Lesson 5. divisibility by 4,8,11 and 12AlpheZarriz
This document discusses divisibility rules for numbers 4, 8, 11, and 12. It provides examples for each rule: a number is divisible by 4 if the last two digits are divisible by 4; a number is divisible by 8 if the last three digits are divisible by 8; a number is divisible by 12 if it is divisible by both 3 and 4; and a number is divisible by 11 if the sum of alternating digits subtracted from each other is divisible by 11. The document concludes by restating the rules and thanking the reader.
This document discusses direct and inverse proportions.
Direct proportion means that as one quantity increases, the other increases by the same ratio. They form a straight line graph passing through the origin.
Inverse proportion means that as one quantity increases, the other decreases. The quantities are inversely related by a constant factor. Their relationship forms a curved line graph.
Examples of direct and inverse proportions are provided along with their equation representations and graphs. Key features of these graphs are highlighted.
Multiplication is used to find the total number of items when they are organized into equal groups. It involves determining the number of groups and the number of items in each group. Some examples provided are calculating the total number of stars when arranged in groups of two, finding the number of sodas needed when purchased in packs of six, and counting flowers, balloons, and tires organized into arrays. Multiplication allows for efficiently calculating totals when items are grouped equally.
This document provides examples and instructions for multiplying mixed decimals. It explains that when multiplying a mixed decimal by a whole number or another mixed decimal, you multiply as usual but pay attention to the number of decimal places in the factors and product. The product should have the same number of decimal places as the total number of decimal places in the factors. Several word problems involving rates and distances are solved as examples using multiplication of mixed decimals.
This document discusses subtracting similar fractions. It states that to subtract similar fractions, you subtract the numerators and copy the denominator, reducing the fraction to its lowest terms if possible. It provides examples of subtracting fractions like 5/8 - 1/8 = 1/2 and 9/15 - 3/15 = 2/5, along with exercises to subtract fractions and reduce the results to their lowest forms.
This document contains notes and instructions for dividing decimals. It includes:
1. A review of vocabulary terms like quotient, dividend and divisor.
2. Steps for dividing decimals that include placing the decimal point in the quotient directly above the decimal point in the dividend and dividing as with whole numbers.
3. Examples of dividing decimals with answers and worked out steps shown.
The document discusses using a number line to subtract whole numbers. It explains that a number line can be used to subtract either by counting back, which involves subtracting the numbers in stages moving from the larger to the smaller number, or by counting on, which involves adding the numbers in stages moving from the smaller to the larger number. It provides examples of using counting back and counting on to solve 16 - 7. It also discusses subtracting larger numbers by either working with the tens place value first then the ones, or vice versa.
Lesson 5. divisibility by 4,8,11 and 12AlpheZarriz
This document discusses divisibility rules for numbers 4, 8, 11, and 12. It provides examples for each rule: a number is divisible by 4 if the last two digits are divisible by 4; a number is divisible by 8 if the last three digits are divisible by 8; a number is divisible by 12 if it is divisible by both 3 and 4; and a number is divisible by 11 if the sum of alternating digits subtracted from each other is divisible by 11. The document concludes by restating the rules and thanking the reader.
This document discusses direct and inverse proportions.
Direct proportion means that as one quantity increases, the other increases by the same ratio. They form a straight line graph passing through the origin.
Inverse proportion means that as one quantity increases, the other decreases. The quantities are inversely related by a constant factor. Their relationship forms a curved line graph.
Examples of direct and inverse proportions are provided along with their equation representations and graphs. Key features of these graphs are highlighted.
Multiplication is used to find the total number of items when they are organized into equal groups. It involves determining the number of groups and the number of items in each group. Some examples provided are calculating the total number of stars when arranged in groups of two, finding the number of sodas needed when purchased in packs of six, and counting flowers, balloons, and tires organized into arrays. Multiplication allows for efficiently calculating totals when items are grouped equally.
This document provides examples and instructions for multiplying mixed decimals. It explains that when multiplying a mixed decimal by a whole number or another mixed decimal, you multiply as usual but pay attention to the number of decimal places in the factors and product. The product should have the same number of decimal places as the total number of decimal places in the factors. Several word problems involving rates and distances are solved as examples using multiplication of mixed decimals.
