and graphs, and explore features of data.

a. To explore features of the data by organizing the data from two viewpoints.

b. To get to know how to interpret and draw broken-line graphs.

[Mathematical Activities]

(1) The content listed in “A. Numbers and Calculations,” “B. Quantities and Measurements,” “C. Geometrical Figures” and “D. Mathematical Relations” should be taught through, for example, the following mathematical activities:

a. Activities to estimate the result of calculations according to one's purpose, and to make proper decisions about the way of the calculations and the results.

b. Activities to explore and explain ways to determine the area of geometrical figures composed of rectangles by using concrete objects, words, numbers, algebraic expressions, figures and diagrams.

c. Activities to actually measure the area of objects found in everyday life.

d. Activities to investigate features of geometric figures, such as parallelograms, rhombuses and trapezoids, by tesselating them on a plane.

e. Activities to find two quantities in everyday life that vary in proportion to each other, and to represent and investigate the relationships of numbers/quantities in tables and graphs.

[Terms and Symbols]

sum, difference, product, quotient, more than or equal, less than or equal, less than, proper fraction, improper fraction, mixed fraction, parallel, perpendicular, diagonal line, plane

3. Handling the Content

(1) As for the content (1) in "A. Numbers and Calculations," cases when
large numbers are expressed by splitting them into 3-digit groups should be touched upon.

(2) As for the content (2)-c, (3) and (4) in “A. Numbers and Calculations,” consideration should be given to enable pupils to do simple mental calculations. Also, consideration should be given to enable pupils to make use of mental calculation when doing the calculation using algorithms in column forms and doing estimation.

(3) As for the content (4)-d in “A. Numbers and Calculations,” it should be dealt with that the quotient remains unchanged when the dividend and the divisor are multiplied or divided by the same number.

(4) As for the content (5)-c in “A. Numbers and Calculations,” the case where a quotient of two integers is expressed as a decimal numbers should be included.

(5) As for the content (1)-a in “B. Quantities and Measurements,” units“are”[a] and “hectare”[ha] should be touched upon.

(6) As for the content (2)-a in “C. Geometrical Figures,” drawing sketches and nets should be dealt with.

(7) As for the content (4)-a in “D. Mathematical Relations,” the examination of data without omissions and duplications should be dealt with.

## [Grade 5]

### 1. Objectives

(1) To help pupils deepen their understanding of properties of integers. To help them deepen their understanding of the meaning of multiplication and division of decimal numbers as well as the meaning of addition and subtraction of fractions, explore ways of the calculation, and use the calculations.

(2) To help pupils determine the area of geometrical figures such as triangles and parallelograms and the volume of solid figures such as rectangular parallelepiped. To help them understand the average of measured value and the ratio of two quantities of different types.

(3) To help pupils deepen their understanding of plane figures, and to help them understand solid figures such as prisms.

(4) To help pupils investigate relationships between numbers/quantities. To help them investigate the features of data by using percentages and pie graphs.
### 2. Content

A. Numbers and Calculations

(1) To help pupils deepen their understanding of the properties of integers.

a. To understand that, if a viewpoint is fixed, integers are classified into some subsets such as even numbers and odd numbers.

b. To get to know divisors and multiples.

(2) To help pupils deepen their understanding of integers and decimal numbers based on the concept of the numeration system, and to use the understanding efficiently in calculation and so on.

a. To make numbers that are 10 or 100 times as much/many, or 1/10 or 1/100 of another number, and to investigate their relationships.

(3) To help pupils deepen their understanding of the meaning of multiplication and division in decimal numbers, and use the calculations.

a. Based on the understanding of calculations in cases when the multiplier and the divisor are integers, to understand the meaning of multiplication and division in cases where the multiplier and the divisor are decimal numbers.

b. To explore ways of multiplication and division of decimal numbers and to do the calculations. Also, to understand the meaning of the size of the remainder.

c. To understand that the same relationships and rules can be applied to the multiplication and division of decimal numbers as in the case of integers.

(4) To help pupils deepen their understanding of fractions, understand the meaning of addition and subtraction of fractions with different denominators, and to use the calculations.

a. To represent integers and decimals as fractions and to transform fractions into decimals.

b. To understand that the results of division of integers can always be represented as a number when using fractions.

c. To understand that a fraction obtained by multiplying or dividing the numerator and denominator of an existing fraction by the same number, has the same size as the existing fraction.

d. To explore equivalence and size of fractions and summarize the
comparison of sizes.

e. To explore ways of addition and subtraction of fractions with different denominators, and to do the calculations.

f. To understand the meaning of multiplication and division of fractions when multipliers and divisors are integers, explore ways of the calculations, and to do the calculations.

B. Quantities and Measurements

(1) To help pupils determine the area of geometrical figures by calculation.

a. To explore ways to determine the area of triangles, parallelograms, rhombuses, and trapezoids.

(2) To help pupils understand the meaning of units and measurements of volume, and determine the volume by calculation.

a. To get to know the units of volume (cubic centimeter $ [cm^{3}] $ , cubic meter $ [cm^{3}] $ ).

b. To explore ways to determine the volume of cubes and rectangular parallelepiped.

(3) To help pupils understand the measured value of quantities.

a. To get to know the average of measured value.

(4) To help pupils understand how to represent and compare quantities that are obtained as a ratio of two quantities of different types.

a. To get to know size of per-unit quantities.

### C. Geometrical Figures

(1) Through activities such as observing and composing geometrical figures, to help pupils deepen their understanding of plane geometrical figures.

a. To get to know polygons and regular polygons.

b. To understand congruence of geometrical figures.

c. To investigate and compose geometrical figures by finding the properties of geometrical figures.

d. To understand the ratio of the circumference of a circle to its diameter.

(2) Through activities such as observing and composing geometrical figures, to help pupils understand solid geometrical figures.

a. To get to know prisms and cylinders.

D. Mathematical Relations