Give us a call : (425) 328-1024
Give us a call : (425) 328-1024
Summer’s coming – time to lounge around the pool, sleep in, and meet up with friends at the park. Three months devoid of homework, calculators, and pop quizzes. School seeps in only in the form of a little bit of summer reading. Life is good.
But what about all those skills we learned last year? Unfortunately, studies show that students lose about 2.6 months’ worth of grade level equivalency in mathematical computation skills. So for every month they spend eating popsicles at the pool, they loose a month of math facts! Regardless of socioeconomic status, the areas of greatest loss are in factual or procedural knowledge. Ouch!
Do you have kids? You can help curb some of that loss, and if you’re sneaky, your kids won’t even know they are learning! Parenting Magazine wrote a great piece on tips to stop summer learning loss (you can read the whole article here: http://www.parenting.com/article/stop-summer-learning-loss?page=0,1) . My favorite tip is to “keep it personal”. Math learning in the summer doesn’t have to be drilling math worksheets- make it fun, and do the math with your kids. Sharing the experience with them enhances their learning in real ways. Show them how you use math every day: adding up prices in the store; doubling a recipe in the kitchen; or deciding when to leave to get to the movie on time. You can build strong positive relationships with math, easing the transition into school next fall.
Here are a few creative activities to get kids hands on, and sneak in some math understanding!
Puzzle 1
I have some pencils and some jars.
If I put 4 pencils into each jar I will have one jar left over.
If I put 3 pencils into each jar I will have one pencil left over.
How many pencils and how many jars?
Puzzle 2
Again I have some pencils and some jars
If I put 9 pencils into each jar I will have two jars left over
If I put 6 pencils into each jar I will have three pencils left over
How many pencils and how many jars?
Check back for the answer tomorrow!
Gaylord Nelson, a senator from Wisconsin, declared Earth Day on April 22, 1970. The idea was inspired by the effect the student anti-war movement was having in the US. He proposed a national environmental “teach-in” to be observed by all school campuses across the US, to bring attention to the environmental catastrophes and degradation at hand. Twenty million people participated in that first Earth Day (Wikipedia).
Now, the holiday has been touted as the largest secular holiday in the world, celebrated by over a billion people in 192 countries. It is used as a day of action, a call to change human behavior and provoke policy changes.
There are so many ways to celebrate earth day at school; plant a garden, clean up the schoolyard, do a project on a rainforest, make pine cone bird feeders, study the food chain, and how extinction or overpopulation affects it.
Talk about Earth Day, and why we should celebrate it. Discuss the lesson plan: to collect and record trash, make deductions about the trash collected, develop strategies to decrease the amount of trash, and take action on those strategies. Create a record sheet with categories of types of trash students might find.
Working in pairs, have students collect trash from a nearby area and record the types of garbage they find. (*note: have students bring in gardening gloves for protection, and collect garbage in baskets or boxes, so not to waste partially filled garbage bags).
When the clean-up is over, have students compile the data from their record sheets, and create a classroom report of their findings. Students should identify the major sources and types of litter and figure out how much of the litter is actually recyclable.
Work with other classrooms, or other schools, to increase data collection (and clean-up!) compare what was collected at different sites or by different classrooms.
Have the students brainstorm ways in which they can work with local people and organizations to decrease litter. Some suggestions include: writing letters, adding trashcans, making posters, maybe even presenting their findings at a city council meeting. Have the students carry out the strategy, and follow its success throughout the year.
The workday is 9-5, but the school day is 8-3. Where do all those kids go in the afternoon? One of the best answers is “to an afterschool program”. Educational after school programs have been shown to have a huge positive impact on learning, behavior, attitude, performance, attendance, aspirations, and discipline (Secrets of Successful After School Programs: What Research Reveals, Harvard, http://www.uknow.gse.harvard.edu). They do this by providing opportunities for students to explore new topics and practice old ones in a positive, hands-on, and differentiated learning environment.
