Interpreting the Remainder

The remainder is the amount left over after division.

Example: 19 cannot be divided exactly by 5.
The closest you can get without going over is 3 x 5 = 15, which is 4 less than 19.
So 4 is the remainder.

So the answer of 19 ÷ 5 is 3 with a remainder of 4, usually written "3 r 4".



There are four ways your kiddo has learned to interpret the remainder. They are drop it, add it, share it, and use it.



The way you interpret the remainder has to do with what the word problem is asking. 

Here are some videos with some real world examples of interpreting the remainder:

Interpreting Remainders Part 1

Interpreting Remainders Part 2

Interpreting Remainders Part 3

Long Division

We are fully into our unit on long division. 

We are working on our division vocabulary and identifying the different ways to represent and solve division problems.

   

We have learned multiple ways to divide. We have looked at division using arrays, base ten blocks, big seven method, and standard algorithm. 

Division with arrays:

Base Ten division:

Big Seven Method:

Standard Algorithm:

Here is a link that will walk you through the big seven method:

Big Seven Explanation

Below is the image that we use to describe big seven.

Big seven keeps place value in division and allows kiddos to solve division problems when they don't have a great grasp of multiplication facts. This makes long division seem easier for the kiddos!

We have also looked at division using the standard algorithm. I am sure you are all familiar with the standard method, but it can sometimes make division difficult because of the removal of place value.
Here is a link that will walk you through the standard algorithm.

Standard Method Review

Below is an image of the notes we have taken regarding the standard algorithm.

As you know, I do not have one way that I require kiddos to solve problems. I want them to do the method that works the best FOR THEM. Have your kiddo show you what method they like the best!

Here are some games to practice these skills:

Pony Pull Division

Demolition Division

Puzzle Pics Division

Dino Park Division

Missing Digits Division

Please let me know if you have any questions!

Properties of Soil

Soil is a mixture of rock, organic material, water, and air in which plants can grow. We study three main types of soil; sand, loam, and clay. We also work with humus.


Sand has large, loose grains, few nutrients, and does not hold water well which washes out nutrients so that it does not support plant growth. This type of soil does not have well developed horizons.

Loam is a mix of sand, silt, and clay. Most potting soil is loamy as it is rich in humus and holds water better than sand so it remains wet longer during dry periods. Loamy soils have a thick topsoil horizon.

Clay has closely pack particles which means there is very little air space. The particles are extremely fine and powdery. It is rich in nutrients and holds lots of water, but doesn't soak it in quickly.

Humus is the remains of decayed plants and animals, which contains nutrients that plants need to grow. It also helps the soil to retain moisture.

When soil forms, it develops layers, called soil horizons. Scientists use a letter to identify each soil horizon. A vertical section of soil that shows the layers is called a soil profile.

Here are some games that can take this concept further:

Soil Games

Watch some funny videos here:

Types of Soil

Soil Profile

Here are some places to go for more information:

Properties of Soil

Double Digit Multiplication

Your kiddo has been working on double digit multiplication. We have learned a couple of ways to calculate these types of problems. I wanted to be sure that you were aware of the methods introduced so that you can support your kiddo at home. We learned the standard algorithm/bow method and the box/partial product method. Below are images of the steps/notes that your kiddo uses for both methods.

Standard Method:

Box Method:

 

Here is a link that can help demonstrate and explain the connection between the box/partial products method and the bow/standard method:

Multiplication Instructions

Partial Products Multiplication

Box/partial products method does a good job of keeping place value in double digit multiplication. This concept can be lost when calculating using the standard method. It is also less overwhelming and therefore seems easier to some kiddos. I do not care which method your child uses as long as it make sense to them and they are consistently successful. Ask them to explain the method that they like the best to you!

Here are some websites that allow you to practice these skills:

Box Method Practice

Box Method Game

Standard Method Practice

Canoe Penguins Game

Here is a fun song explaining the standard method:

Standard Method Song

Please let me know if you have any questions.

Distributive Property of Multiplication

The distributive property of multiplication lets you multiply a sum by multiplying each addend separately and then adding the products.

For example: 6 x 9 = 6(4+5) = (6 x 4) + (6 x 5) = 54

The Distributive Property of Multiplication is worth its weight in gold because:

• It allows students to solve multiplication problems that are otherwise too hard for them.
• It helps students to develop a better sense of numbers because it clearly illustrates that a number is equal to the sum of its parts.
• It helps students develop a more creative and flexible use of numbers through “number crunching”.
• It helps students to more fully understand the concept of multiplication.

Here are some example of how your kiddo might see it:

Here are a couple of videos about the distributive property:

Angry Birds Distributive Property

Distributive Property Race

Here is a game to practice this skill:

Distributive Property

Please let me know if you have any questions.

Forms of Energy

Objects have energy and can gain energy from or lose energy to other objects. A moving car has energy, a pot of water heating on a burner is gaining energy from the burner, and a bowling ball loses energy as it hits the pins. Energy forms are either potential or kinetic. Potential energy comes in forms that are stored including chemical, gravitational, mechanical, and nuclear. Kinetic energy forms are doing work like electrical, thermal, light, motion, and sound. Though each form is different, they are all the same in the fact that one form of energy can change into another. Energy can be changed from one form to another, but excluding nuclear processes, it can never be created or destroyed.

We study five forms of energy; mechanical, electrical, light, thermal, and sound.

