Summer is here...Yippeee! Today I listened to a news story discussing how much time our students have off due to summer break. From kindergarten to 5th grade, they have 15 months of summer! That's a ton! Summer is an important break from "book" learning, but there's no need for students to slide.

Turn this into the Summer of Measurement. Have students cook, doubling recipes or cutting them in half. Give them only a 1/4 and 1/3 cup measuring cup so they have to multiply fractions. Have them weigh ingredients. Try a measurement scavenger hunt, looking for metric and customary measurements.

Taking a vacation? Let them track mileage, figure out miles per gallon, and use maps. Have them use an analog watch to keep track of time and estimate arrival times or elapsed time. If you need to arrive at 2:30, and it takes 4 hours, what time do you need to leave? If you have children of different ages, you can differentiate the problems. An older child can get the same problem, but be told you need to arrive at 2:30 and have to drive 240 miles, at about 60 mph.

Your phone most likely has a great app to help them with walking, biking, or driving (you, not them!) They will learn how far a mile is only when they have multiple experiences.

Don't forget to practice your math facts! Also an important step in preventing summer slide. Enjoy the summer and make math an everyday part of your break.

Just saw this on YouTube...worth watching, although it's about the differences based on socioeconomics.

Summer Learning Loss

# Digging Deeper Into Math

## Monday, June 9, 2014

## Monday, May 26, 2014

### Real Life Problems

What happens when math people get together for dinner? We see dinner as a series of real-life problem solving! First, I'll give you the problem--division of a fraction by a fraction. It's often hard to think of real-life examples of this type of problem. This problem is a good one to solve concretely (with manipulatives) or pictorially (with model drawing.) An added bonus;;; This no-bake pie is a refreshing summer dessert!

Sharon wants to make a Lemonade Ice Cream Pie. The recipe calls for ½ gallon of ice cream, but when she gets to the store, she finds that ice cream containers now come in only 1.5 quart containers. How many containers does she need to buy, and how much does she need to use, to make the pie?

Recipe for Lemonade Ice Cream Pie

2 Oreo-cookie pie crusts

1/2 gal. vanilla ice cream, softened

1 container (12 oz.) frozen lemonade concentrate (either pink or regular), completely thawed

Chocolate sauce

Using a mixing spoon or a whisk, combine the ice cream and lemonade. Pour into the pie crusts. Freeze overnight. Drizzle with chocolate sauce before serving.

Notes: It seems to be fine to let the ice cream get almost liquid, which makes it a cinch to mix. And you can thaw the lemonade right in the can; just open it when you can squish the can.

Labels:
division of fractions,
fractions,
Model Drawing,
recipes

## Monday, May 19, 2014

### Is it Enough?

I've been so busy that I haven't sat down to blog more about my trip to Singapore. It's coming, I promise. Another experience that had quite an impact on me was teacher response to student work. In every class, we watched students work in happy, noisy groups. It was rare we saw a student off-task. (Honestly, I can't think of a time we saw someone goofing off, but there must have been one!!)

When students thought they completed their work and approached the teacher, we never heard them ask if the answer was correct. Instead, the more common question was, "Is this enough?" In one class, we watched a group of boys given a very challenging problem. Three times they approached the teacher to ask, "Is this enough?"

Each time, the teacher looked at them and responded, "It it enough?"

After the third time, one of the boys looked at his partners and said, "If the teacher asks 'is it enough,' it isn't enough."

How can we get our students to focus on the process, not the product? Isn't that what the NCTM Math Practices and CCSS are asking us to do? Enjoy these examples of journals from Primary 2 (second grade) journals. I think they show enough!

When students thought they completed their work and approached the teacher, we never heard them ask if the answer was correct. Instead, the more common question was, "Is this enough?" In one class, we watched a group of boys given a very challenging problem. Three times they approached the teacher to ask, "Is this enough?"

Each time, the teacher looked at them and responded, "It it enough?"

After the third time, one of the boys looked at his partners and said, "If the teacher asks 'is it enough,' it isn't enough."

How can we get our students to focus on the process, not the product? Isn't that what the NCTM Math Practices and CCSS are asking us to do? Enjoy these examples of journals from Primary 2 (second grade) journals. I think they show enough!

## Wednesday, March 26, 2014

### School Visits in Singapore Day 1

**http://tinyurl.com/m7tsc7j**is being updated to meet the Ministry of Education's requirement that all schools run on a single schedule within a few years. The old school is quite beautiful. The school's enrollment is nearly 2400 students, with grades 4-6 coming from 8-1 and grades 1-3 coming from 1:30-6:30. We were greeted so warmly by Dr. Chin Kim Woon, who talked about the joys and challenges of being a principal in Singapore.

This building is used as rotating temporary housing as schools are being updated. This is one section out of 4!!

We were privileged to see three lessons taught to two groups of students. The first was a science lesson taught to sixth graders b Mrs, Fiona Soh, a master teacher. As we entered the room with the teacher, the students stood up. The prefect said, "Bow." The students bowed in unison and said, "Good morning Mrs. Soh." After she introduced us, we got a bow and a choral welcome also. It showed such respect!!

The content of the lesson was interesting and engaging. More important was how it was taught, Mrs, Soh gave some very brief instructions on data that was to be collected. Eliza Thomas and I were so impressed at how the students worked together on how they would organize their data Each group had different ideas and charts, but all were very neat and clear. All students had journals, pencil boxes, and white out!