This document discusses subtracting similar fractions. It states that to subtract similar fractions, you subtract the numerators and copy the denominator, reducing the fraction to its lowest terms if possible. It provides examples of subtracting fractions like 5/8 - 1/8 = 1/2 and 9/15 - 3/15 = 2/5, along with exercises to subtract fractions and reduce the results to their lowest forms.
This document contains notes and instructions for dividing decimals. It includes:
1. A review of vocabulary terms like quotient, dividend and divisor.
2. Steps for dividing decimals that include placing the decimal point in the quotient directly above the decimal point in the dividend and dividing as with whole numbers.
3. Examples of dividing decimals with answers and worked out steps shown.
The document discusses using a number line to subtract whole numbers. It explains that a number line can be used to subtract either by counting back, which involves subtracting the numbers in stages moving from the larger to the smaller number, or by counting on, which involves adding the numbers in stages moving from the smaller to the larger number. It provides examples of using counting back and counting on to solve 16 - 7. It also discusses subtracting larger numbers by either working with the tens place value first then the ones, or vice versa.
The document discusses ratios and proportions. It defines ratios as a comparison of two quantities that can be written as fractions using a colon or fraction form. It provides examples of setting up and solving ratios and proportions. Key points covered include: writing ratios in lowest terms, setting up cross multiplication to solve proportions, and using variables like n as unknowns to solve for in proportions.
This document provides an overview of the Singapore Math bar modeling strategy for addition, subtraction, multiplication, and division word problems. It explains how to use part-whole and comparison models to represent word problem situations visually with bars. It also provides an example of using these models to solve a multi-step word problem from a 5th grade Singapore textbook, demonstrating how to set up and solve the problem using the bar model representations.
This document contains materials for a mathematics lesson on ratios and proportions. It includes examples of writing ratios using fractions and colons, forming proportions, and finding missing terms in proportions. Activities guide students to form ratios, write proportions, solve word problems involving ratios, and evaluate their understanding through questions and applications using visual representations. Cooperative learning strategies and using various tools like charts and presentations are suggested for instruction.
Adding Dissimilar Fraction with and without regroupingAlpheZarriz
This document discusses how to add dissimilar fractions with and without regrouping. It provides examples of adding fractions without regrouping by finding the lowest common denominator and then adding the numerators. For fractions requiring regrouping, it explains finding the lowest common denominator to write equivalent fractions, adding the numerators, and copying the common denominator. Mixed numbers are added by first changing the fractions to equivalent fractions with the same denominator, then adding the whole numbers and fractions separately before simplifying the final answer.
Multiplying 3-digit numbers by 2-digit numbers gemmajoaquin
This document provides a lesson on multiplying 3-digit numbers by 2-digit numbers. It begins with a review of multiplication and then demonstrates multiplying without and with regrouping using short methods and lattice methods. Examples and exercises are provided for students to practice. Key skills learned are multiplying 3-digit and 2-digit numbers in various ways including short and lattice methods.
The document provides instructions on how to create and use factor trees to factorize numbers. It explains that a factor tree involves repeatedly dividing a number by prime factors until only prime numbers remain. Examples are given to show drawing the factor tree, writing the expanded and simplified forms. Students are then asked to complete factor trees for various numbers and self-assess their understanding of factor trees.
This document provides a 3-step process for teaching younger students how to multiply two-digit numbers by one-digit numbers. The steps are to 1) write down the multiplication problem, 2) multiply the ones place, and 3) multiply the tens place by the same one-digit number and combine the results. An example problem of 11 x 4 is shown to equal 44 by first calculating 4, then 4, and combining them. The document was created by Callie Wadler, Mikayla Mykytyn, and Hannah Hoisington to teach multiplication to younger students.
The document provides examples and instructions for adding and subtracting integers using a number chip method. It explains that to add integers with the same sign, the numbers are added together, while to add integers with different signs, the smaller number is subtracted from the larger number and the sign of the larger number determines the sign of the answer. For subtracting integers, the opposite of the number being subtracted is added instead. Several examples are worked through to demonstrate these methods.
