Complementary and Supplementary Angles

Today we looked at complementary and supplementary angles. Complementary angles are angles which add up to 90 degrees. Supplementary angles are angles which add up to 180 degrees. We can use what we know about these angles, as well as look at their adjacent angles, to determine missing angle measurements.

Types of Triangles

Today we learned about different types of triangles - right, acute, and obtuse. We discussed that all triangles have two acute angles. The third angle is what determines its type. If the third angle is also acute, it's an acute triangle. If the third angle is right, it's a right triangle. If the third angle is obtuse, it's an obtuse triangle.

Naming and Measuring Angles

We began the week naming angles. Most of the students were familiar with the types of angles, but we reviewed the important characteristics of straight angles, obtuse angles, acute angles, and right angles.

Next we worked on measuring angles. Measurement is still a very abstract idea for 4th graders, so we began by discussing measurement as a whole. What do we use different measurement tools to measure? I posed the question, "Would a ruler work when trying to measure angles?" In the beginning of our discussion, many kids believed it would. After trying it out, they came to the conclusion that we needed something that measures in degrees. They understood the unit wasn't correct, but weren't sure what degrees actually are, though we had discussed degrees when classifying angles as right, acute, obtuse, and straight.

We went back to everything we already know about angles. Going in a complete circle means we have gone 360 degrees, while only going halfway around means we have gone 180 degrees. We already know that a right angle is 90 degrees. We already know a straight angle is 180 degrees. We know an acute angle measures between 1 degree and 89 degrees. We know an obtuse angle measures between 91 and 179 degrees. Once we illustrated that, we decided we could half each 90 degree piece and figure out where 45 degrees and 135 degrees are located. Next we moved to

Lines and Angles

We began lines and angles this week. We began with introductions of the different types of lines and angles, then moved to making them on dot paper. We moved on to looking at specific lines and angles within a large collection. This lead to the discussion of why it is important to have points on our lines - so we can name the ones we're specifically trying to reference. 

Mixed Numbers and Improper Fractions

We introduced fractions greater than one by modeling them with pattern blocks and writing them as a mixed number, and also as an improper fraction. Then we discussed the similarity between the two numbers.

After lots of examples with pattern blocks, we moved to pictures in our journals. We started with the mixed number, drew the picture, then named it as an improper fraction. After several of those, we started with the improper fraction, drew the picture, then named it as a mixed number.

The next day, we talked about how we went between the two types of fractions using pictures to help us. After examining our pictures, we noticed some shortcuts to help us be more efficient when changing from one type of fraction to the other. Eventually, the kids discovered the multiplication and division connection to help speed them along.

Our Classroom Poster

Strip Diagrams to Model Computation

Most students at this point can read a word problem, figure out the operation(s) needed, and solve the problem(s). What might be a little more difficult for them is modeling their operation(s) with a strip diagram. This week we worked through all four operations, and discussed what the strip diagrams for each operation could look like. If a student truly understands what is happening with each operation, he/she should be able to model it.

Division and Subtraction Strip Diagrams

Multiplication and Addition Strip Diagrams

Fraction Review and Intro to Improper Fractions

This week we took a brief look at fractions. We started by reviewing what we already know about fractions such as definitions and pictures.

After we reviewed, we looked at pieces of fractions and discussed what happens when the numerator and denominator are the same number. We looked at pictures of pizzas cut in half. Once I have two halves, I have one whole. Finally, we explored what happens when we have more than one whole. We discussed how we would name these improper fractions (we'll learn about mixed numbers a little later this year.) We named them on a number line, as well as in picture form.