# 5th Grade Resources

### Here are all 5th grade resources. Click on the navigation to see resources designed for specific strands.

Enter two fractions, then watch as they are added together. "Why is the sum partitioned like that?"

This uses an area model approach for multiplication. Use as a tool to support students as they learn multi-digit multiplication, or take an inquiry approach by clicking "Randomize" and working slowly, carefully to figure out the two factors. What's the fewest pieces of information you need?

Use the sliders to adjust the factors, then "Slide me" to see the area model being constructed. This particular approach is meant to give additional visual support to students as they gain understanding of how tens x tens = hundreds, tens x tens = tens, and ones x ones = ones.

A simple tool for students who need support when finding a common denominator (or any other context in which they are looking for a common multiple).

Use the given quantity to estimate the others. Use the sliders to adjust the size of the numbers (10 to 1000) and number of questions. Kindergartners might use this to talk about more/less, while 6th graders might have highly sophisticated approaches involving unit rate.

Enter data in a list (or click RANDOMIZE), then see it displayed as a lineplot and/or boxplot. Select which of {Mean, Median, Mode} you want shown for each data set. Possible teaching moves include:

Make predictions about where each measure of center will fall

Justify why the mean would be above or below the median

Look for the connections between the lineplot and boxplot

Enter two whole numbers, then move the slider to see what happens when each is the dividend and divisor. (Works better with smaller numbers). Meant to help students understand the significance of dividend and divisor, including situations where the quotient would be a fraction.

This applet, while designed primarily to accompany contextual multiplication and division tasks, will work to illustrate any situation in which students are multiplying or dividing whole numbers. The main thinking behind it is that students can struggle with conceptualizing the three components of the majority of these problems: total number of objects, number of groups, and objects in each group. By providing a visual to accompany their thinking, we can help them to see the math they are doing, whether correct or incorrect based on the context. A specific way of using this would be to pair it with the Mathematical Language Routine Co-Craft Questions. Provide the beginning of the stem (like "Four friends have a recipe that makes 15 cookies"), and use this to help students consider different questions they could pose based on it.

Establish the decimal/fraction/percent connection by seeing three connected representations of a number [0,1).

Shows one factor and the product on the number line. Adjust the second factor (by increments of 0.1) and see the result on the product. Meant to develop understanding of 1 as a threshold for bigger/smaller product.

** **What dimensions (of a right rectangular prism - whole numbers only) can produce a given volume? What dimensions will minimize the surface area of a given volume?

An "Open Middle" format problem: What combination of digits and units would give you the greatest distance? What would give you the least? You must combine your number sense with an understanding of relative unit sizes as you develop a strategy.

Shows a quotitive approach for dividing a whole number by a proper fraction.

This resource is intended to get students to use proportional reasoning to estimate quotients. Use the sliders to generate random dividends and divisors, or input your own numbers. Start by dragging the numbers to the correct locations, then predict the number of "jumps" to land on the dividend.

This is designed to help students connect division algorithms to the "action" that is actually taking place. As students develop repeated subtraction or partial quotient approaches, use this to support them thinking "What is happening here?" as they represent the problem mathematically and attend to the meaning of the quantities.

In the style of "connect the dots." Enter ordered pairs and this will draw the lines connecting them.

An Egyptian fraction is the expansion of a non-unit fraction into a sum on unique unit fractions. For instance, 2/3 = 1/2 + 1/6 is an Egyptian fraction expansion, while 2/3 = 1/3 + 1/3 (not unique) and 2/3 = 1/3 + 2/9 + 1/10 + 1/90 (not all unit fractions) are not. Use this resource to explore these ideas, while getting some visual supports and an answer if needed. The provided answer is generated with what is called the Greedy Algorithm, which is not always the "best" expansion. See https://en.wikipedia.org/wiki/Egyptian_fraction for further explanation.

Place fractions sums and/or differences on the number line. You'll have (mostly) different denominators, so you'll have to use number sense to estimate. (These should be relatively QUICK placements!) Feedback provided.

Use the sliders to adjust the addends, then consider the size of the sum relative to the two bounds you are given. "Would the sum be closer to ___ or ___? How do you know?" As the level of precision increases, the level of mathematical reasoning increases with it. And the GRAND purpose behind this is to get students using an estimation strategy called front-end addition. Consider building this around a central question of "How do we make our estimates more precise?"

Use this applet to engage in some pre-algorithmic thinking. Enter any fraction, then use the sliders to see it arranged in various ways. Make connections to multiplication, division, addition, and (perhaps) even subtraction. Notice and describe patterns!

How do fractions map to the number line? How big do the numerator and denominator need to be to make it "full"? Is it even possible? Explore some of these questions and many others (like finding patterns in equivalent fractions) with this simple, but powerful applet.

Place 4 randomly generated rational numbers on the number line. Feedback provided.

What if we took a hundreds chart and replaced the whole numbers with fractions? Explore this idea by clicking "Add to path," then click on a square to show its values...but try to predict the value first!

**T**his tool is designed for students to explore the relationships within (and between) a mixed number fraction. The two main goals I'm envisioning are (1) make the number as big (or as small) as possible and (2) make some equivalent fractions. The best part is when students realize that the numerator can be bigger than the denominator.

Set upper and lower bounds. A random fraction in generated between the two bounds, with denominators limited to 2,3,4,5,6,8, and 10. Drag a dot to the correct location on the number line for the given fraction. Feedback provided.