The National AfterSchool Association (NAA) is a strong advocate for these augmented learning experiences. The Association recognizes the positive affect after school programs can have on students’ development. The NAA is “working to assure that the vision of high-quality learning experiences for all children and youth both in and out of school becomes a reality” (naaweb.org). Next week in Indianapolis, the NAA is holding their annual convention (the only national convention for afterschool professionals) for those involved or looking to be involved in after school enrichment. MANGO Math will be there, along with STEMfinity, illustrating how MANGO Math crates and totes are a great addition to any after school program, and learning how we can be involved with bettering our students’ afterschool education. If you’re in Indianapolis, stop by the booth to say hello and get a free deck of MANGO playing cards!
Here is am example of a MANGO Math game that reinforces hard math skills, encouraging students to practice deductive algebra reasoning.
The NCAA tournament provides a great real-world math learning opportunity for any age. From playing a mini-basketball game in the classroom and adding up the score to calculating how many games a team should win based on their seed and RPI, every classroom can benefit from this math-heavy popular sports event.
To help students interact with the teams, put up a map of the country with pins for each team in the tournament. Have students remove pins as the teams are knocked out.
Thanks to Mark Colgan for the below March Madness math problems and activities.
Shooting Hoops
Work in groups of four to collect data for the following table.
You will need:
Each person takes 5 shots at the basket. For each shot, you may choose to take a 1-pointer (from 5 feet), a 2-pointer (from 10 feet), or a 3-pointer (from 14 feet) in any combination. Record the result of each shot in your table. When finished shooting, record your totals on the overhead or chalkboard with the rest of the class.
1. (1-pt) What percentage of 1-pointers were made by our class? How about 2-pointers? 3-pointers?
2. (2-pt) What percentage of overall shots were made by our class?
3. (3-pt) What strategy appears to be the best: shooting all 1-pointers, or all 2-pointers, or all 3-pointers?
March Madness Bracket word problems
(there is a link to answers at the bottom of the page)A. (1-pointer) If there are 64 teams, how many games are played in the entire tournament?
(2-pointer) If they played a double-elimination tournament, how many games would be played?
(3-pointer) If they played a round-robin tournament (each team played every other team), how many games would be played?
B. (1-pointer) How many games must a team win in order to win the championship?
(2-pointer) How many games would a team have to win if there were 256 teams in the tournament?
(3-pointer) If your team is ranked 10th with an RPI of 12, how many games would you expect to win? (this one will need background info on how seeds work and what the RPI is. See “answers” for an overview)
C. (1-pointer) How many of the 64 teams lose their last game?
(2-pointer) How many teams are eliminated after 3 rounds of the tournament?
(3-pointer) What percentage of the 64 teams are left after 4 rounds?
D. (1-pt) If every team has the same probability of winning the championship, what is the probability your team will win?
(2-pt) If the Big Ten gets 7 teams in the tournament, what is the probability that a Big Ten team will win?
(3-pt) If the probability IU will win each game is 1/2, what is the probability IU will win the championship?
Fill out Brackets
And of course, have your students fill out brackets and follow the progress! You can have them choose to follow Men’s or Women’s or both. As the tournament progresses, ask them questions about how they are doing compared to the rest of the class, and to the average. Have them declare a “favorite” team at the beginning of the tournament to follow closely, keeping track of scores and statistics to share.
March 14 (3.14) is just a few days away. Here are some creative activities to celebrate the day and reinforce some important math skills. Thank you to Mrs. Burke, who has put together some wonderful Pi Day activities, some of which we have linked to below.
and take measurements of the circumference and diameter (it helps to lay the measurements out flat to visualize the proportion of circumference to diameter)Just 9 days to go until #PiDay !
Write a poem, or a story, or even a song about Pi!
Here is a great Pi Day song for you written and sung by Alfa:
Reversibility is an underlying concept in mathematical understanding. At a young age, this idea can manifest itself in the understanding that if there is a tall skinny glass of milk, you 
can pour that milk into a short, wide glass and then back into the tall skinny glass and it’s original properties will be restored – in other words, the glass of milk will look just the same as when you started. As students advance, they will be able to apply this simple visual understanding to more complicated and abstract situations.
