# Archive for October, 2012

## Great Grade Level Mathematical Practice Posters

The Jordan School District Mathematical Posters have been redesigned for specific grade levels! Kowabunga (I’m sorry, sometimes the California in me just comes out!) Be sure to scroll through all of them because they are differentiated by grade level– each practice.

Happy Mathing,

Dr. Nicki

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## Another Energizer for Number Flexibility

This energizer is called Rule of the Day. The teacher states a rule like:

Doubles,

Doubles Plus 1

Half Facts

Ten More

Ten Less

Multiples

Then the game begins. The teacher says a number and the students have to answer following the rule. For example, if the teacher said, the rule is “Half Facts” the starter number is 20 then students would say 10, 5, 2.5 depending on the grade level. If the prompt is doubling and the starter number was 50 the students would say 100,200,400 etc.

This can be a fun, energetic, academically rigorous game that gets students very flexible with math facts. Look at your standards and pick your rules based on what the students need to know!

*See ThinkMath for more on this energizer!

Happy Mathing,

Dr. Nicki

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## Student Friendly Mathematical Practices Posters

Here are some great student friendly mathematical practices posters. Use these or make some like these with your students. The most important thing is to have a conversation about each one of the practices and then PRACTICE the practices. Make sure you have routines to reinforce the practices throughout your math curriculum. I will be writing more about the practices this week.

Happy Mathing,

Dr. Nicki

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## Multiple Representations of Math Problems Increase Understanding

It is important to have your students model their ideas in several ways. Lesh, Post & Behr (1987) have proposed 5 different representations for concepts (cited in Van De Walle, 2006 p. 10).

1. Pictures

2. Written symbols

3. Oral Language

4. Real World Situations

5. Manipulative Models

Researchers have found that when students can represent ideas in various ways “there is a better chance of a concept being formed correctly and integrated into a rich web of ideas” (Van De Wahl (2006 p.10)

Let’s use a decimal example. Ask the students “What is 4 x .25?”

**Oral Language (reason it out and explain your thinking)**: First have them reason out the answer. Think 4 quarters.

**Real World Situations**: Then have them tell you a real life story where you would use this equation.

**Manipulative Models**: Next have them represent it with decimal squares.

**Abstract Model:** Then have them show it on a numberline.

**Pictures**: Then have them draw it out with a pictorial representation such as circles or squares.

**Written Symbols**: Finally, solve the equation with numbers.

Do this with your students on a regular basis. Think about your current unit of study and the concepts you are teaching. Are you emphasizing multiple representations that require thinking beyond just “getting the answer.” How do the anchor charts in your classroom support this type of thinking? How does your Problem of the Day support this type of thinking?

Happy Mathing,

Dr. Nicki

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## Teaching the Area Model for Division

The CCSS Math Practice 5 talks about different tools that students will use to solve problems. Here is a great digital tool from the National Library of Virtual Manipulatives that helps students to learn and practice division using the area model.

Happy Mathing,

Dr. Nicki

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## The Open Array for Division

The Math CCSS states that 4th and 5th grade students should have a variety of strategies for doing multiplication and division. In my work around the country, many teachers don’t have as many strategies for division as they do for multiplication. The **4th grade math** Core (2010) says that students will “Find whole-number **quotients and remainders with up to four-digit dividends and one-digit divisors**, using strategies based on place value, the properties of operations, and/or the relationship between multiplication and division. Illustrate and explain the calculation by using equations, rectangular arrays, and/or area models.”

The **5th grade math** Core (2010) says that students will “Find whole-number **quotients of whole numbers with up to four-digit dividends and two-digit divisors**, using strategies based on place value, the properties of operations, and/or the relationship between multiplication and division. Illustrate and explain the calculation by using equations, rectangular arrays, and/or area models.”

Here is the Open Array for Division!

Happy Mathing,

Dr. Nicki

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## More Math Energizers and Routines

When:

- As part of the do now
- Before Lunch
- Before School Ends
- Before Recess
- Right after Recess
- Anytime is a good time!

Remember that energizers are quick! Here’s one!

**Make 5, 10, 20 100, 1, ½, 2/3, **

This is a quick number game that gets students to practice their basic facts based on the **CCSS Math Fluency levels**. The basic premise of the game is that students have to name the complement.

So, in **Kindergarten you say Make 5**…then you have someone pull a number card and then the students raise their hands and the student who pulled the card chooses someone…that person has to say what number will make 5 with that number. For example – John picks 3 (he calls on Josephine) She says “2 plus 3 makes 5.”

In 1^{st} grade, you play Make 10. In 2^{nd} grade you play Make 20 and Make 100. In the upper grades the students have to make fractions and decimals. For example, if you said 4/6 then the students would have to tell you how to get to the next whole number but not using sixths. This forces them to think about equivalent fractions.

Happy Mathing,

Dr. Nicki

Good Resources:

- http://www.washmath.org/files/GamesAndActivities.pdf
- http://www.geniekids.com/250ways/math-energizers
- http://cherieholt.wiki.westga.edu/file/view/Math+Energizers.pdf/283308842/Math%20Energizers.pdf

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## More Great Math Routines

**What is a math routine?**

A math routine is a whole class math activity that you do overtime. There are a variety of different types of routines. You can do routines to:

1) Build Number Sense

2) Build Vocabulary

3) Build Conceptual Knowledge

4) Build Mathematical Modeling Skills

5) Build Procedural Fluency

6) Build Strategic Competence

7) Build a Strong Mathematical Disposition

**When: **Anytime (they usually last between 5-10 minutes once the students know them)

**How:** Routines are set up in a variety of ways – individual, partner, small group or whole class

Ideas:

1.** Half It!** Teacher gives an even starter number. Kids verbally toss it around the room- each child halving it until you get to the first odd number. So for example,

Starter number 20 – Trevor says 10 – Mica says 5 – we stop.

Starter number 200 – Michael says 100 – John says 50…they keep going till they can’t go anymore

Starter number 1/2 – Carlos says 1/4 – Trina says 1/8 ….

2. **Double It!** Teacher gives a starter number and kids verbally toss it around the room…this time doubling the number.

3. ** Number Line It!** – Draw an unlabeled numberline and then have the students plot numbers.

Teacher says…draw a numberline…start it with 500 end it with 1000…write where 650 is…write where 899 is….

Teacher says…draw a numberline…start with 2/3 and end with two and a half…write where one and a half goes…write where 1 and 3/4 goes… write where 2 goes

Other Resources

1) Number of the Day & More

Happy Mathing,

Dr. Nicki

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