Mathematical Processes

To work on third grade mathematical processes standards, click on the numbers below to visit pages with plenty of internet resources for each of the learning standards on the right.

Checks for Understanding are at the top of this page. Scroll down to find internet resources related to the State Performance Indicators (SPIs).

Checks for Understanding (Formative/Summative Assessment)

6.1.1	Reads and write time to the nearest minute (0306.1.1)
6.1.2	Compare and order decimal amounts in the context of money (0306.1.2)
6.1.3	Count the value of combinations of coins and bills up to five dollars (0306.1.3)
6.1.4	Analyze problems by identifying relationships, distinguishing relevant from irrelevant information, and observing patterns (0306.1.4)
6.1.5	Determine when and how to break a problem into simpler parts (0306.1.5)
6.1.6	Use estimation to check answers for reasonableness, and calculators to check for accuracy (0306.1.6)
6.1.7	Make and investigate mathematical conjectures (0306.1.7)
6.1.8	Explain and justify answers on the basis of mathematical properties, structures, and relationships (0306.1.8)
6.1.9	Use manipulatives to demonstrate that the commutative property holds for addition but not for subtraction (0306.1.9)
6.1.10	Use correct, clearly written and oral mathematical language to pose questions and communicate ideas (0306.1.10)
6.1.11	Develop strategies for solving problems involving addition and subtraction of measurements (0306.1.11)
6.1.12	Analyze and evaluate the mathematical thinking and strategies of others (0306.1.12)
6.1.13	Create and use representations to organize, record, and communicate mathematical ideas (0306.1.13)
6.1.14	Use age-appropriate books, stories, and videos to convey ideas of mathematics (0306.1.14)

State Performance Indicators

6.1.1	Solve problems using a calendar (SPI 0306.1.1)
6.1.2	Solve problems involving elapsed time (SPI 0306.1.2)
6.1.3	Determine the correct change from a transaction less than a dollar (SPI 0306.1.3)
6.1.4	Match the spoken, written, concrete, and pictorial representations of fractions with denominators up to ten (SPI 0306.1.4)
6.1.5	Represent problems mathematically using diagrams, numbers, and symbolic expressions (SPI 0306.1.5)
6.1.6	Identify and use vocabulary to describe attributes of two- and three-dimensional shapes (SPI 0306.1.6)
6.1.7	Select appropriate units and tools to solve problems involving measures (SPI 0306.1.7)
6.1.8	Express answers clearly in verbal, numerical, or graphical (bar and picture) form, using units when appropriate (SPI 0306.1.8)

Read and write time to the nearest minute (0306.1.1)

1. A Matter of Time - interactive quizzes on half hour, 15 minute intervals and five minute intervals - (story problems)
2. Analog Clock - [ whole class activity ] You call out a time and ask a student to set the clock.
3. Bang On Time - Read the time in words then stop the clock when the hands reach the right time.
4. Beat the Clock - interactive time game
5. Bedtime Bandits - (students try to stay up as late as possible by blasting killer clocks that drop from the ceiling) After each stage, identifying the correct clock gets harder and harder.
6. Clock Program - Start with either an analog or a digital clock, then set the other clock to the time given on the first clock.
7. ClockWise and Matching Time - select either of these two activities to practice telling time
8. Clock Works - [ 1 minute increments at the advanced level ] select hour and then minute by clicking on the clock
9. Draw Hands - free worksheets from Math Slice, time intervals from 1 hour to one minute
10. Kid Klock - use pull down menus to select the time you would like to see on an analog clock
11. Right Time - explore the meaning of AM and PM while they tell time to the hour and half hour. ( Author - Linda Burke )
12. Stop the Clock - match digital time to analog clocks, or written time, by dragging the digital clocks, or written time | to the nearest hour | to the nearest half hour | to the nearest fifteen minutes
13. Tell Time - free worksheets from Math Slice, time intervals from 1 hour to one minutes
14. Telling Time - Drag the five digital times to the correct analog clock, then press Stop the Clock to record your time. ( 30 minute increments ) ( 15 minute increments ) ( 5 minute increments )
15. Telling Time - Draw a line between matching items in each column.
16. Telling Time Practice - Drag the hands of the clock to show the correct time.
17. Telling Time Worksheets - topics from various grades are covered [ there is a link to .pdf worksheets, but fewer activities per sheet are presented in those worksheets ]
18. Time Theme Unit - worksheets to print, various grades
19. Time Words - Read the time in words and then stop the clock when the hands are in the matching position.
20. Time To Go - tell time to the half hour ( Author - Randy Russell ) [hour and half hour only]
21. Travel Time - Which train falls in between the time limit?
22. Worksheet Generator - You decide on the variables; students tell the time or draw the hands on the clock face, time increments from half-hour to one minute, and answer sheet.

