Fifth Grade - November 3rd - 7th, 2008

Fifth grade students are finishing up their unit on addition and subtraction. They are using the strategies they have already explored (see blog entry on October 22nd) to solve problems with larger numbers like 69,703 - 55,675.

Fifth graders will also be assessed on how well they know their division facts. Students should be able to solve 30 problems in about two minutes. Students who are not this proficient with their facts should practice at home.

Fourth Grade - November 3rd - 7th, 2008

4th graders are beginning a unit on 2-D geometry and measurement. This week we will study linear measurement using both the U.S. system and the Metric system. Students will identify objects they can use as benchmarks to help them estimate lengths. For example the length of a piece of notebook paper is about 1 foot. Students will explore rulers, yardsticks, and metersticks and use these tools to measure the length of the classroom and other objects. They will also explore the idea of perimeter and measure different items in the room. Finally, students will design a path in the school that is 100 feet long. Most students (and many adults) find it difficult to picture 100 feet. This will be an eye-opening experience.

Third Grade - November 3rd - 7th, 2008

This week, third graders are focusing on how to find the difference between a 2-digit number and a number over 100 (128 - 36). Students have already worked on finding how far a number is from 100. Students should be able to reason that 36 is 4 away from 40 and then 60 away from 100 (36 + 4 = 40 and then 40 + 60 = 100). So, 36 is 64 away from 100 (36 + 4 + 60 = 100). Students are now reasoning that if 36 is 64 from 100 and 128 is 28 from 100, then the difference between 36 and 128 is 64 + 28, or 92.

Second Grade - November 3rd - 7th, 2008

Our second graders are working on adding three numbers at a time. They will explore the idea of whether order matters when adding a group of numbers. When adding 2 + 3 + 5, does it matter if we add 2 + 3 first? 2 + 5? 3 + 5? As students discover that order does not matter, they are really investigating the associative property of addition. a + (b + c) = (a + b) + c.

Students are also reviewing their doubles - 2 + 2, 3 + 3, 4 + 4, etc. Students use this knowledge to determine the near-doubles. 2 + 3, 3 + 4, 4 + 5, etc. Students should notice that the answer is just one more than the answer to the doubles combination.

By this point in the year, second graders should be fluent (not necessarily instantaneous recall) with the following combinations: plus 1 (4 + 1), plus 2 (4 + 2), combinations that make 10 (7 + 3), and doubles (6 + 6).

First Grade - November 3rd - November 7th, 2008

Our first graders are still working on addition problems. We're looking for students who can use the strategy of Counting On to add numbers together. To help students with this strategy, we are playing games with a number cube and a dot cube. When students add the two numbers together, they will not be able to Count All the dots because one of the cubes only has numbers. For example, imagine that you roll a 4 on the number cube and a 3 on the dot cube. A student has to start at 4 and count 3 more to get a total of 7. This idea of Counting On is much more efficent than Counting All the items in two groups.

Another strategy for addition is to use combinations already known to figure out new combinations. If a student knows that 5 + 5 = 10, they can reason that 6 + 4 = 10 because you just take one away from one of the 5's and give it to the other 5.

We are also working on the idea of finding all the addition combinations that equal a given number. Students are told that they have 7 items. Some of the items are blocks and some of the items are marbles. What are all the different combinations of blocks and marbles? We want students to develop a systematic way of finding all the combinations. Start with 1 block and 6 marbles, then move to 2 blocks and 5 marbles, then 3 blocks and 4 marbles, etc. Students should also realize that they can find opposites. If they have 3 blocks and 4 marbles, they can also have 4 blocks and 3 marbles.

Finally, we will start to study subtraction this week. It will be interesting to see the different types of strategies students use to solve subtraction problems.

5th Grade - Adding and Subtracting Large Numbers

Next week, our fifth graders will continue using different strategies to add and subtract large numbers.

Let's look at some different strategies to solve the problem 892 - 567.

• Subtracting in Parts - Start with 892 and subtract 500 (892 - 500 = 392). Next, subtract the tens place (392 - 60 = 332). Finally, subtract the ones place (332 - 7 = 325).
• Adding Up - For this strategy, start with 567 and add up until you get to 892 (567 + 33 = 600 and 600 + 292 = 892). Finally, add your numbers to get the final answer (33 + 292 = 325).
• Subtracting Back - For this strategy, start with 892 and subtract back until you get 567 (892 - 92 = 800 and 800 - 200 = 600 and 600 - 33 = 567). Finally, add your numbers to get the final answer (92 + 200 + 33 = 325).
• Changing the numbers to make an easier problem. For this strategy, it is important to remember that if you change one number you must also change the second number. Imagine you have 84 pennies and your brother has 55 pennies and you want to find the difference. What would happen if both of you got an additional 6 pennies? The difference would still be the same. Using this idea, we can change 892 into 900, but we must also change 567 into 575 (we added 8 to each number). Now we can use one of our first three strategies to solve this problem (575 + 25 = 600 and 600 + 300 = 900, so 25 + 300 = 325).