6 + 7 = 13 is the same thing as 7 + 6 = 13. And if that is true, then 13 – 7 = 6 and 13 – 6 = 7. This is also called the Commutative property, the idea that addends (numbers to be added) can be added in any order and the sum remains the same. Students will have an easier time grasping orders of operation, a crucial step in solving complex algebraic equations, if they have a strong foundation in the concept of reversibility.
Here is a game to practice Reversibility:
On George Washington’s 281st birthday, we posted the following math problem:
George left his home in Mount Vernon one morning, and on the way to work decided to stop and buy a few gifts for his wife, Martha. He bought her a checkerboard that cost 2 shillings, 6 pence, 1 farthings and a fancy new dress that cost 1/2 guinea and 9 shillings. He gave the shopkeeper 1 pound and 1 guinea.
Here’s how we answered it:
The checkerboard cost 2 shillings, 6 pence, 1 farthing
2 shillings = 24 pence + 6.25 pence = 30.25 pence
The dress cost 1/2 guinea and 9 shillings
1/2 guinea = 10 shillings 6 pence = 126 pence
9 shillings = 108 pence
Cost of dress in pence: 234 pence
Total cost: 30.25 + 234 = 264.25 pence
The president gave the shopkeeper 1 pound and 1 guinea
1 pound = 20 shillings = 240 pence
1 guinea = 21 shillings = 256 pence
240 + 256 = 492 pence
His change would be:
492 – 264.25 = 227.75
That can be made with 1 half guinea, 2 shillings, 5 pence, 1 halfpenny, and 1 farthing.
Today is George Washington’s birthday! He would be 281 years old today. Here are some interesting facts about George Washington (from buzzle.com):
Our quarter has a picture of George Washington on it. But George Washington didn’t know that – he wouldn’t even know what a quarter was! When Washington was president in the late 1700’s, the currency in use was a British system full of pence, shillings, and farthings. George Washington’s face did not appear on the quarter until 1932! It was meant as a commemorative model to celebrate his bicentennial, but instead it became the long-lasting quarter design (Wikipedia.com).
Let’s do a math puzzle using the currency Washington would have used.
George left his home in Mount Vernon one morning, and on the way to work decided to stop and buy a few gifts for his wife, Martha. He bought her a checkerboard that cost 2 shillings, 6 pence, 1 farthings and a fancy new dress that cost 1/2 guinea and 9 shillings. He gave the shopkeeper 1 pound and 1 guinea.
Check back tomorrow, we’ll show our work and give the answers!
California After School Resource Center accepts Mango Math curriculum
into state-wide after school programming
Snohomish, WA – Jan 31, 2013 – After an extensive review process, The California After School Resource Center (CASRC) has accepted Mango Math curriculum into their repertoire of quality after school educational tools. Mango math’s supplemental curriculum is filled with games and activities that are fun and engaging, encouraging mathematical development in students kindergarten through eighth grade. These activities will now be available to 5,000 California after school programs through CASRC’s comprehensive resource library. Part of CASRC’s mission is to support quality after school programming state-wide with examined instructional materials to promote literacy and mathematics skills in all grade levels (californiaafterschool.org/about). All materials pass through a four-month review process by the Center’s Material Review Board, which is comprised of educators and after school staff throughout California.
After school programs can enable students to gain confidence and understanding, while providing a safe, positive learning environment. Students have the opportunity to explore topics in depth, develop conceptual understanding, and use new tools to stay engaged in learning. According to one study focused on after school programs for low-income elementary and middle school students, children that regularly attended one of 35 programs were academically far ahead of their peers. In addition to higher test scores, the participating students had better work habits, social skills, and behavior. Deborah Lowe Vandell, PhD., Chair of the Department of Education at University of California at Irvine, emphasizes the study’s results: “These findings underscore the importance of high quality afterschool programs and activities for both elementary and middle school youth.” (http://www.education.com/magazine/article/Afterschool_Programs/)
As part of the CASRC’s resource library, Mango Math will have the opportunity to reach thousands of California elementary and middle school students. After school participants will have access to Mango Math’s unique game-based activities and lessons designed to engage students, build confidence, and inspire mathematical dialogue. “It is just so exciting to know that students will have more opportunities to do math,” says Mary Curry, founder and owner of Mango Math Group. “Our activities are engaging and fun. Through this opportunity we hope to encourage more students to pursue math in high school and college”.