Mechanical energy is the sum of kinetic and potential energy in an object that is used to do work. In other words, it is energy in an object due to its motion or position, or both.

Electrical energy can be used to move charged particles through a wire from a power plant to our homes and businesses. The movement of a charged particle through a wire is called current, or more commonly, electricity. Electricity is used to work various appliances in our homes.

Light energy is carried in light waves. Most objects don't emit visible light, but reflect from other sources. Our primary source of light is the sun.

Thermal energy is the random motion of molecules. molecules in matter are always in motion, but the hotter something is the faster the molecules move. Temperature is a measure of that motion.

Sound energy is carried through sound waves. Sound waves carry energy through air or other materials as the molecules in them are pushed and pulled by a vibrating source. All sounds begin when something vibrates.

Here are some examples of the different forms of energy:

Here are some places to visit where kiddos can explore the different forms of energy:

Energy Kids

MELTS Energy

The Dr. Bionocs Show on Energy

Bill Nye The Science Guy Energy

EIA Energy Kids

StudyJams Energy and Matter

Here is a fun music video that shows force and motion:

This Too Shall Pass Video

Strip Diagrams

Strip Diagrams are a tool designed to help students solve math word problems accurately and efficiently. Students model mathematical relationships and identify known and unknown quantities. The model provides students with an image that organizes information and simplifies the problem solving process. By modeling the word problems, students develop strong reasoning skills which will help them as they transition to algebra. Students are familiar with problem solving maps, now they will use strip diagrams as a tool to solve problems.

Here are a couple of examples of solving problems with strip diagrams.

Strip Diagrams Broken Down Into Steps:

Step 1: Read the entire problem.
Alicia has $6 more than Bobby. If Bobby has $10, how much did they have altogether?

Step 2: Decided who is in the problem. Alicia and Bobby

Step 3: Decide what is involved in the problem. Money

Step 4: Draw unit bars: here we are drawing unit bars of equal length for each person to represent that they have the same amount of money.

Step 5: Read each sentence, 1 at a time to fill in the information.

Step 6: Put a ? in the place to show the information we need to find out. (When students are comfortable with the question mark switch to use a letter to represent the unknown)

Step 7: Write an equation and work computation to the side.

Step 8: Answer in a complete sentence to check for reasonableness.

Strip Diagrams Broken Down Into Steps:

Step 1: Read the entire problem.
Carlie sold 32 raffle tickets for the school fundraiser. That’s 4 times as many as many as Caroline sold. How many more raffle tickets did Carlie sell than Caroline?

Step 2: Decided who is in the problem. Carlie and Caroline

Step 3: Decide what is involved in the problem. Raffle tickets

Step 4: Draw unit bars: here we are drawing unit bars of equal length for each girl to remind us that are equal.

Step 5: Read each sentence 1 at a time to fill in the information.

Step 6: Put a ? in the place to show the information we need to find out. (When students are comfortable with the question mark switch to use a letter to represent the unknown)

Step 7: Write an equation and work computation to the side.

Step 8: Answer in a complete sentence to check for reasonableness.
   32 tickets

Here are some videos working through some problems:

Strip Diagram Example

Strip Diagram Problems

Here is an activity we play at school that helps us practice strip diagrams:

Thinking Blocks

Let me know if you have any questions!

Adding and Subtracting Decimals

Adding Decimals

To add decimals, follow these steps:

• Write down the numbers, one under the other, with the decimal points lined up
• Put in zeros so the numbers have the same length (see below for why that is OK)
• Then add using column addition, remembering to put the decimal point in the answer

Example: Add 1.45 to 1.3

Line the decimals up:			1.45
		+	1.3
"Pad" with zeros:			1.45
		+	1.30
Add:			1.45
		+	1.30
			2.75

Example: Add 3.25, 0.07 and 5

Line the decimals up:			3.25
			0.07
		+	5.
"Pad" with zeros:			3.25
			0.07
		+	5.00
Add:			3.25
			0.07
		+	5.00
			8.32

That's all there is to it - just remember to line up the decimals, then add normally.

Subtracting Decimals

To subtract, follow the same method: line up the decimals, then subtract.

Example: What is 7.368 − 1.15 ?

Line the decimals up:			7.368
		−	1.15
"Pad" with zeros:			7.368
		−	1.150
Subtract:			7.368
		−	1.150
			6.218

To check we can add the answer to the number subtracted:

Example (continued): Check by adding 6.218 to 1.15

Line the decimals up:			6.218
		+	1.15
"Pad" with zeros:			6.218
		+	1.150
Add:			6.218
		+	1.150
			7.368

It matches the number we started with, so it checks out.

Adding Zeros

Why can we add zeros?

A zero is really saying "there is no value at this decimal place".

In a number like 10, the zero is saying "no ones"

In a number like 2.50 the zero is saying "no hundredths"

So it is safe to take a number like 2.5 and make it 2.50 or 2.500 etc.

But DON'T take 2.5 and make it 20.5, that changes the number.

Here is a song we listened to to help us remember what to do:

Line Em Up Song

Here are some videos to watch:

StudyJams Addition and Subtraction of Decimals

StudyJams Making Change

Here are some games to play to practice this skill:

Adding Decimals Soccer Game

Subtracting Decimals Soccer Game

Hungry Puppies Adding Decimals

Decimal Subtraction

Decimal Addition

Hotel Decimalfornia – An Adding and Subtracting Decimals Game

Math at the Mall

Please let me know if you have any questions!