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Math

Hands-On Doubles and Halves Part 2 for Jr. High, and High School

A fundamental concept weaved throughout any math standards is the idea of doubling quantities and halving quantities. Though not explicitly stated often it is implied in most strands. It functions as a good rule of thumb for orienting numbers.
A Collection By Mary Page
  • 8 Collection Items
  • 8 Collection Items
  • Discussion
Hands-On Doubles and Halves Part 2 for Jr. High, and High School
  • Mary Page says:
    Full set of lessons of algebraic exponents involving 2 and 1/2 for high school. Practicing doubling and the inverse increases flexibility of thinking and prevent redundant patterning that causes common errors. Think and let think. As a district person I had to visit with Jr. High campuses and had a Jr. High partner to build bridges in math to make it easier on students going to high school. Elementary was soaring but high school most kids did not graduate because of math scores on state exams.
  • Mary Page says:
    Online simulation of a pandemic shows how quickly something can change if the math is exponential. If it is germs that is negative but if it is money that is a good thing. When I would give my students a simulation like this math would come alive and they would bring in current events and show off. In Jr. High it gave students a chance to be worldly in a healthy way.
  • Mary Page says:
    How money doubles using exponents and interest is a life skill. Learning to save a portion of a person's resources then using present financial techniques to increase wealth helps provide long term sustanance for senior years. Kids love to learn about money. I used to collect pennies and students would get a plastic bag of real pennies to play with. Jr. High students surprisingly have trouble with money problems.
  • Mary Page says:
    A set of games that double and half whole numbers and decimal numbers. Games are simulations with a variety of perspectives and variables coming in. This develops flexibiity in thinking. Anytime learning becomes more pleasurable it increases retention and input into long term memory. Plus sending a game home for parents, siblings or other family members to play makes for good family time. You want to encourage good family time because it also makes kids successful in school.
  • Mary Page says:
    Medical application using Jr. High algebra concepts of how flu spreads and infects people. The math of epidemics is algebraic. The good news of doing graphics on such problems is it shows it has a beginning and an ending. Best of all it shows many strategic points medical people can intervene to slow down an epidemic. Games also invite other people in such as experts to do math talks with students. Career day opportunities show the importance of numbers and puts a human face to a school subject
  • Building Bridges

    Lesson plan
    illuminations.nctm.org
    illuminations.nctm.org
    Mary Page says:
    A lesson bridging arithmetic thinking to algebraic thinking using a problem task involving a valentine and questioning strategies. Questions can be from simple yes/no to open ended. Open ended questions develop deep thinking and helps internalize knowledge. Yes/no questions tend to make people pleasers and not learners. Open ended questions invite the other ideas.
  • One Grain of Rice

    Lesson plan
    illuminations.nctm.org
    illuminations.nctm.org
    Mary Page says:
    A lesson bridging arithmetic thinking to algebraic thinking using the math literature One Grain of Rice. Problems are similar in 5th to 6th grade. The amount of word problems increase in Jr. High and the language is that of algebra not arithmetic. As an educator you have to intentionally build that bridge for the language.
  • Mary Page says:
    Arithmetic defines properties and manipulates numbers. Algebra language communicates math ideas and inspires reasoning. It is the generalizations of algebraic thinking that develops problem solving skills for life. Students would tell me after a year of teaching that they could not do the problems on standardized testing. I sat down one day and took each failing student through each word on a word problem. They absolutely could not tell me what the words meant.
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