The New License Plate Game (Computation/Patterns)

image from: stevemarshart.wordpress.com

Going on a road trip this summer?  One way to pass the time is playing the license plate game.  While you might know many variations of this game, here is one you may not have played.  When looking at the numbers included on license plates, see if you can find a relationship among them.  Can you add or subtract two of the numbers to make a third?  Can you multiply the first number by 2 to make the second?  Is there a pattern present (i.e. adding 3) between the numbers?

Check out these license plates and some of the relationships I saw.  Can you see any others? (All pictures below found on a list of 50 State License Plates.)  **Remember: Have FUN with this.  The relationships you see can be as creative as you would like!  Don't worry about using all of the numbers; the key is to use any math skills you know to find any relationships you can.  Have a great trip!

 

   7 - 3 = 4

3 x 8 = 24

                   

    4 + 5 = 9 and 8 - 5 = 3 and 5 - 1 =4

             

   4 + 6  and 9 + 1 both equal 10

         

8 subtracted from 9 equals 1

          

numbers in consecutive order

7 - 5 = 2 

 87 - 30 = 57

6 - 6 = 0

8 divided by 2 = 4 then 4 + 2 = 6

7 - 4 = 3 then 3 x 2 = 6

Age/Grade Guidelines:

This activity is accessible to most children from kindergarten/1st grade and higher.  Students of different abilities and ages can use any math skills they have to find relationships among numbers.

How many months have 31 days? (Calendar/Months of the Year)

This question came up on a recent episode of Jeopardy (yes, this is my second Jeopardy reference [see post from 3/18/15] - I watch it almost nightly) and no one even buzzed in to attempt an answer.  I understand most people might not know the answer by heart.  The reason I was able to answer immediately is because my daughter was born on the 31st of August.  So when I take Hannah's "monthly birthday" pictures (as mentioned in my post from 4/4/15), I can only actually do this on the 31st for seven months of the year, and just the last day of the month for the other five.

Knowing the months of the year (and how many days are in each one), as well as the number of days (don't forget about leap years!) or weeks in the year are prior knowledge needed to solve many math problems.  Here are two ways to help children learn how many days are in each month:

• Months of the year poem

• Months of the year knuckle trick
• As seen below, every knuckle represents a month that has 31 days and the gaps between the knuckles represent the months that have either 28/29 (February) or 30 days

Calendar Questions

Use the calendar below to answer the questions that follow.  Click HERE (or visit my "Worksheets/Solutions" page) for an editable/printable version of this exercise, with solutions.  Some of these questions are basic and some are more advanced.  Different groupings of these questions could be used for different grades/ages or to allow for differentiation for different abilities in the classroom.

• What day of the week does your birthday fall on this year?
• Do you know what day it will be next year?
• How many months are in a year?  How many weeks? Days?
• How many months have 31 days? How many months have 30 days?
• How many months have five Fridays this year?  Which one(s)?
• How many months begin on a Sunday this year?  Which one(s)?
• What do you notice about the dates in February and in March?
• Does this happen with any other months that fall in a row? How come it occurs in February and March?  Will this ALWAYS happen in February and March EVERY year?
• Take a look at the Saturdays in August.  What pattern do you notice in the dates?  Explain why this pattern occurs throughout the months in the calendar.

Other fun information/tips about the months of the year:

• Check out the video below to help your preschooler learn the months of the year

• If you've ever wondered about the endings that some months share (-ary, -ber), check out this website for some information about the meanings of the names of the months (and days of the week)

• Have children practice how to write the date (short, long, numerical format and with abbreviations) - here is a good outline as well as some practice worksheets

• How come February has 28 days some years and 29 days other years?  Read this information about leap years

Age/Grade Guidelines:

Learning the names of the months of the year is typically a preschool skill.  The calendar-related questions included in this post will be accessible to elementary and middle school students.

Kids in the Kitchen (Fractions/Multiplication)

clipartpanda.com

Baking and cooking are great ways to have children work with numbers (especially fractions) and measurement in a meaningful way.

inubugydenu.site11.com

Here are some possible discussions to have with children when baking/cooking:

• Discuss the different measuring cups and spoons you are using and compare the sizes
• Which cup is biggest? Which cup is smallest?  Is the 1/2 cup or 1/3 cup bigger?
• How many 1/4 cups of sugar would we need to make a whole cup?  Test it out!