This document provides examples of estimating products by rounding numbers to the greatest place value. It shows rounding dollar amounts and whole numbers to the nearest hundred, ten, or ones place. The steps shown are to round each number, then multiply the rounded numbers using mental math. Examples include estimating $187 x 18 by rounding to $200 x 20 = $4,000, and 147 x 353 by rounding to 100 x 400 = 40,000.
This document provides an easy trick for multiplying numbers by 9 without a calculator. The trick involves using your hands to represent numbers 1-10. To multiply a number by 9, put down the corresponding finger on your hands and count the fingers to the left and right to get the digits of the answer. Several examples are shown multiplying numbers 1-10 by 9 using this hand trick.
Divisibility refers to whether a number can be divided by another number without a remainder. A number is divisible by another number if when you divide them, the result is a whole number. The document then provides rules for determining if a number is divisible by 2, 3, 5, 6, 8, 9, 10, and 4. It explains that you cannot divide by 0 because there is no number that when multiplied by 0 equals the original number.
Ratios compare two sets of numbers and can be written in three ways: using "to", with a colon, or as a fraction. Proportions are two equal ratios where the cross products are also equal. To solve a proportion, cross multiply, divide both sides by the number connected to the variable, and check that it makes a true proportion.
1. This document provides step-by-step instructions for multiplying decimals.
2. It explains that when multiplying decimals and whole numbers, you don't need to worry about decimal placement until the end.
3. The steps show working through multiplying 1.2 x 5.3, including multiplying each digit and carrying numbers to get the final answer of 6.36.
This document provides instructions for adding double digit numbers to single and double digit numbers. It explains that when adding a double digit number to a single digit number, you add the ones place numbers first and then bring down the leftmost number. When adding two double digit numbers, you add the ones places first, put the sum under the line, then add the tens places and put that sum underneath in the tens column. The document aims to teach basic addition skills through examples of single and double digit number addition problems.
This document provides instructions and examples for subtracting mixed numbers. It explains the steps as: 1) finding the least common denominator, 2) rewriting the mixed numbers with the common denominator, 3) subtracting the fractions, 4) subtracting the whole numbers, and 5) simplifying the final fraction if possible. Two examples are shown working through each step. The document concludes by asking the reader to try subtracting two additional mixed numbers on their own.
Skip counting and using a hundreds chart and multiplication chart can help students learn multiplication facts. The hundreds chart allows students to visually count by a given number to see the pattern and connection to multiplication. Colouring numbers on the hundreds chart when counting by 3s, 4s, and 5s shows the repeating patterns that are the basis for the 3, 4, and 5 times tables. These patterns translate to the multiplication chart, where students can fill in facts by seeing the connection between addition and multiplication statements. Regular practice using the charts, such as in a multiplication master game, reinforces understanding of multiplication.
The document provides steps for adding multi-digit numbers with regrouping. It explains that when adding numbers in columns, if the total in a column is 10 or more, you regroup by adding 1 to the column to the left and carrying the 1 to the next column. It then works through an example of adding 3,243 mathematics books and 4,659 science books. Finally, it provides additional practice problems for readers to try adding multi-digit numbers themselves.
The document discusses ratios and proportions. It defines ratios as a comparison of two quantities that can be written as fractions using a colon or fraction form. It provides examples of setting up and solving ratios and proportions. Key points covered include: writing ratios in lowest terms, setting up cross multiplication to solve proportions, and using variables like n as unknowns to solve for in proportions.
This document provides an overview of the Singapore Math bar modeling strategy for addition, subtraction, multiplication, and division word problems. It explains how to use part-whole and comparison models to represent word problem situations visually with bars. It also provides an example of using these models to solve a multi-step word problem from a 5th grade Singapore textbook, demonstrating how to set up and solve the problem using the bar model representations.