Compare and order decimal amounts in the context of money (0306.1.2)

1. Compare Decimal Numbers - select problem type, select New and then type the correct answer; <, >, or =
2. Money and Decimals - online quiz. Add up money and choose correct answer.
3. Scottie Nickel's Change Maker - become a human CoinStar machine - Calculate the total amount of change the customer has. Next, think of a way to make $1.75 with as few coins as possible.

Count the value of combinations of coins and bills up to five dollars (0306.1.3)

1. Adding Nickels and Pennies - find the sum of the coins
2. Adding Dimes and Pennies - find the sum of the coins
3. Adding Dimes, Nickels and Pennies - find the sum of the coins
4. Change It! - practice adding up all of your coins - You select the number of problems that you want to use as well as the number of pennies, nickels, dimes, quarters, and half dollars that may appear in each problem. You may elect to express your questions in words only, coins only, or a combination of both
5. Change Maker - Figure out how many of each bill or coin that you expect to get back when you pay for something. Select Medium for problems involving less than $5.00
6. Count the Money - You're given a target amount and the number of coins you already have. You must determine how many more coins of a certain type are needed to reach the target.
7. Counting Coins - coins only, values to $2.00
8. Counting Coins - [ no bills ] up to 5˘ , up to 20˘ , up to 50˘ , up to 99˘ , customize amounts - from FreeMathTest
   1. Worksheets to print are also available supporting instruction of this topic [ no bills ]
9. Counting Money - select difficulty level and then drag the right amount of coins
10. Counting Money - Help Kristen, Ryan, or Evan with their shopping. Six pages of problems are available; three easy and three hard.
11. Grandpa's Game - count money ( Author - Sandi King )
12. Learn to Count Money - add the value of the coins - (Teacher can set this activity easy or harder)
13. Let's Do Lunch - use a menu to order lunches that meet various criteria ( Author - Sandi King )
14. Let's Go Shopping - estimate by rounding to the nearest dollar as they shop ( Author - Sandi King )
15. Lunch Lady - The Lunch Lady (you) must total the three items on ten lunch trays (one at a time) in three minutes. [ a money counting game from Mr. Nussbaum ]
16. Making Change - count money and make change ( Author - Sandi King )
17. Making Change at the Math Playground - calculate change back on a purchase then click and drag the change to the counter using the smallest number of bills or coins
18. Making Change from One Dollar - amounts are shown on a cash register, find the correct change
19. Money Flashcards - Coins and bills, or just coins, are displayed and students determine the value. Best used as a whole class review; this is not a game with an end.
20. Money Program - three levels; easy (ends in multiples of five), medium, and advanced (giving change back) [ advanced ]
21. Piggy Bank - As coins drop students click on the right coins to equal some target amount. Two games are available; easy or hard.
22. Scottie Nickel's Change Maker - become a human CoinStar machine - Calculate the total amount of change the customer has. Next, think of a way to make $1.75 with as few coins as possible.
23. Show Me The Money - add using columns ( Author - Sandi King ) [amounts over $5 are used]
24. Too Much Noise - determine the fewest number of coins needed to produce a given amount ( Author - Sandi King )

Analyze problems by identifying relationships, distinguishing relevant from irrelevant information, and observing patterns (0306.1.4)