• Discuss the ways to measure different ingredients
• What measuring tools are typically used for dry ingredients? Liquid ingredients?
• A liquid measuring cup usually has measurements for cups, as well as ounces
• Are there any other ways you have seen liquids measured before [thinking the metric system - liters (L), milliliters (mL)]?

imgkid.com

illuminations.nctm.org

• Discuss other measurements used in the kitchen
• In addition to cups, foods can also be measured in pints, quarts, and gallons (use Gallon Man, at right, to help remember the relationships between these measurements), or by weight (pounds and ounces)

• When looking at recipes, discuss how many servings or items the recipe should yield
• A cookie recipe might yield 2 dozen cookies
• How many cookies is that?
• What would we need to do to the ingredients in the recipe if we only wanted 1 dozen cookies? What about if we wanted 4 dozen cookies? 5 dozen?
• Sometimes there can be situations trickier than halving or doubling a recipe
• Recently, I made Maple Butternut Squash Puree.  The ingredient list is below on the left.  I needed to do some calculating to figure out how to make more servings for a large family dinner (see image below on the right).

• I had bought two butternut squashes at the grocery store, totaling 5.8 pounds according to my receipt.  Since the original recipe called for 3 1/2 pounds of squash I needed to figure out what to multiply each ingredient amount by in order to proportionally change the other ingredients in the recipe.
• I chose to convert 5.8 pounds to a fraction (see previous post from 4/4/15 for more on that!) and subtract 6 ounces (3 oz for each squash that are lost when peeled).  Then I rounded to the nearest half pound and subtracted to find that I had two extra pounds, meaning that I had 1 2/3 times the amount of squash that is called for in the original recipe.  I was then able to multiply each ingredient by 5/3 to find the new amounts I needed to measure for the larger recipe.

• HOME/SCHOOL ACTIVITY
• Have children find copies of their favorite recipes, then have them use those recipes to complete the Recipe Worksheet posted on my Worksheets/Solutions page.
• The numbers on the worksheet can be modified for different ages/grades or in order to differentiate for different abilities in the classroom.

Age/Grade Guidelines:

In Massachusetts, the Common Core State Standards have been adopted.  Multiplication of fractions is a 5th grade standard.  In order to change the amounts of ingredients needed in a recipe, children will need to be able to multiply a fraction or whole number by a fraction (CCSS.MATH.CONTENT.5.NF.B.4).  It would also help for children to understand that one can get a smaller product by multiplying by a fraction smaller than 1 (CCSS.MATH.CONTENT.5.NF.B.5.B).  Additionally, children show that they are able to solve real life math problems and show the math work necessary to calculate the answer (CCSS.MATH.CONTENT.5.NF.B.6).

How much does a 7 month old weigh? (Subtraction/Regrouping/Conversions)

keepcalm-o-matic.co.uk

My daughter, Hannah, recently had her seven-month birthday.  We have been taking a photo of her each month in her children's armchair with her giraffe stuffed animal, and putting them in a small album.  In addition to the picture, we record Hannah's weight and height, as well as some memorable moments from the past month.  Since we don't go to the doctor each month, I need to weigh Hannah myself in order to record her stats.  Our bathroom scale cannot measure such a light person, so we had to come up with another strategy besides sitting Hannah on our scale.  Another point to mention about a baby's weight and our scale, is that the doctor measures the baby's weight in pounds and ounces, while the scale measures by two tenths of a pound, in decimals.  From this scenario, I ended up coming up with several ways math skills are used to calculate Hannah's weight.  Below, I have grouped some questions by skill.  In the document on my Worksheets/Solutions page, there is a multi-step math problem incorporating the categories below.  Different groupings of these questions (or different numbers) could be used for different ages/grades or to allow for differentiation for different abilities in the classroom.

funny-pictures.picphotos.net

Logic/Problem-Solving

• I wanted to be able to weigh Hannah in between doctor's appointments, but did not have a scale that could measure such a light person.
• How could I use a regular adult bathroom scale to measure Hannah's weight?

Conversions

• At the doctor's office, the nurse measures Hannah in pounds and ounces (example: Hannah weighed 6 pounds, 12 ounces when she was born).  However, my bathroom scale measures in pounds, with decimals that go up by two tenths (0.2).
• How could I use the bathroom scale to measure in pounds and ounces?
• What is an important piece of information you need to know in order to be able to solve this problem?
• According to my scale, I weigh 139.4 pounds.  Approximately, how many pounds and ounces is this?
• According to my scale, if I weigh myself while I am holding Hannah, we weigh 156.2 pounds total.  Approximately, how many pounds and ounces is this?

Subtraction with REGROUPING

(previously referred to as "borrowing")

• Using the decimal numbers given by the scale, how much does Hannah weigh?
• Using the conversions above, approximately how much does Hannah weight in pounds and ounces?
• Are the two answers above equivalent?  Why or why not?
• Check out THIS VIDEO for a tutorial on regrouping, in the base-10 number system, as well as with pounds & ounces, feet & inches, and with mixed numbers

**You can find an editable/printable version (using Word) of the above questions, along with solutions, on my Worksheets/Solutions page.

