Topic: Understanding Two-Dimensional Shape Properties: Quadrilaterals

Standard: 5.G.3b

Student Slide Example:

Self-Paced Directions and Resources Provided:

Steps:

2. Then you MUST go to “File” and  “Make A Copy”.

Now it’s yours to use and make any changes.

3 Ways To Master Multiplication Without Memorizing

By middle school students are expected to know their multiplication facts 1-12 fluently.  However, many students can’t memorize all of them.  In fact, students who are good problem solvers are often the students who don’t memorize, but rather know them through other methods such as modeling, repeated addition, and working from facts they do know.

Modeling

A common multiplication fact that many students struggle with is  8 x 7.   To get a deeper understanding, start with modeling this with pictures. For example, there are 7 soccer teams with 8 players on each team.   Have your child count until they get 56 or a total of 56 players.

Practice with modeling should lead to the idea of repeatedly adding the same number.  Multiplication is repeated addition.  After modeling over and over, students start to realize they are doing this:

8 + 8 + 8 + 8 + 8 + 8 + 8 = 56      OR     7 + 7 + 7 + 7 +7 + 7 + 7 + 7 = 56

I tell me students this is fair game and to add every time if they need to.

Repeated addition leads to another strategy students can do without having to memorize all facts.  Let’s say your child knows their 5 multiplication facts well.  They can use this knowledge to count to the others they struggles with.  Let’s use 8 x 7 again.  If they know 8 x 5 = 40 then they just need two more groups of 8 to get to 8 x 7.   Most students get faster at doing this in their heads.  I will have students make flashcards like these with that facts they struggle with.

Here is another example:

A Clever Way To Understand AREA

The idea behind AREA is a basic concept that most students, and even adults, don’t understand.  Most people know to label area with square units such as 30 square feet.  But WHY?

The area of a shape or room is simply describing how many actual squares (measured by feet, meters, or another unit) that fit inside the shape.  Most students learn that area is what’s “inside the shape” but they don’t connect it with the physical squares it takes to fill it up.

For example, if a living room measures 10ft by 12ft, the area is 120 sq ft. That means 120 squares that are a foot by a foot would fit inside like a PUZZLE.

Here is a great way to start piecing together a PUZZLE that demonstrates the foundation of AREA!

These foam pieces connect to make a rectangle measuring 2 pieces by 3 pieces.  It’s area is 6 sq. pieces. Meaning, to fill the shape it would take 6 squares, which can be easily observed.

Here is another example using foam mats. This rectangle is measuring 3 pieces by 4 pieces giving it’s area 12 sq. pieces.  Have your child count the actual squares connected, which should come to 12!

Look for other examples of area using squares!

Using LEGOS to Introduce Fractions!

Legos are wonderful toys that can be used for more than building.  They can be used for counting, color ratios, AND as an introduction to fractions.

Before we start we need to understand that what we call a “whole” can vary.  For example, if you offer someone a whole candy bar one person might think of a King Size and someone else might think of a Fun Size.  With Legos, we can count each color as a whole or a single unit (1, 2, 3…).  We can also change the unit we are counting by (1/3, 2/3, 3/3).

Here is a basic example of using Legos to talk about fractions.

This example illustrates equivalent fractions.

Here is one more to get you thinking about making fractions out of toys!

8 Counting Activities for Your Toddler

There are opportunities everywhere to make counting a game and begin teaching important basic math skills.  Counting activities lead to modeling on number lines which is a large part of Common Core Math taught in school.  The main purpose of a number line is to model counting whether it’s by 5’s or by fractions.  Therefore, it’s essential for kids start at an early age.

1. Shapes– Shapes are everywhere! It’s easy to count specific shapes with your child when traveling or in a restaurant.
2. Candy– For obvious reasons, kids love to count candy.  Candy can be used as an incentive to get young kids to start counting.  Challenge them not to eat until they have finished a task. This leads to the idea of subtraction! Literally! Eating and taking away candy is the basic idea for subtraction. It’s gone; we no longer count it.
3. Balls– Make it a physical game! Challenge your child to throw 5 balls as fast as they can. Count with them as they throw.
4. Cups– My son loves stacking cups.  Build a pyramid and count as you go. Talk about the pattern made with each level.
5. Crayons– Crayons can again be used to count by color.  Also, Crayons usually come in large packs and are great to start to count to 20. Try introducing them to counting by 2 or 5 crayons at a time.
6. Non-Toys– My son and I spend time all around the house like in the bathroom.  I let him play with items like Q-tips and cotton balls. I’ll ask him to count 3 items and put them in a basket.
7. Books– Before bed we always read.  I’ll choose a number for the night and that’s how many books he gets to pick to read.
8. Picking up toys– My son loves to help me clean.  I will challenge him to pick up a certain number of toys. Then, I will have him choose a number of toys I should clean up as well.  We’ll take turns counting and cleaning!

Make all opportunities COUNT!

Why I LOVE Area Models!

Area models come from the basic idea of solving for area.  They are a wonderful tool for younger students to do multi-digit multiplication problems (for example 14 x 17).  They develop student understanding of multiplication, place value, and the distributive property that is later used in Algebra.

I did not learn area models in school but I swear by them with my students and can’t wait for my children to do them!

Let’s review the basic idea of area.  If I want to put tile down in my bathroom and it measures 5ft by 6ft.  We multiply 5 x 6 and 30 total square feet.

Here is the model of this situation.  It shows 6 feet extended across and 5 feet extended down.  When they overlap they create 30 squares that are a foot by a foot.  This example is an area model.

Here is an examples of a double-digit multiplication problem solved with an area model.  This example can be done by students starting in 3rd grade.  I know it is not the fastest way but it teaches students understanding and skills they can use when problems get more difficult.  By 6th grade they will learn to do it the traditional method, which yes, is more efficient.

Let’s solve 14 x 17.

First, setup a square just like real life area problems.

Take each number, 14 and 17, and break them down by place value.  14 becomes 10 and 4 and 17 becomes 10 and 7.

Just like with the bathroom floor problem, we are going to extend each number and draw 4 boxes.  Inside each box will be the answer of the over lapping multiplication problem.

We first solve 10 x 7 and write 70.  Then multiply 10 by 10 to get 100.  (This idea represents an Algebra concept called distribution.  We have distributed the 10 to 7 and 10.)

Next we are going to multiply 4 by 7 to get 28 and 4 by 10 to get 40.  Answers go in each box.

238 is the same answer we would get if we did it the traditional way.

Ratio Tables 101

Ratio Tables are my FAVORITE math thing to do and to teach!  They are an invaluable tool for ALL students.  They can be intimidating to work with at first and therefore, require practice.

Ratio Tables can be used for:

• Solving fractions (fractions are ratios!)
• Brainstorming how to solve a problem

The basics of Ratio Tables can be helpful later when your child is doing:

• Coordinate Planes
• Functions
• All Fraction Operations

Here is an example of using a Ratio Table when working with a recipe.

Ratio Tables use multiplication and division operations.   As well as adding and subtracting groups of ratios.  You might see ratio tables more complex with decimals and fractions within them.   I will show those next time!

Here is another example.  This table shows equivalent ratios, which are the same thing as fractions.  4/6 is equal to 2/3 and 12/18 by scaling down (division) or scaling up (multiplication).

The COOLEST part of ratios tables is you can combine, or add, any equal ratios from the table, like 2/3 and 12/18, to get another equal ratio, 14/21.

I challenge YOU to try them!