The mood was very relaxed and light as the students got to work. This class is the gifted class, so it is quite small by Singapore standards--only 18 students. but they were all on task and engaged.

Then the teachers moved to save instructional time and we saw a math lesson with the same students by Mrs Ngoh Poh Sze Wei. First, they were asked to explore the relationship between two angles within a circle on a computer. Then, using only a piece of paper and a ruler, they were asked to find the exact center of a circle.

Students got right to work and would excitedly approach the teacher if they thought they had the answer. Usually, her response was, "Are you sure?" or "Is that enough?" Eliza and I had to cover our mouths when one boy said to another, "If she asks if it's enough, it isn't."

We were so impressed with how the students persevere and work together. Students would share their answers with the group so others could learn from them. It really exemplifies what we're trying to get to with the CCSS Practice Standards.

The third lesson, taught by Mr. Clifton Lim, was a fill the bucket lesson using a computer program, with gifted 4th graders. I must admit we were happy to go the air conditioned computer lab!! This lesson was very challenging to the students but they worked together and were gently guided by the teacher. The lesson was not completed but they agreed to continue and discuss it again later in the week, after they'd had more time to explore the concept. as we left the class, they bowed and said, "Thank you for teaching us."

We ended the day with a discussion with one of the Vice Principals, Ms. Cheryl Chee about the challenges in the Singapore Schools. She talked about how hard they are working to move away from summative testing and its pressures and develop portfolios. We also talked about teacher evaluation, professional development, and improvement plans. It was a packed morning and we learned so much. We are so thankful to the staff at Tao Nan School!

Labels:
GATE,
Gifted Education,
Singapore,
Singapore Math,
testing

## Saturday, March 1, 2014

### Fascinated by the Iditarod!

I've always been fascinated by the Iditarod. So are your students. And there's so much great math involved. The dogs eat 200,000 calories a day. How many calories will they need over the course of the race? How many per dog? How many miles do the mushers have to cover? How many miles do they need to cover per day to finish in 9 days? 10 days? Compare highs and lows and find the difference. Compare to your city. Follow the Iditarod and ask your students to write their own math stories. Iditarod.com

Labels:
Iditarod,
math stories,
Real life connections,
story problems

## Thursday, February 27, 2014

### Don't Be So Helpful!

I had the joy of spending a day learning from Dr. Yeap Ban Har, from Singapore, again last week. I've seen him many times and always learn something new. This time he talked about the importance of social learning for our students--how they can learn from each other with less help from us.

I use these strips for lots of activities, including vocabulary, divisibility rules, rounding and estimating, ordering, etc. But this was a task for teachers.

Students have built the number 3,246.

You've asked them to find the number that is 300 less than this number, but they're struggling. What

**questions**can you ask the group to help move them? And can you sequence your questions from the least helpful to the most helpful? We tend to jump in and tell students what to do and rescue them. As we work to build more perseverance, we need to be a lot less helpful.
These are the questions a group in TX came up with. How would you sequence them from least helpful to most helpful? What other questions would you add? It's interesting to take the time to think through our questions. To help our students more, we need to be a lot less helpful!

I've been working with place value strips for a long time. ( I'm very excited about Crystal Spring Book's new student-sized strips. They come in sets of 10 or 30. http://www.crystalspringsbooks.com/student-size-4-digit-place-value-strips-small-group-set.html .)

## Monday, February 17, 2014

### What is Number Sense?

We throw the
term around but rarely define it. I had
two experiences this week that help bring the concept into sharper focus.

I was
fortunate enough to work with second graders on Oahu, in a Hawai’ian language
school. I had beansticks and bundles
and leftovers with me. After the keiki
(children) became familiar with beansticks, I posed this question to them; “Build
the number that is 1 beanstick and 15 beans.”

All children
were able to figure out it equaled 25. But some children built it with two beansticks
and 5 loose beans and some did exactly what I’d asked. Then we had to discuss if both answers were
correct and equal. It led to a lively
discussion and some very strong opinions!

It was
developmentally interesting to see the children struggle when we moved to
bundles and leftovers. Since they couldn’t
see the 10s as clearly, building one bundle with 20 ones was much more
problematic. The children spent a great
deal of time taking the bundles apart, counting 10s, and putting them back
together. Obviously, they didn't trust my
bundling skills!!

My second
experience was sitting in a workshop with Dr. Yeap Ban Har, our favorite expert
from Singapore. He talked about number
sense as a complete understanding of number bonds. Our children need to understand 25 is 20 + 5,
but also 10 + 15. Without this
understanding, they won’t be prepared for regrouping. As they get older, that understanding needs
to generalize. 3/5 is 2/5 + 1/5. If one dividing 351 by 3, it doesn’t help
much to break the number into 300 + 50 + 1.
Number sense means the child understands that 300 + 30 + 21 is a much
more logical way to decompose the number.
Ban Har will be joining us at our National Conference for Singapore Math
on July 9-10. http://sde.com/nationals/2014/

Try posing
some number sense questions to your students and then give them some time to
struggle with the concepts. Don’t jump
in and help too soon!

Labels:
2nd grade,
Dr Yeap Ban Har,
number bonds,
number sense,
Singapore Math

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