Age/Grade Guidelines:

In Massachusetts, the Common Core State Standards have been adopted.  Subtraction with regrouping is introduced in second grade (CCSS.MATH.CONTENT.2.NBT.B.7), and an algorithm for this is solidified by the end of fourth grade (CCSS.MATH.CONTENT.3.NBT.A.2, CCSS.MATH.CONTENT.4.NBT.B.4).  The skills necessary to complete the conversions in this scenario are introduced in fourth grade (fraction/decimal equivalence [CCSS.MATH.CONTENT.4.NF.C.6], multiplication with fractions [CCSS.MATH.CONTENT.4.NF.B.4]) and solidified during elementary school.  
The multi-step math problem on the Worksheets/Solutions page uses skills learned in elementary school; however, seeing as these skills need to be synchronized to reason about and calculate solutions, the problem (as written) would be appropriate for a challenging upper elementary, or middle school assignment.  As previously mentioned, different groupings of these questions (or different numbers) could be used for different ages/grades or to allow for differentiation for different abilities in the classroom.

Final Jeopardy: Numbers (Prime/Composite)

Did you answer Tuesday night's Final Jeopardy problem correctly?  If not, you are not alone.  Colin, who had a considerable lead during much of the show, lost by a narrow margin when he answered it incorrectly.  If you didn't see it, give it a try now:

THIS 2-DIGIT NUMBER IS THE SMALLEST PRIME NUMBER WHOSE DIGITS ARE BOTH THEMSELVES PRIME NUMBERS

Alright, what have you got?  Scroll down to see if you got the correct solution.  If you think you need a little refresher on prime numbers first, use the following resources for review/practice.

A PRIME NUMBER is one that has exactly two factors, 1 and itself.  The first few prime numbers are 2(the only even prime), 3, 5, 7, 11... 

If we are talking about prime numbers, we should discuss composite numbers as well.  A COMPOSITE NUMBER is one that is not prime; it can be divided evenly by numbers other than 1 and itself.  The first few prime numbers are 4, 6, 8, 9, 10...

***SPECIAL CASE: the number 1 is neither prime nor composite***

For more information on prime and composite numbers, check out this information from Maths Is Fun.  There is a quiz at the bottom of the page that you might find helpful for some extra practice.  If prime numbers interest you, here are some advanced concepts related to primes.  

Another great resource for more challenging problems related to this concept is the website for the Intermediate Math League of Eastern Massachusetts (IMLEM).  Check out the "Categories/Topics" section to see which topics are covered in each category for every meet.  Then look through "Old Competitions" for PDF's of meet questions, along with answers and explanations.

Here are some fun prime/composite questions from past IMLEM competitions:

• What is the sum of all the prime numbers between 40 and 60 ? (Category 3, Number Theory, Meet #1 - October, 2014)
• Two of the four prime factors of 17,017 are 13 and 17. What is the larger of the other two prime factors ? (Category 3, Number Theory, Meet #1 - October, 2013)
• Two prime numbers p and q have a sum of 38. Given that p > q, find the value of p – q. (Category 3, Number Theory, Meet #1 - October, 2012)
• Thinking of the natural numbers from 2 to (and including) 20, what is the positive difference between the sum of all composites and the sum of all primes? (Category 3, Number Theory, Meet #1 - October, 2010)

**************************************************************************************************************

Final Jeopardy Answer: THIS 2-DIGIT NUMBER IS THE SMALLEST PRIME NUMBER WHOSE DIGITS ARE BOTH THEMSELVES PRIME NUMBERS

Final Jeopardy Question: What is 23?

Explanation and strategy:  Considering the problem and what we know about prime numbers, a systematic way to approach a solution would be to consider each two-digit number starting at 10 to determine whether it meets the necessary conditions.  A common error regarding primes (and the one Colin made) is considering 1 a prime number - this is why Colin (and the winning contestant first wrote this, then scratched it out and wrote the correct answer) gave the answer of 11.  Since we know 1 is not a prime number, we can skip to 20 and consider whether 20 and the numbers that follow have more factors than just one and itself.  You will quickly arrive at 23, notice it is prime, and that 2 and 3 are also prime.

**************************************************************************************************************

Age/Grade Guidelines:

In Massachusetts, the Common Core State Standards have been adopted.  Work with factors (and multiples), primes and composites is part of the fourth grade standards. (Find all factor pairs for a whole number in the range 1-100. Recognize that a whole number is a multiple of each of its factors. Determine whether a given whole number in the range 1-100 is a multiple of a given one-digit number. Determine whether a given whole number in the range 1-100 is prime or composite.) - CCSS.MATH.CONTENT.4.OA.B.4

Pi Day Bonus!

