3 module 10 · lesson students multiply to determine the number of units of measure when ½nding...

2
© ORIGO Education NEWSLETTER How many tiles will be needed in total? How can you use multiplication to quickly figure it out? This picture shows that square tiles are being used to cover a floor. Step In Area: Using multiplication to calculate area 10.3 5 4 5 × 4 = 20 so the area is 20 square units. There are 5 rows and each row will have 4 squares. 5 × 4 = 20 so 20 tiles will be needed. What is the area of the whole floor? How do you know? (e Needs to KNoW tHe area oF tHe floor to calculate how much paint to buy. The dimensions are shown to the right. %stimate the area of the floor Would it be more or less than 100 sq yards? How could you calculate the exact area? Hassun drew this grid to help He split into tens and ones then multiplied ¤ and ¤ &eLIX Is PaINtING tHe coNcrete floor oF a WareHouse. Step In Multiplication: Using the distributive property with two-digit numbers (partial products) 10.8 (oW couLd You use tHIs strateGY to caLcuLate ¤ 10 6 5 You can split a rectangle INTO PARTS TO ½ND THE partial products. Length is 15 yards Width is 6 yards Area is sq yards 3 × 20 is 60 and 3 × 8 is 24. I then put these partial products together to calculate the total. Module 10 3 Geometry 3TUDENTS ½ND THE AREA OF RECTANGLES !T ½RST THEY COUNT ALL THE SQUARES INSIDE A SHAPE BUT SOON SEE HOW THOSE SQUARES ARE ARRANGED IN ROWS AND COLUMNS SIMILAR TO THE arrays THEY HAVE BEEN USING WITH MULTIPLICATION FACTS Multiplication 3TUDENTS INVESTIGATE HOW SEPARATING ONE RECTANGLE INTO TWO OR MORE RECTANGULAR SECTIONS MAKES CALCULATIONS EASIER &OR A RECTANGLE THAT IS ¤ STUDENTS THINK OF IT AS TWO RECTANGLES ¤ ß AND ¤ 4HE AREA IS ß ß ß 1 Core Focus 'EOMETRY 5SING CUSTOMARY UNITS AND MULTIPLICATION TO CALCULATE AREA -ULTIPLICATION 5SING THE DISTRIBUTIVE AND ASSOCIATIVE PROPERTY WITH TWODIGIT NUMBERS !LGEBRA 3OLVING PROBLEMS INVOLVING MULTIPLE OPERATIONS Ideas for Home -EASURING AREA IS A PRACTICAL SKILL AND A COMMON WAY PEOPLE REFER TO THE SIZE OF A ROOM OR A SPACE 5SING MEASURING TAPE WORK TOGETHER TO ½ND THE AREA OF SMALLER RECTANGULAR SPACES IN YOUR HOME SUCH AS A STOVE TOP A CUPBOARD OR A CLOSET 7HEN IN A STORE NOTICE BOXES AND LABELS THAT HAVE LENGTH AND WIDTH DIMENSIONS LISTED LIKE CARPETS PHOTO FRAMES OR FURNITURE $ETERMINE THE AREA TOGETHER USING THE DIMENSIONS LISTED Glossary !N array IS AN ARRANGEMENT OF OBJECTS IN EQUAL AND ORDERLY ROWS OR COLUMNS )N THIS LESSON STUDENTS MULTIPLY TO DETERMINE THE NUMBER OF UNITS OF MEASURE WHEN ½NDING THE AREA OF RECTANGLES )N THIS LESSON STUDENTS SPLIT RECTANGLES INTO TWO PARTS AND USE DISTRIBUTIVE PROPERTY TO ½GURE OUT THE AREA OF RECTANGLES

Upload: others

Post on 07-Aug-2020

0 views

Category:

Documents


0 download

TRANSCRIPT

Page 1: 3 Module 10 · lesson students multiply to determine the number of units of measure when ½nding the area of rectangles )n this lesson students split rectangles into two parts and

© O

RIGO

Edu

catio

nNEWSLETTER

How many tiles will be needed in total?

How can you use multiplication to quickly fi gure it out?

This picture shows that square tiles are being

used to cover a fl oor.Step In

Area: Using multiplication to calculate area10.3

5

4

5 × 4 = 20 so the area is 20 square units.

There are 5 rows and each row will have 4 squares. 5 × 4 = 20 so 20 tiles will be needed.

What is the area of the whole fl oor? How do you know?

e eeds to o t e area o t e fl oor to calculate how much paint to buy.

The dimensions are shown to the right.

stimate the area of the fl oor Would it be more or less than 100 sq yards?

How could you calculate the exact area?

Hassun drew this grid to help He split into tens and onesthen multiplied and

e s a t t e co crete fl oor o a are ouse. Step In

Multiplication: Using the distributive property with

two-digit numbers (partial products)10.8

o cou d ou use t s strate to ca cu ate

10

6

5

You can split a rectangle INTOPARTSTO½NDTHEpartial products.

Length is 15 yards

Width is 6 yards

Area is sq yards

3 × 20 is 60 and 3 × 8 is 24. I then put these partial products together to calculate the total.