This document contains materials for a mathematics lesson on ratios and proportions. It includes examples of writing ratios using fractions and colons, forming proportions, and finding missing terms in proportions. Activities guide students to form ratios, write proportions, solve word problems involving ratios, and evaluate their understanding through questions and applications using visual representations. Cooperative learning strategies and using various tools like charts and presentations are suggested for instruction.
Adding Dissimilar Fraction with and without regroupingAlpheZarriz
This document discusses how to add dissimilar fractions with and without regrouping. It provides examples of adding fractions without regrouping by finding the lowest common denominator and then adding the numerators. For fractions requiring regrouping, it explains finding the lowest common denominator to write equivalent fractions, adding the numerators, and copying the common denominator. Mixed numbers are added by first changing the fractions to equivalent fractions with the same denominator, then adding the whole numbers and fractions separately before simplifying the final answer.
Multiplying 3-digit numbers by 2-digit numbers gemmajoaquin
This document provides a lesson on multiplying 3-digit numbers by 2-digit numbers. It begins with a review of multiplication and then demonstrates multiplying without and with regrouping using short methods and lattice methods. Examples and exercises are provided for students to practice. Key skills learned are multiplying 3-digit and 2-digit numbers in various ways including short and lattice methods.
The document provides instructions on how to create and use factor trees to factorize numbers. It explains that a factor tree involves repeatedly dividing a number by prime factors until only prime numbers remain. Examples are given to show drawing the factor tree, writing the expanded and simplified forms. Students are then asked to complete factor trees for various numbers and self-assess their understanding of factor trees.
This document provides a 3-step process for teaching younger students how to multiply two-digit numbers by one-digit numbers. The steps are to 1) write down the multiplication problem, 2) multiply the ones place, and 3) multiply the tens place by the same one-digit number and combine the results. An example problem of 11 x 4 is shown to equal 44 by first calculating 4, then 4, and combining them. The document was created by Callie Wadler, Mikayla Mykytyn, and Hannah Hoisington to teach multiplication to younger students.
The document provides examples and instructions for adding and subtracting integers using a number chip method. It explains that to add integers with the same sign, the numbers are added together, while to add integers with different signs, the smaller number is subtracted from the larger number and the sign of the larger number determines the sign of the answer. For subtracting integers, the opposite of the number being subtracted is added instead. Several examples are worked through to demonstrate these methods.
This document provides examples of estimating products by rounding numbers to the greatest place value. It shows rounding dollar amounts and whole numbers to the nearest hundred, ten, or ones place. The steps shown are to round each number, then multiply the rounded numbers using mental math. Examples include estimating $187 x 18 by rounding to $200 x 20 = $4,000, and 147 x 353 by rounding to 100 x 400 = 40,000.
This document provides an easy trick for multiplying numbers by 9 without a calculator. The trick involves using your hands to represent numbers 1-10. To multiply a number by 9, put down the corresponding finger on your hands and count the fingers to the left and right to get the digits of the answer. Several examples are shown multiplying numbers 1-10 by 9 using this hand trick.
Divisibility refers to whether a number can be divided by another number without a remainder. A number is divisible by another number if when you divide them, the result is a whole number. The document then provides rules for determining if a number is divisible by 2, 3, 5, 6, 8, 9, 10, and 4. It explains that you cannot divide by 0 because there is no number that when multiplied by 0 equals the original number.
Ratios compare two sets of numbers and can be written in three ways: using "to", with a colon, or as a fraction. Proportions are two equal ratios where the cross products are also equal. To solve a proportion, cross multiply, divide both sides by the number connected to the variable, and check that it makes a true proportion.
1. This document provides step-by-step instructions for multiplying decimals.
2. It explains that when multiplying decimals and whole numbers, you don't need to worry about decimal placement until the end.
3. The steps show working through multiplying 1.2 x 5.3, including multiplying each digit and carrying numbers to get the final answer of 6.36.
This document provides instructions for adding double digit numbers to single and double digit numbers. It explains that when adding a double digit number to a single digit number, you add the ones place numbers first and then bring down the leftmost number. When adding two double digit numbers, you add the ones places first, put the sum under the line, then add the tens places and put that sum underneath in the tens column. The document aims to teach basic addition skills through examples of single and double digit number addition problems.
