Multiplying Decimals 3 Act Task

Multiplying Decimals 3 Act Task

Earlier this year, students built conceptual understanding of multiplication of whole numbers and decimals and multiplication of decimals by decimals. They used concrete models and grid paper to model the multiplication to find the product. The standard, MAFS.5.NBT.2.7, requires students to, “Add, subtract, multiply, and divide decimals to hundredths, using concrete models or drawings and strategies based on place value, properties of operations, and/or the relationship between addition and subtraction; relate the strategy to a written method and explain the reasoning used.”

Many times, students can regurgitate the steps in “solving” a math problem yet, many students lack the skills to apply the learning to real life situations. Connecting Math to the real world is an integral part of learning and encourages retention of the skill. There are many opportunities for students to engage in real life math that encourages them to practice the skill of multiplying decimals.

Check out these videos from https://gfletchy.com/gassed/ where students can apply their understanding of multiplication of decimals to a real life situation.

How much will it cost to fill up the gas tank?

Show students this quick video and have them make predictions about the cost of filling the gas tank. Estimation is an underutilized skill that is beneficial to helping students decide on the reasonableness of their answer.

Show the tank capacity and price per gallon to the students and watch them solve! Note the strategies they use when solving for the cost to fill up the car.
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Once students arrive at their answer, show them the following video to discuss if their answer was reasonable.

For more 3 Act Tasks ideas, check out https://gfletchy.com/3-act-lessons/

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FREE Common Core Aligned Online Interactive Math Practice

FREE Common Core Aligned Online Interactive Math Practice

kid at computer
Checkout these two FREE interactive websites for additional math practice: www.tenmarks.com and www.frontrowed.com

Both websites allow you to set up a free teacher account. You can then enter in your student roster, assign specific standards-based practice to each student, and track their progress. Students are given a log-in and password, so they can access the program from home, too.

FrontRowEd includes a diagnostic with adaptive practice to provide students practice at their level in addition to teachers’ ability to assign targeted practice. Students can click to view a youtube video for more information on a concept, and there is an option for fact practice.

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TenMarks provides students with real-time feedback, and students can access “hints” and videos for immediate scaffolding. Students can work on building fluency in “Jam Sessions”. It also has teacher resources, including lessons with anticipated misconceptions. This program

Sample Student View:
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Sample Class Assignment Summary Report:
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Sample Individual Student Assignment Report:
studentreport
Either program could be beneficial for differentiating instruction and providing students with practice responding to technology enhanced math items. Keep in mind, there may be slight variations between the Common Core Math Standards and our Mathematics Florida Standards, so you will want to make sure that all assignments align with MAFS.

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Keeping Math Fun During and After Testing

Keeping Math Fun During and After Testing

Franklin Boys
Checkout this quick and easy read “Tips to Keep Math Fun During Testing” from the tenmarks.com blog.

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5th grade HCTM Problem of the Month Winner February Edition!

5th grade HCTM Problem of the Month Winner February Edition!

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Congratulations to the 5th grade winner of the Problem of the Month competition for February! There was more than 1,000 students that entered to win. The winner is Millay from Ms. Cannella’s classroom at Mitchell Elementary!

5th grade POM winner February 2017 1

5th grade POM winner February 2017 2

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3rd grade HCTM Problem of the Month Winner February Edition!

3rd grade HCTM Problem of the Month Winner February Edition!

3rd-grade-pom-header

Congratulations to the 3rd grade winner of the Problem of the Month competition for February! The winner is Andrew from Ms. Bailey’s classroom at Chiles Elementary

3rd grade POM winner February 2017

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1st grade HCTM Problem of the Month Winner February Edition!

1st grade HCTM Problem of the Month Winner February Edition!

header-pom-1st-grade

Congratulations to the 1st grade winner of the Problem of the Month competition for February! The winner is Abigail from Gitlin/Shepard classroom at Trapnell Elementary.

1st grade winner February 2017

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13 rules that expire in Math!

13 rules that expire in Math!

Have you ever heard someone say, “When you multiply, your product is always greater than your factors”, “When you divide, your quotient is always less than your dividend and divisor.” Are these statements always true? Are we inadvertently teaching misconceptions to our students by stating these “rules?”

If you multiplied 3 x 1/3, would the product be greater than the factors?
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Many students are taught that when you multiply your product is always greater than your factors, but that rule only applies when you are working with positive whole numbers. When fractions, decimals and negative numbers are later introduced, the rule is no longer true.