No matter what grade level or which curriculum standard is in place, patterns are a crucial aspect of math learning. They are a unifying theme- from creating separate piles of yellow and green blocks to understanding the role of “y” in a multi-variable equation. In fact, there are patterns everywhere we look – in shapes, time, language, desk arrangements, buildings, calendars, etc.
But we’ll keep it to mathematical patterns for now. Specifically- number patterns. Number patterns are important because they allow students to make predictions and generalizations, which helps them generate solutions to broader and more complicated problems. Recognizing patterns in numbers is a precursor to recognizing patterns in functions, which are simply rules that define the relationships between various quantities (learner.org).
And so- with moms standing in the aisles of Halmark, wavering between “my little pony” and “care bears” 100-pack valentine cards, let’s work on a Valentine-Card Number-Pattern Math-Problem!
If there are 24 students in class and each student gives one valentine to every other student, how many valentines will be given?
Every grade level can work on this problem, because there are many different ways to get the answer. For younger students, simplify by asking them to start with a smaller number- 3, perhaps- and count or draw the relationships. With 3 students there would be 6 valentines:
A – B
A – C
B – A
B – C
C –A
C –B
How about with 4 students? Create a chart showing the pattern as the number of students increases.
More advanced students can use multiplication to find the answer. With 3 students, each student would hand out two valentines. 3 students x 2 valentines = 6. What about with 4 students? 8? 24?
Bring it to life! Ask your students to each bring one valentine for every other student in class. Have them distribute them, then count them and add them up. Did it work?
A more complicated version of the question can be asked of older students with valentine hugsinstead of valentine cards. If there are 24 students in class and every student hugs every other student once, how many hugs will be given?
Ask them to start by indicating the pattern-
A hugs B
A hugs C
B hugs C
For a classroom of 3 students, there would be 3 hugs. (notice we did not include C hugs B, because that hug has already been counted)
What is the difference between the cards and the hugs? Why?
Ask them to find the formula in the pattern, and explain how they got there. Since they don’t give valentines to themselves, for any number of students, n, each student gives out one less valentine than there are students. That gives us n(n-1), but stopping there would double-count the hugs (because B hugs C is the same as C hugs B). So we divide by two: n(n-1)/2
In a class of 24 students, there would be 24(24-1)/2 or 276 hugs!
Happy Valentine’s Day!
I posted that question on Facebook and had the response that it meant a “headache” and then some people posted that they liked that response. Which I think is actually the first thought of many a teens, parent of a teen and possibly some teachers. Why is that? And what can we do to change that?
This year I am dedicated to trying to help inform educators, parents and child care providers about fun and engaging ways to help children, in the elementary grades, with algebraically thinking with the hope that this starts a math revolution…. well maybe at least prevent a math revulsion.
Algebra is the “gateway” to higher education. Failure rates in algebra are staggering is schools district across the country. This lack of success is disproportionately high among higher needs students and impacts high school graduation rates. Some schools have looked at having students take algebra over a two or three year period or having double periods of algebra but the success rates has not changed.
There are a few key algebraic concepts that we want student to understand, even in the earliest grades, and each month we will touch on one of these key components and give examples how to implement it in your classrooms, afterschool programs or homes.
First Key Component is Patterns: Patterns exist in math all of the time. We need to train students to look for patterns and to expect to find patterns in all math work. Starting in kindergarten, students should frequently make and find patterns. As they do this they will become more skilled with basic problems, which will prepare them to find patterns in their natural world, notice growing patterns, and make generalizations to harder problems. When student find pattern in smaller problems, they are learning mathematical concepts that will equip them to solve more complex problems such as proportionality.
Here are two lessons on patterning. Check our website to see what other algebraic thinking lessons we offer.
Fifth Grade Lesson Adult Information Fifth grade lesson student directions
First Grade Lesson Adult Information First Grade Lesson Student Directions