1. Attribute Trains - complete the pattern
2. Cyber Pattern Maker - click on the squares to create a musical pattern.
3. Domino Number Patterns - class activity or can print it out. Determine what dots go between two dominos to create the pattern.
4. Explore the World with Math Cats - large number of ways to explore and identify patterns
5. Geometry Through Art - What children can learn about art and geometry
6. Logic Zoo - put similar animals into the correct pens
7. Working with Patterns - video lesson

Determine when and how to break a problem into simpler parts (0306.1.5)

1. Barrels of Milk - Seven barrels are full of milk. Seven others half filled, and the remaining seven are empty. Please help divide the barrels fairly.
2. Measurement - break problem into simpler parts, online quiz.

Use estimation to check answers for reasonableness, and calculators to check for accuracy (0306.1.6)

1. Animal Legs - use repeated addition as a strategy to solve multiplication story problems ( Author - Sandi King )
2. Basket Math provides rounding practice
3. Comparison Estimator - Similar to Estimator but compares two sets of objects.
4. Estimate - [ use as a whole class activity ] Select a range, display tick marks and estimate before revealing the answer.
5. Estimating by Rounding - addition with regrouping
6. Estimating by Rounding - subtraction with regrouping
7. Estimating and rounding decimals - a lesson, examples, and an interactive practice page
8. Estimating Sum - no hints or clues given
9. Estimator - Practice estimation skills by determining the number of objects, length, or area. (parameters: error tolerance)
10. Guess the Number - developing skills in halving and estimation
11. Home Run Derby Math - you don't have time to add, just estimate the correct answer [ addition, subtraction, or multiplication ]
12. Laser Beams - rounding decimals to the nearest whole number - three levels are available; rounding, rounding and computing sums and differences, and rounding and computing with all four operations
13. Let's Go Shopping - estimate by rounding to the nearest dollar as they shop ( Author - Sandi King )
14. Math Story Problems! - Kid created math story problems ("Kitten" pages are the easiest.) There are lots of links to pages of problems... scroll way down to see them all
15. More or Less Estimator - Similar to Estimator activity but states a quantity and asks the user to estimate whether the set of objects is more or less than the number given.
16. Round About - estimate by rounding ( Author - Sandi King )
17. Round the decimal to the nearest whole number - [ this link opens on a new page ] matching, flashcards, or concentration (from Quia)
18. Rounding - to the nearest ten or dollar, a quiz from Saxon math
19. Rounding to nearest ten - to nearest hundred - to nearest thousand
20. Rounding Off - three levels are available in this game from BBC Education
21. The Seashell Rounding Activity Page - Look at the number on each shell. Click on the nearest ten.

Make and investigate mathematical conjectures (0306.1.7)

1. Walrus World - learn strategies for solving real world problems ( Author - Randy Russell )

Explain and justify answers on the basis of mathematical properties, structures, and relationships (0306.1.8)

1. Figure this Math Challenge - How long do you have to stand in line?
2. Estimate the Difference between the two Numbers . - Online quiz

Use manipulatives to demonstrate that the commutative property holds for addition but not for subtraction (0306.1.9)

1. Activities at Illuminations - Illuminations has 100 online activities available. Select which types of activities you’re looking for, and click Search.
2. Base 10 Blocks - virtual manipulative
3. Electronic Examples - index of manipulatives from NCTM
4. GeoBoard - this two-part example describes activities that use interactive geoboards
5. Integer Bars - learning fractions and more with on-line manipulatives
6. Math Playground - a small but growing collection of manipulatives for teaching and learning
7. National Library of Virtual Manipulatives - select topic and grade level to find appropriate manipulatives
8. Pattern Blocks Program - use tools to solve a variety of problems
9. Tangrams - interactive geometric site
10. Virtual Manipulatives - a list of various manipulatives for grades 1-6
11. Wolfram Demonstrations Project - a free resource of interactive visualizations from elementary education to the frontiers of research