How about when you divide 2 and 1/2? Would the quotient be less than the dividend and divisor?
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When students first learn about division they focus on the partitive understanding, that when you are sharing a quantity you cannot have more than what you started with. However, that rule expires when you begin dividing whole numbers and fractions/decimals and fractions by fractions or decimals by decimals.

Karp, Bush, and Dougherty, state, “Overgeneralizing commonly accepted strategies, using imprecise vocabulary, and relying on tips and tricks that do not promote conceptual mathematical understanding can lead to misunderstanding later in students’ math careers.” Check out this article written by Karp, Bush and Dougherty, on more rules that expire in Math! http://www.scusd.edu/sites/main/files/file-attachments/13_rules_that_expire_0.pdf

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Looking at Line Plots in 4th Grade

Looking at Line Plots in 4th Grade

In 3rd grade, students measured objects to the nearest half and quarter of an inch and displayed that data on a line plot. In standard MAFS.4.MD.2.4, 4th graders extend that learning to include displaying measurements to nearest half, quarter, and eighth of a unit on a line plot. They must also solve problems involving addition and subtraction of the fractions to interpret data from a line plot.

4th graders are required to synthesize a lot of prior learning: creating and interpreting line plots, measuring to nearest fraction of a unit, displaying fractional amounts on a number line/ordering fractions, and addition and subtraction of fractions (note that our FSA Item Specifications state that addition and subtraction are limited to like denominators). Students may need support with any one of these concepts; the resources below can be used to access their prior knowledge or to scaffold instruction.

“Magnify an Inch” – blog post with instructional ideas for teaching students about fractional parts of an inch; can easily be extended to include eighths
magnified inch compare

“Measuring Length with Fractions” – blog post with lesson ideas for measuring objects to the nearest half and quarter of an inch; can also easily be extended to include eighths
paper rulers marked

LearnZillion Lesson: “Measure and Represent Objects to the Nearest Whole, Half, and Quarter Inch Using a Ruler and Line Plot” – lesson ideas to access students’ prior knowledge about measuring to nearest faction of a unit, and displaying and interpreting measurement data on a line plot
line plot

LearnZillion Video- “Identify Equivalent Fractions on a Number Line” – video that can be used to reteach representing fractions on a number line, as well as using a number line to find equivalent fractions; students may need reteach on these skills in order to create the horizontal axis of their line plot to display measurement data to the nearest fraction of a unit
equiv fract

LearnZillion Video: “Add and Subtract Fractions with Like Denominators” – video to revisit why only the numerators are added or subtracted when adding or subtracting with like denominators
add fractions

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Engaging Computer Games to Build Multiplication Fact Fluency

Engaging Computer Games to Build Multiplication Fact Fluency

kid at computer
Checkout these engaging online games to help increase fluency of multiplication facts. These games could be incorporated into a math block at school or accessed from home:

Clear It
clear it
http://www.abcya.com/clear_it_multiplication.htm

Math-Man Mutliplication
math man
http://www.sheppardsoftware.com/mathgames/mathman/mathman_multiplication10.htm

Multiplication Blocks
multiplication blocks
http://www.mathplayground.com/multiplication_blocks.html

Number Trails
number trails
http://www.mathplayground.com/number_trails_multiplication.html

Kakooma
kakooma
http://gregtangmath.com/kakooma

The following games are great for those students who may not know all of their facts. Students can select which facts will be included in the game, so they can build fluency with the facts they know.

Multiplication Snake
multiplication snake
http://www.mathplayground.com/ multiplication_snake.html

Zogs and Monsters
monsters
http://www.mathplayground.com/zogs_and_monsters/zogsandmonsters_multiplication.htm

Puzzle Pics
puzzle pics
http://www.mathplayground.com/puzzle_pics_multiplication.html

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4 Strategies to Engage ALL Learners in Mathematical Discourse

4 Strategies to Engage ALL Learners in Mathematical Discourse

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We know that today’s math instruction is very different from our experiences as students. The teacher takes on the role of the facilitator, presenting students with problem solving scenarios and using students’ sharing as the primary means of promoting understanding. It is the discussions about students’ thinking that serve to engage students in the mathematics and advance the learning of the whole class…often relying on the assumption that the rest of the class is actively listening and engaged. In the March 2017 issue of NCTM’s Teaching Children Mathematics, Damon and Kim Bahr’s research based article “Engaging All Students in Mathematical Discussions” cautions against this assumption, and offers four strategies to ensure that students are actively listening and consistently engaging in discussions.