This document provides instructions and examples for subtracting mixed numbers. It explains the steps as: 1) finding the least common denominator, 2) rewriting the mixed numbers with the common denominator, 3) subtracting the fractions, 4) subtracting the whole numbers, and 5) simplifying the final fraction if possible. Two examples are shown working through each step. The document concludes by asking the reader to try subtracting two additional mixed numbers on their own.
Skip counting and using a hundreds chart and multiplication chart can help students learn multiplication facts. The hundreds chart allows students to visually count by a given number to see the pattern and connection to multiplication. Colouring numbers on the hundreds chart when counting by 3s, 4s, and 5s shows the repeating patterns that are the basis for the 3, 4, and 5 times tables. These patterns translate to the multiplication chart, where students can fill in facts by seeing the connection between addition and multiplication statements. Regular practice using the charts, such as in a multiplication master game, reinforces understanding of multiplication.
The document provides steps for adding multi-digit numbers with regrouping. It explains that when adding numbers in columns, if the total in a column is 10 or more, you regroup by adding 1 to the column to the left and carrying the 1 to the next column. It then works through an example of adding 3,243 mathematics books and 4,659 science books. Finally, it provides additional practice problems for readers to try adding multi-digit numbers themselves.
13. Ito ang tinatawag nating
REPEATED SUBTRACTION.
Kung saan ang 18 ay
tatlong binawasan ng 6
hanggang maging 0.
18 – 6 = 12
12 – 6 = 6
6 – 6 = 0
18 ÷ 6 =
3
14. Sa repeated subtraction,
nagagawa ang division kapag
paulit-ulit na babawasan ang
kabuuang bilang mula sa
naibibigay sa bawat grupo o
hinahatian. Matutukoy ang
sagot kapag iyong bilangin
ang
mga bahaging nabigyan.
15. Iba pang halimbawa:
Sa inyong apat
na magkakaibigan,
binigyan kayo ng 28
pirasong cupcake ng
inyong guro.
Kailangan nyo itong
hatiin nang parehas
sa bawat isa. Paano
Hinati sa 4 ang 28
28 – 4 = 24
24 – 4 = 20
20 – 4 = 16
16 – 4 = 12
12 – 4 = 8
8 – 4 = 4
4 – 4 = 0
17. Pagsasanay 1
Panuto: Tignan at suriin ang
mga larawan. Sagutin ang
division equation gamit ang
repeated subtraction. Gawing
gabay sa pagsagot ang unang
bilang. Isulat ang iyong
sagot sa sagutang papel.
18.
19.
20.
21. Pagsasanay 2
Panuto: Isulat ang
repeated subtraction
equation upang
maipakita ang
paghahati. Isulat din
ang division equation.
Gamiting gabay ang
28. Upang magawa ang dibisyon gamit
ang 1.______________ lamang o
2._____________division, gamitin
ang paulit-ulit na pagbabawas o
3. _________________
subtraction. Bawasan ang
4.____________________ sa
naghahati o divisor hanggang sa
isip
menta
l repeate
d
dividend
zero
29. Pag-aralan at gawin ang Repeated
Subtraction.
Paglalapat:
Mayroong anim (6) na upuan
sa bawat hanay ng mga upuan
sa silid-aklatan. Ilang
hanay ng upuan ang
magagamit ng mga nasa
ikalawang baitang kung
30. Mga Hakbang:
1. Isulat muli ang sitwasyon ayon sa
iyong pag-unawa.
Sagot: Mayroong 30 mag-aaral sa
Ikalawang baitang. Kung may 6 na
upuan sa bawat hanay, ilang hanay ng
upuan ang kailangan para makaupo
lahat ng mga bata?
2. Isulat ang tanong ng pasalaysay.
31.
32. Panuto: Sagutin ang bawat bilang
sa talahanayan gamit ang repeated
subtraction bilang gabay. Isulat
ang iyong sagot sa sagutang papel
Pagtataya:
Halimbawa:
12 ÷ 6 =
__
12 – 6 = 6
6 – 6 = 0
Sagot:
12 ÷ 6 =
2