Module 103

Geometry

�3TUDENTS½NDTHEAREAOFRECTANGLES�!T½RST�THEYCOUNTALLTHESQUARESINSIDE ASHAPEBUTSOONSEEHOWTHOSESQUARESAREARRANGEDINROWSANDCOLUMNS�SIMILARTOTHEarraysTHEYHAVEBEENUSINGWITHMULTIPLICATIONFACTS�

Multiplication

�3TUDENTSINVESTIGATEHOWSEPARATINGONERECTANGLEINTOTWOORMORERECTANGULARSECTIONSMAKESCALCULATIONSEASIER�&ORARECTANGLETHATIS�¤���STUDENTSTHINK OFITASTWORECTANGLES��¤�ßAND�¤��4HEAREAIS�ß��ß�ß�

1

Core Focus

�'EOMETRY�5SINGCUSTOMARYUNITSANDMULTIPLICATIONTOCALCULATEAREA�-ULTIPLICATION�5SINGTHEDISTRIBUTIVEANDASSOCIATIVEPROPERTYWITH TWO�DIGITNUMBERS

�!LGEBRA�3OLVINGPROBLEMSINVOLVINGMULTIPLEOPERATIONS

Ideas for Home

�-EASURINGAREAISAPRACTICALSKILLANDACOMMONWAYPEOPLEREFERTOTHESIZEOFAROOMORASPACE�5SINGMEASURINGTAPE�WORKTOGETHERTO½NDTHEAREAOFSMALLERRECTANGULARSPACESINYOURHOME�SUCHASASTOVETOP�ACUPBOARD�ORACLOSET�

�7HENINASTORE�NOTICEBOXESANDLABELSTHATHAVELENGTHANDWIDTHDIMENSIONSLISTED�LIKECARPETS�PHOTOFRAMES�ORFURNITURE�$ETERMINETHEAREATOGETHERUSINGTHEDIMENSIONSLISTED�

Glossary

!NarrayISANARRANGEMENTOFOBJECTSINEQUALANDORDERLYROWSORCOLUMNS�

)NTHISLESSON�STUDENTSMULTIPLYTODETERMINETHENUMBEROFUNITSOFMEASUREWHEN½NDINGTHEAREAOFRECTANGLES�

)NTHISLESSON�STUDENTSSPLITRECTANGLESINTOTWOPARTSANDUSEDISTRIBUTIVEPROPERTYTO½GUREOUTTHEAREAOFRECTANGLES�

Page 2: 3 Module 10 · lesson students multiply to determine the number of units of measure when ½nding the area of rectangles )n this lesson students split rectangles into two parts and

© O

RIGO

Edu

catio

nNEWSLETTER

Module 103

2

�3TUDENTSWORKWITHMULTIPLYINGASINGLE�DIGITNUMBERBYMULTI�DIGITNUMBERS USINGTHEpartial productsSTRATEGY�-ULTI�DIGITNUMBERSAREDECOMPOSEDINTOPLACE�VALUEPARTSSOTHEMULTIPLICATIONISEASYTODOUSINGANARRAYMODEL�%ACHPARTISMULTIPLIED�ASINAREA��THENADDEDTOGETHER�RESULTINGINTHETOTALPRODUCT�

�3TUDENTSUSETHEassociative propertyTOMULTIPLY�7HENONEFACTORISDOUBLEDANDTHEOTHERHALVED�THEQUANTITYOFTHEPRODUCTISTHESAME�!NARRAYMODELILLUSTRATESWHYITWORKS�

Ideas for Home

�0RACTICETHEDOUBLINGANDHALVINGSTRATEGYWITHFACTORSSUCHAS��ì��(ALFOF��IS ANDDOUBLE�IS�ß�SO ��ì��ì�ß�WHICHISEASIERTOMULTIPLYMENTALLY�ß��.OTE�ONEOFTHEFACTORSMUSTBEEVEN�

Glossary

4HEpartial products

strategy USESTHEDISTRIBUTIVEPROPERTY�MULTIPLYINGEACHPLACEVALUESEPARATELYTOGETAPARTIALPRODUCTANDTHENADDINGTHEPRODUCTSTOGETHER�RESULTINGINASINGLE½NALPRODUCT�

4HE associative property of

multiplicationALLOWSTHREENUMBERSTOBEMULTIPLIEDINANYORDER�E�G��ì�ì�CANBE��ì��ì���ì����� OR�ì��ì����ì������ OR��ì��ì���ì��

4

18

Imagine the array is cut in half

and the new array below is made

with the two pieces.

How could you calculate the number

of squares in this array?Step In

Multiplication: Using the associative property with

two-digit numbers (double and halve)10.9

What is di erent a out the arrays?

Has the num er of squares changed?

Is it easier to calculate the total number

of squares for the new array? Why?

Write an equation to describe each array.8

9

Doubling one number and halving the other can make it easier to figure out the product.

Imagine you want to buy one issue of A and three issues of B .

Look at these comic books.Step In

Algebra: Investigating order with multiple operations10.10

What steps would you use to calculate

the total cost?

What equation could you write to show

your thinking?

If there is one type of operation in a sentence, work left to right.

If there is more than one type of operation, work left to right in this order.1. perform any operation inside

parentheses2. multiply or divide pairs of numbers3. add or subtract pairs of numbers

These are the rules for the order of operations.

DINO STORIES

$6 an issue

DETECTIVEMYSTERY

$8 an issue

SPACEADVENTURE

$7 an issue

ACTIONCOMICS

$9an issue

C DBA

)NTHISLESSON�STUDENTSLEARNTHERULESFORTHEORDEROFOPERATIONS�

3TUDENTSUSEARECTANGULARARRAYTOSHOWHOWONEFACTORCAN BEDOUBLEDANDTHEOTHERCANBEHALVEDTO½GUREOUTTHETOTAL�

Algebra

�3TUDENTSDISCUSSEVERYDAYSITUATIONSTHATINVOLVEMORETHANONEOPERATION�3TUDENTSCONSIDERINWHICHORDERTODOTHEOPERATIONSTOENSURETHECORRECTRESULT