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)

When should kids know their combinations?

I have had many parents ask me when their child should know their addition or multiplication facts. I would first like to say that Investigations prefers to call them combinations. Calling them facts implies that you can't learn them through reasoning. However, if I know 8 x 3 = 24, then I should be able to reason that 8 x 6 is double 8 x 3 or 48.

What does it mean to know your combinations? Fluency means that you can immediately recall an answer or quickly perform a calculation to get the answer. If it takes longer than two seconds to figure a combination, a student is not fluent. This includes single digit addition and multiplication pairs and their counterparts for subtraction and division. We encourage students to work on combinations that they don't immediately know. This can be done during downtime in class or at home. I also encourage 3rd, 4th, and 5th graders to use arrays when working on their combinations.

The following are guidelines for learning combinations through the grades:

Addition - fluent by the end of Grade 2, with review and practice in Grade 3.

Subtraction - fluent by the end of Grade 3, with review and practice in Grade 4.

Multiplication - fluent with multiplication combinations with products to 50 by the end of Grade 3; up to 12 x 12 by the middle of Grade 4, with continued review and practice.

Division - fluent by the end of Grade 5.

Adding by Place Value

How would you solve the problem 254 + 763?

Many of us would line the numbers up like this:

However, there are other ways to solve this problem. One way is to break the numbers down by place value.

• We can start with the hundreds place and solve 200 + 700 to get 900.
  
• Moving to the tens place, we can solve 50 + 60 to get 110. If you have trouble adding these two numbers, think of the problem as 50 + 50 + 10.

• Finally, move to the ones place and solve 4 + 3 to get 7.

• Now we have the numbers 900 + 110 + 7. Another way to think of this problem is 900 + 100 + 10 + 7 which is 1,017.
  

Why does this strategy make more sense than lining up the numbers like above? Let's talk our way through solving that problem. The first step is pretty easy. 4 + 3 = 7. Now have a student explain the second step. You will probably hear something like "5 + 6 is 11, so put down a 1 and carry the other 1." What does this mean? The actual step is adding 50 + 60 to get 110. So, you are putting 10 down and carrying the 100. This explanation get a little confusing for kids.

While lining up your numbers and following the steps will work, it doesn't give students any meaning about what they are really doing. Adding, or subtracting, by place value makes sense of the problem. As our students move through Investigations, they will become more efficient at solving problems like this and may even begin doing them in their head.