What do I Have?


homework 1 22 18

This is an image from our smart-board today, and what students took notes on in the their journals at the beginning of class. We were exploring strategies for solving word problems. Our focus right now is word problems involving multiplying fractions, and will change to dividing fractions later this week.

Students often do what I call smooshing the numbers together. Students will pull out numbers and add, subtract, multiply, or divide without taking the time to understand the situation. This strategy causes students to arrive and unreasonable solutions, and also makes it difficult for students to evaluate for reasonableness.

A way to avoid this is to start with asking: “What do I have?” Students can then draw a picture of what they have. This helps the student to understand what is happening. To explore this we did numberless word problems. These are problems that start with no numbers at all, and then gradually give you more information.

This is an example halfway through our word problem, and a model that was created to go with it.

homework 1 22 8 bucket.PNG

Notice that the 1/2 a gallon is also the full bucket. This allowed us to have a conversation about what the word “whole” means, which we will continue tomorrow.

Equivalent Fractions

Your mathematician should be noticing that two fourths make a half, just like two quarters make 50 cents. A conversation you can have can begin by showing this image. What patterns do you see? What do you notice?

equivalent fractions


Homework Wednesday November 15th

For homework tonight students are asked to model 0.5. For this work students will create representations that are equivalent to 0.5. An important equivalency is that 0.5 is the same value as 1/2. This representation could look like this:

half image.jpg

Comparing to quarters is another important benchmark equivalency is that 0.25, 1/4 and a quarter are all equivalent values. Another representation could look like this:

two quarters

Students could also use the number line. A possible representation could look like this:

half number line

Students could also demonstrate their knowledge that two 1/4s make a half, and that 1/2=0.5 using the number line.

number line quarters halves.jpg


Reviewing Fractions

Fraction work is one of the critical areas of 5th grade math. Students in my class will soon begin this work and will continue exploring fractions for some time. We find that students have often forgotten or missed some of the concepts that underlie our work, so reviewing the fundamentals is a vital first step. Please check out the videos in the Fractions tab to begin to explore some of the foundational thinking that the fraction work is built on.

The concept of a unit fraction is one of the most fundamental concepts in fractions. Students with a strong understanding of unit fractions have a much stronger conceptual foundation of fractions, and are much more successful in their fraction work. Two areas of focus would be to ensure that you students can:

  1. Explain what a unit fraction is, and describe how fractions are built by combining unit fractions.
  2. Accurately compare the relative sizes of unit fractions.

Manipulatives should be used when students are doing this work. A math manipulative is something that the student can physically manipulate is space. Fraction tiles are extremely valuable during this work.

Image result for fraction tiles

Fraction Tiles

Free printable fraction tiles

Fraction tiles for sale

You can also contact me for help obtaining fraction tiles for your child to use at home.

Here is a video outlining how to begin reviewing and exploring fractions. There are other videos in the Fractions tab that can help to further clarify this work.

Adding Math Explorations to Your Nightly Routine

You and your child have already been engaging in math explorations at home through the number talks activities as part of the nightly homework. You can also use this number talks activity the same way it is used at school, as a warm-up for further explorations into math. If you would like to explore math further with your child this website will give you some of the information and resources you need to get started.

A good way to start is by watching the videos from the tabs at the top of this site. Watch the videos and do some math on your own using the concepts and strategies presented. Check in here for suggestions about math explorations, resources, and to see what others are posting and asking about. When you are ready, delve into some more math after you do a number talks at home. Have fun!

Math Explorations

Adults have been telling me for years that they are having difficulty helping their children with math. Students are thinking about math in much different ways than most of the adults did when we were in school. This website is designed to introduce adults to the mathematical concepts being taught in schools throughout the country. You can use the resources to first explore and do some of the math yourself, then to share in your exploration with your little mathematicians at home.

If I am your child’s teacher then checking in here will also help you keep informed about what your mathematician is currently thinking about during school.

Please feel free to comment here with questions or with suggestions for posts or videos.