Happy Pi Day, everyone!

I came across this article about MIT admissions decisions being released today (3/14/15) at 9:26 am - the first 8 digits of pi!  This article also mentions "tau," two times pi, and how MIT typically uses these two numbers when sending out admissions decisions emails.

Also, please check out my blog post below for some great ways to celebrate Pi Day!

Happy Pi Day!

Image from: mathematicianspictures.com

Each year, March 14th brings the celebration of Pi Day.  This year, 3/14/15, is even a little more special.  Pi (represented by the greek letter shown to the right) is an irrational number which is equivalent to the ratio of the circumference of a circle to its diameter.  This ratio can be simplified to approximately 22/7 or 3.14159...  This is why Pi Day is celebrated every March 14th (since 3/14 are the first three digits of pi) and this year is extra special since 3/14/15 are the first five digits of pi.


This post is a week early in order to give you time to prepare for your Pi Day celebrations.  Here are some ways you could celebrate Pi Day at home and/or in the classroom:

• bake a pi(e) or decorate some other Pi Day treats
• baking is a great way for children to practice following directions, measuring, and working with fractions

Image from: geek.com

Image from: community.babycenter.com

• listen to or write your own Pi Day song
• here is one of my favorites


• dress up in Pi Day attire
• you can find a ton of great options online from onesies (like the one below that Hannah will be wearing) to t-shirts and coffee mugs

Image from: etsy.com (knitwhitscouture shop)

Image from: cafepress.com

• read a book about pi
• here is one I have used in the classroom - with Prime shipping you could get it from Amazon in plenty of time!

Image from: amazon.com

• complete an activity to learn more about pi
• this is an activity I have used (parts of) in my classroom for several years (that accompanies Sir Cumference and the Dragon of Pi, above) - you could also complete part or all of it as an activity at home

• memorize as many digits of Pi as you can
• here are ONE MILLION of them, to get you started!

• How do you celebrate Pi Day?  Share your Pi Day traditions in the COMMENTS section below!

Age/Grade Guidelines:
In Massachusetts, the Common Core State Standards have been adopted.  Pi is introduced in 7th grade when students use pi in formulas to calculate the area and circumference of circles.  Students learn about irrational numbers, in general, in 8th grade.  (CCSS.MATH.CONTENT.7.G.B.4, CCSS.MATH.CONTENT.8.NS.A.1)
But remember, Pi Day can be celebrated by mathematicians of all ages!

What a difference! (Temperature/Integers/Absolute Value)

It has been quite the winter in the Boston area.  So far, we have had 101.8 inches of snow this winter; the second snowiest winter of all time!  Along with snow, there have been some extremely cold temperatures, often measuring below zero when waking up in the morning.  Sometimes these temperatures fluctuate a lot during a given day or over the span of a week.

Weather, especially negative temperatures, presents a great opportunity to talk to kids about integers, absolute value, and the difference between temperatures.  Some children might benefit from using number lines to help them work with integers.

graphic courtesy of: myfoxboston.com

Given the above graphic from a recent weather forecast, there are many questions students can answer (or ask!) from the given seven-day forecast.  Some of these questions are more basic, and some are more advanced.  Different groupings of these questions could be used for different ages/grades or to allow for differentiation for different abilities in the classroom.  Some children might benefit from the use of a number line while others might have other strategies for answering the questions.

• What is the highest temperature during the week?  What day is the temperature that high?
• What is the lowest temperature during the week?  What day is the temperature that low?
• What is the difference between the high and low temperature for Saturday? For Thursday? For Tuesday?  Explain, in writing or in conversation, how you calculated each temperature difference?
• What day has the largest temperature difference? What is the temperature difference?
• What day has the smallest temperature difference? What is the temperature difference?
• What is the difference between the highest and lowest temperatures of the whole week? Write a subtraction number sentence to illustrate this difference.

**You can find an editable/printable version (using Word) of the above questions, along with solutions, on my Worksheets/Solutions page.

Age/Grade Guidelines:

In Massachusetts, the Common Core State Standards have been adopted.  Integers & absolute value are introduced in grade 6.  Some of the harder questions above would be suitable for 6th grade or higher, while others could be discussed with younger children as well.  If negative integers were omitted, many of the questions above could be solved by children as early as 2nd grade. (CCSS.MATH.CONTENT.6.NS.C.5, CCSS.MATH.CONTENT.6.NS.C.7