Use correct, clearly written and oral mathematical language to pose questions and communicate ideas (0306.1.10)

1. Evaluating Math Knowledge - video lesson

Develop strategies for solving problems involving addition and subtraction of measurements (0306.1.11)

1. Draw a Picture to solve the problem - online quiz
2. Draw a Picture - answer the problem by drawing a picture
3. Problem Solving Strategies - work backwards lesson
4. Work Backwards - online quiz
5. Work backward to solve the problem - online quiz

Analyze and evaluate the mathematical thinking and strategies of others (0306.1.12)

1. Evaluating the explanation - video Lesson -

Create and use representations to organize, record, and communicate mathematical ideas (0306.1.13)

1. What Percentage of your Class is Right or Left Handed? - a data collection and analysis class experiment

Use age-appropriate books, stories, and videos to convey ideas of mathematics (0306.1.14)

1. Brian P. Cleary - author of books conveying math ideas - Mission of Addition, The, Action of Subtraction, The, How Long or How Wide?: A Measuring Guide
2. Children's Picture Book Database at Miami University - type in math or numbers in the search box.
3. Flatland: A romance of many dimensions - fifty-five pages if printed
4. Literature for Learning Math Concepts - using books to teach math
5. Note of Caution: the books below are not available to read online, they are given as a reading list only
   1. Fiction about Math - a 3 page reading list in MS Word format
   2. Math Month in the Library - article about books to consider
   3. Math Novels - use this list of novels as a reading list rather than a shopping list
   4. Math and Science Related Books - a reading list from Math Forum
   5. Mathematical Fiction - large database of titles
   6. Mathematics fiction books - Wikipedia index to articles about 19 books
   7. Mathematics in Fiction - a reading list of novels in which mathematics play a large role

Solve problems using a calendar (SPI 0306.1.1)

1. Calendar Ideas for teacher s -Learn activities that develop calendar reading skills.
2. Calendar Quiz - Answer the questions on this interactive calendar.
3. Calendar Quiz - online quiz
4. Calendar and Minutes - convert the minutes into months, days, hours and minutes.
5. Calendar Worksheets - select a month, five questions are on each worksheet
6. It's A Date - use a calendar ( Author - Sandi King )
7. Time and Money - online quiz
8. Understanding the Calendar - Solve the problems using the calendar shown below

Solve problems involving elapsed time (SPI 0306.1.2)

1. Bedtime Bandits - (students try to stay up as late as possible by blasting killer clocks that drop from the ceiling) After each stage, identifying the correct clock gets harder and harder. Eventually, students have to blast the clock that is "4 hours and 15 minutes past 2:30", for example.
2. Clock Works - [use challenge level] select hour and then minute by clicking on the clock
3. E-Lab: Elapsed Time - [ designed for 4th grade ] use an analog clock to measure elapsed time
4. Elapsed Time - Practice finding elapsed time given a starting time and an ending time. Elapsed Time is one of the Interactivate assessment explorers.
5. Elapsed Time - show what time it will be in a given number of minutes
6. Elapsed Time - quiz
7. Elapsed Time - match game quiz
8. Elapsed Time - PDF worksheet to print - days, months, years
9. Elapsed Time - PDF worksheet
10. Elapsed Time - worksheet
11. Elapsed Time - worksheet
12. Elapsed Time - worksheet
13. Elapsed Time - worksheet
14. Elapsed Time - PDF worksheets with teacher instructions
15. Elapsed Time - free worksheets from Math Slice, time intervals from 1 hour to one minute
16. Elapsed Time on a Clock - an E-Lab activity from Harcourt School Publishers ( rated for 4th grade )
    1. Recording sheet to use with the activity above
17. Elapsed Time Quiz - ten multiple-choice questions
18. Is It PE Time? - use a chart (table) to solve problems ( Author - Sandi King )
19. Right Time - explore the meaning of AM and PM while they tell time to the hour and half hour ( Author - Linda Burke )
20. Telling Time Word Problems - ten multiple choice elapsed time word problems