A random function (or "rule") is generated based on the sliders. Send the numbers through the machine to figure out what the rule is. Click on the boxes to see the rule in equation or word form. Alternatively, show the rule then predict the outputs before sending the number through.

Enter a whole number, and the program will sort it in the Venn Diagram according to the two randomly determined rules. Play along with your students as you try various numbers to figure out the rules. Once you know the rules, add additional numbers to each part of the diagram. Possible rules include: bove or below a certain number; Rounds within 100 to a 10; Rounds within 1000 to a 100; Multiple of 3,4,5,6,7,8,9,10,11,or 12; Prime; Composite; Even; Odd

Enter a fraction or let the applet generate a random one for you. Estimate, name it, find some equivalent fractions, write it as an improper or mixed number, or (maybe) even as a decimal!

This activity is meant to develop flexible, creative thinking about numbers and operations. Your goal is to move a from a starting number to a target number, but there are many ways to do this! Adjust the sliders to control the bounds of the numbers involved.

How does multiplying or dividing by a power of 10 affect a number? Is the decimal point moving? (No!) Or are the digits? (Yes!) If I wanted to change 723.1 into 72,310, how would I do that?

Shows an array/area model for multiplying two proper fractions.

An extension of Multiplying Fractions. Shows an array/area model for multiplying two proper fractions, then allows you to simplify the product. NOTE: The simplification doesn't work perfectly, but should work well enough for simple fractions.

Demonstrates a visual model for finding products of mixed number fractions.

There's a randomly generated point somewhere in the first quadrant of the coordinate plane . You have 10 guesses to find it, with hints provided along the way.

A simple activity in which you put multiplication expressions in increasing order. Adjust the sliders to change the number of expressions and the number of digits in the factors, focusing more on *estimation *for large products.

A simple activity in which you put division expressions in increasing order. Adjust the slider to change the number of questions.

Enter a whole number (under 1 million) and it will be shown as a bar partitioned along base-10 values. Use this for a visual demonstration of, for example, why 543 > 345, beyond "because 5 is bigger than 3".

Drag the sliders to change the dimensions of the prism. Allow students to "see" how the volume formula is the product of the 3 dimensions, and how a 3D array evolves from a 2D array.

Designed to make a more concrete connection between dividend, divisor, and quotient. Use number sense to estimate the relative size of dividend and divisor, then use that to estimate the quotient.

Put various lengths (randomly generated) in the correct order. Select the units you want to use. Feedback provided.

A tool designed to investigating the notion of resistance in measures of center. A randomly generated dot plot is drawn (size determined by user). Drag the blue point to see how the mean and median are affected.

Enter a dividend, then adjust the slider to see it "divided" into groups and, if necessary, a remainder. If you wish, display the division equation and the related multiplication equation.

Enter a division expression, then select an approach to the division (partitive or quotative).

Designed to give an understanding of factors and prime/composite numbers. Enter an integer, then see it arranged in arrays. Move the slider to see the resulting array for various divisors.

Type any denominator into the box, drag the slider to change the number of wholes (up to 10). Drag the dots to shade various amounts. This tool has a wide variety of uses. Possibilities include:

Comparing fractions

Equivalent fractions

Mixed ↔ improper forms

Fraction sums and differences

Really, this can handle just about anything you'd want to do with fractions!

This is designed to accompany students as they begin to develop algorithmic approaches to subtracting mixed number fractions. This uses a comparison approach. (Do you see the difference, 2 5/6, in the GIF?) Go slowly and really dig into the conversation when you "regroup" (like when 5 2/6 → 4 8/6) so that students develop fluency with a strong conceptual base.

Designed to accompany this Open Middle-style task. Can you arrange the 9 numbers to maximize (or minimize) the total area of the four shapes? Can you make the areas as equal as possible?

Designed to build understanding of the connection between the area formulas of trapezoids and rectangles. Drag the slider to animate the illustration. Drag the vertices to change the shape. NOTE: This also works for parallelograms.

See the area and perimeter of any triangle.

Shows how the area for a right triangle is half that of a rectangle.

Designed to build understanding of the connection between the area formulas of triangles and rectangles. Drag the slider to animate the illustration. Drag the vertices to change the shape.

Select the units you want to use, then guess the volume of the liquid in the container. Feedback provided.

It's easy for students to develop bad habits when rounding. By rounding to "weird" numbers (i.e. those that are NOT powers of ten), we can focus on proximity to multiples, not just digits. Choose your own numbers - which can be "weird" (like 27 or 3.13) or "normal" (like 10, 100, 0.1, etc.) - or let the applet pick them randomly. Then slowly reveal the information on the number line, with lots of predictions and discussion along the way. When you DO switch to focusing on powers of 10, focus your students' attentions on the patterns that emerge.

Use this activity to develop definitions of simple polygons by noticing patterns. Build math language from informal to formal.

A random fraction is placed on the number line between 0 and the upper limit of your choosing (up to 10). Guess what it is, then click the buttons to provide additional information and refine your guess. When you're ready, see the answer in mixed number form.

Set the bounds (-1000 to 1000) and the level of precision (wholes, tenths, hundredths, thousandths). Then a random number is generated and placed on a blank number line. Your job is to guess where it landed. Click "next" to zoom in and refine your guess.