4th Grade - Multiplication

Next week, our fourth graders will continue their study of multiplication. We are espcially using the idea that you can multiply by 10 to solve a 2-digit problem. For example, to solve 15 x 13, students can think of the number 13 as 10 + 3. So, instead of 13 groups of 15, there are 10 groups of 15 and 3 groups of 15. 10 groups of 15 = 150 and 3 groups of 15 = 45. Add 150 + 45 to get your answer of 195.

4th Graders will also take a test next week on thier multiplication combinations. It is expected that students should be able to solve 30 problems (1-digit x 1-digit) in 3 minutes. Students who do not meet this expectation should continue to study thier combination cards at home.

3rd Grade - Addition and Subtraction

Next week, our third graders will continue working on addition strategies and begin studying their subtraction facts. By now students should be comfortable with at least one strategy for addition.

One strategy they have learned is Adding By Place Value. For example, to solve 184 + 235, students can add the hundreds first (100 + 200 = 300), then the tens (80 + 30 = 110) and finally the ones (4 + 5 = 9). Add your numbers to find the final answer - 300 + 110 + 9 = 419.

Another strategy is Breaking One Number Apart. To solve the same problem, 184 + 235, first add 184 + 200 = 384. Then add 384 + 30 = 414. Our students have been studying how to add groups of 10, so this step should be fairly easy. Finally, add 414 + 5 = 419.

Students will bring home some subtraction fact cards later in the week. It is expected that students are fluent with their subtraction facts by the end of third grade.

2nd Grade - Rectangles

Next week, our second graders will continue exploring rectangles. Students will build rectangles with tiles and write descriptions of what they build so that other students can build the same shape. Students should realize that it is important to include the number of tiles that are in each row and the number of rows. Students should also understand that a rectangle has 4 sides and 4 right angles.

After studying rectangles, we will move our study into rectangular prisms. Students will build boxes in the shape of a rectangular prism and discover that all the faces are rectangles and that opposite sides are congruent (equal).

1st Grade - Counting On and Finding All Possible Solutions

Next week, first graders will be working on the strategy of Counting On. Young students typically count two groups by counting all the items. For example, if one group has 5 buttons and another group has 6 buttons, students will count the 5 in the first group, the 6 in the second group, and then start with 1 again to count all the buttons. We are working with our students to learn the strategy of Counting On instead of Counting All. Once you count the number of items in one group, keep that number in your head and then continue counting the items in the second group. Students will play a game next week to reinforce this idea. The game is like Bingo where students are trying to get 5 numbers in a row on a game board. Earlier in the year students played this game by rolling two dot cubes and adding the numbers together to find a number on the board. This time students will roll one dot cube and one number cube. This will encourage students to Count On.

Another big idea we are studying next week is finding all possible solutions. Students are given a number and asked to find all the different ways to make that number. For example, we can make the number 5 by adding 0 + 5, 1 + 4, 2 + 3, 3 + 2, 4 + 1, and 5 + 0. First graders may not organize thier work in a systematic way, but we hope they will discover a method for making sure they have every possible answer. Another idea students will discover is that if I have 1 + 4 I can also have 4 + 1.

3rd Grade Measurement

Students in third grade are using measuring tools to collect data. Today they used rulers to measure the length of their classroom.

One important idea during this investigation is how to use measuring tools, specifically 12-inch rulers and yard sticks. We discussed that 1 yard is equal to 3 feet and that 1 foot is equal to 12 inches. I found it interesting that as students measured the room, they came up with answers like 21 feet, 29 inches. They were able to determine that 7 yardsticks was the same as 21 feet. What they did not think about was that 29 inches could be broken down into feet and inches.

After some discussion, we decided that 21 feet, 29 inches could be written as 21 feet + 12 inches + 12 inches + 5 inches. We then changed this to read 21 feet + 1 foot + 1 foot + 5 inches which is the same as 23 feet, 5 inches.

As you talk withyour child, talk about the idea of converting measurements. Ask questions like:

• What is another way to say 17 inches? (12 inches + 5 inches or 1 foot, 5 inches)
• How many inches are in 3 feet, 4 inches? (12 inches + 12 inches + 12 inches + 4 inches = 40 inches)