Math comes to us in picture, word, and numbers. I taught Hispanic at risk students grades K - 5 and discovery this was a fundamental gap in our math teaching. Many standards have a basis in doubles and halves. It is benchmark numbers for mental math. Teaching this intentionally raised many students scores to near passing. This lesson for doubling uses mirrors giving a visual representation of double and the book Two of Everything is available on Youtube https://www.youtube.com/watch?v=WdmI32qY_c
Here is what doubling becomes in Jr. High. I did this story with at risk 5th graders scaffolded to prepare them for algebraic reasoning and language in when they graduated. http://jwilson.coe.uga.edu/EMT668/EMAT6680.F99/Martin/instructional%20unit/day4.exponential/excel/grainofrice.html
Math has a specific language and it has to be specifically taught. Here is the Common Core language used in standards and on tests. Teach it and it prepares students for higher mathematics.There is nothing worse than having a student who made A's in elementary go to 6th grade and fail. I got the honor of visiting with 6th grade students that it had happend to. What they would tell me over and over again was Mrs. Page I did not understand what it asking. I investigated.
This video is application level of the concept of doubling used for multiplication. I had many students who worked harder than the others to memorized facts and the facts would fade if not reinforced everyday. The child and I would grieve. One day I decided that the teaching was wrong for that child's brain. I went and found other ways to know your facts. Asian math programs have other techniques and it worked with these children.
Teachers hear me now---Math is a system of relationships to investigate and understand not a collection of rules. This article explains the difference and shows how to do a number talk. It shows how to create benchmark numbers in a child's schema. Most of all it shows how children can develop math talk between each other internalizing for future use at the high school level. Math language in the general public and on media is not common.
With at risk studens transitioning language such as Hispanics it makes a huge difference what words you choose to communicate math with. Just a change in the teacher phrasing of a lesson can get students to passing. Notice the language the person is using to explain the concept of doubles. This is application level of the concept. The language communicated to students matters. It sets students up for success in algebra in Junior High.
This is a resource found in the British system who are much better at teaching the concept of doubles and halves. I used the games associated with the British system before school in a math computer lab I set up. We had a scope and sequence so I took it and scheduled game time for the lowest students before the day started. Nothing better than greeting students who were excited about math because as one little 3rd grader told me "Here I am successful. I win here." He did pass.
Math comes to us as specific visual representations such as graphs and charts. One of the best things a teacher can do is let students recreate data as a visual.Students love post it notes. If you have a white board you have an instance class graph. This lesson creates data that students learn to record for double and halves. You have a real life problem interpreted into numbers representing double and half then displayed visually in a graph.