Determine the correct change from a transaction less than a dollar (SPI 0306.1.3)

1. Cash Out - give correct change to as many customers as you can in the time allowed
2. Change It ! - practice adding up all of your coins - You select the number of problems that you want to use as well as the number of pennies, nickels, dimes, quarters, and half dollars that may appear in each problem. You may elect to express your questions in words only, coins only, or a combination of both
3. Change Maker - Figure out how many of each bill or coin that you expect to get back when you pay for something. Select Easy for problems involving less than $1.00
4. Counting Change - a match game, counting coins to find amount of change and matching it with numerical number
5. How Much Change? - calculate cost of items and change from a set amount
6. How much change? - word problems.
7. Making Change - count money and make change ( Author - Sandi King )
8. Making Change from One Dollar - amounts are shown on a cash register, find the correct change
9. Spending Spree - Pick the item that you would like to buy. Then choose the correct amount of coins you need to pay for that item. This game has 10 questions.
10. School Store - subtract using decimals as they make change [Regrouping required] ( Author - Kaye Maddox )
11. Shopping - What did each child buy with the money he had left over?
12. Shopping - Go on a shopping spree! Make sure you get back correct change.
13. Too Much Noise - determine the fewest number of coins needed to produce a given amount ( Author - Sandi King ) [not making change, but practicing a related skill]

Match the spoken, written, concrete, and pictorial representations of fractions with denominators up to ten (SPI 0306.1.4)

1. Bowling for Fractions - students click to color spaces, identify the fraction covered and get a bowling pin for a correct answer
2. Comparing Fractions - compare fractional parts with same denominator
3. Comparing Fractions - compare fractional parts with different denominators
4. Concentration Style Game - match the squares showing the fraction to the corresponding picture
5. Equivalent Fractions - concentration game style of matching fractions
6. Estimate Fractional Distance - watch Grammy carefully and estimate the fractional distance that represents where she jumped over the hedge
7. Fraction Bar - add a bar then break it into fractions, decimals, or percents
8. Fraction and Picture Match - in Fishy Fractions click on , then click on Begin Game . When the sign up screen comes up click to begin the game.
9. Fraction, Name, and Picture Match - in Fishy Fractions click on , then click on Begin Game . When the sign up screen comes up click to begin the game.
10. Flowering Fractions - understand common fractions by using model representations ( Author - Roseanne Phillips )
11. Fractional Distances - find Grampy by entering a fractional distance
12. Fraction Review
13. Fractions II
14. I Want My Half - understand the concrete and symbolic representations of fractions ( Author - Sandi King )
15. Identify With Circles - fraction practice where student types in numerator and denominator
16. Old Egyptian Math Cats Fractions - Add fractions like a true Old Egyptian Math Cat!
17. Shade - Shade in the correct amount of units to equal the fraction by clicking on the unit.
18. Tug of War Fractions - a multiplayer tug of war game for comparing fractions
19. Who Wants Pizza? - work through ten interactive pages on pictorial representations of fractions

Represent problems mathematically using diagrams, numbers, and symbolic expressions (SPI 0306.1.5)

1. Finding Multiple Ways to Solve a Problem - lesson plan
2. The Mathmatics behind maps - lesson plan and printable activity.

Identify and use vocabulary to describe attributes of two- and three-dimensional shapes (SPI 0306.1.6)

1. 2D Shapes - Move the mouse over the shapes to discover their properties
2. Buzzing with Shapes - play tic tac toe by identifying attributes of shapes.
3. Describe the Shapes - lesson plan
4. Two and Three dimensional shapes - online quiz

Select appropriate units and tools to solve problems involving measures (SPI 0306.1.7)

1. Measuring tools - select measurement tools for real-world measuring situations [ Works in Internet Explorer ] ( Author - Sandi King )

Express answers clearly in verbal, numerical, or graphical (bar and picture) form, using units when appropriate (SPI 0306.1.8)

1. Pictograph - Choose the data that belongs in the pictograph
2. Pictogram, Bar & Line - video Lesson -

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