1. Tell students what to listen for. Specifically assign a listening role to your students; give them a purpose for listening to their classmates’ thinking. The authors used thinking levels to create a “menu of thinking levels and listening roles” categorized by teacher’s purpose.
listening roles

2. Teach them how to engage in the listening role. Tell students the listening role, model it and provide them with wording and sentence stems. Many of the accountable talk stems referred to in the blog post “How to Get Your Students Talking About Math”could be connected to specific listening roles.

3. Call on listeners to respond during and after sharing. Students can be asked to respond while the sharing takes place at those key points that will help all students move towards a deeper understanding of the learning goal; this can occur in the midst of a student’s sharing or after. Students may be purposefully called on to respond in their listening role, or it may be random.

4. Have routines in place. The authors identify three main reasons why listening students will not or can not respond: (1)the task may be inappropriate, (2)the shared understanding was too difficult for listeners, or (3)the students were not listening. If the task was inappropriate, it may lack personal meaning for students, not capture their interest, or it may not be developmentally appropriate. In the case that the students did not understand what was shared or chose not to listen, they can use routine responses, such as, “I’m sorry, I was listening but I don’t really understand what you said. Could you explain it another way?” or “I’m sorry, I wasn’t listening. Would you mind repeating what you said?”

These 4 four strategies, in conjunction with established math norms and an effective classroom management plan, will dramatically impact student engagement in mathematics discussions.

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How Does Teacher Language Affect Student Learning?

How Does Teacher Language Affect Student Learning?

Quick, but interesting read on how our descriptions and language used to describe student learning and goals could potentially affect student learning. For instance, when we describe a certain skill as a “3rd grade skill” or say “a 4th grader should have been able to do this”, what does this do to the child?

STEM News Article – Teacher Language

The article doesn’t readily offer a solution, but we can all reflect on our own practices after reading.

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Joining and separating….using actions to understand addition and subtraction

Joining and separating….using actions to understand addition and subtraction

According to MAFS.K.OA.1.1, students in kindergarten are required to, “Represent addition and subtraction with objects, fingers, mental images, drawings, sounds (e.g., claps), acting out situations, verbal explanations, expressions, or equations.” They are also required to, “Solve addition and subtraction word problems, and add and subtract within 10, e.g., by using objects or drawings to represent the problem.” (MAFS.K.OA.1.2)

As students begin to understand addition and subtraction, the focus should be on joining and separating situations. These situations should reflect students’ real-world experiences with joining and separating. When exploring joining and separating situations, students will act out the situation using tools or pictures. This is called direct modeling. Direct Modeling will help them develop a strong foundation of the operations. As students directly model the problem, the focus should be on using the ACTIONS in the problem to determine the operation, NOT KEYWORDS.

When solving a problem similar to this, counters may be used to model the action of the frogs jumping into the pond.
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Or they can be used to model the eating of apples.
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Tens frames are also a great tool to be used in conjunction with counters to model the actions in a word problem.
Join

This hands on approach will help Kindergarten students develop a strong understanding of addition and subtraction concepts through the actions of joining and separating.

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Make a Ten Card Game

Make a Ten Card Game

MAFS.K.OA.1.4, states that, “For any number from 1 to 9, find the number that makes 10 when added to the given number, e.g., by using objects or drawings, and record the answer with a drawing or equation.”

A fun game to reinforce this standard is the “Make a Ten” card game.

To play this game, you will need a deck of playing cards. From the deck, you will use the Ace-9 cards from each suit.

Use 9 cards to create a three by three array as shown in the picture below:
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This game can be played individually or with multiple players.

In this example, the game is played with 2 players.

To begin play, Player 1 will select one card. In the image below, the first card selected by Player 1 was a 6.
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Then, Player 1 will select a second card that would, when combined with the first card, make a value of ten. In this case, the card that would make the value of ten is a 4.
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Player 1 will use the two cards to record the answer with a drawing or an equation.
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The two cards that were selected by Player 1 are replaced with two new cards and play switches to Player 2.
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Player 2 will then begin his/her turn by selecting their first card, in this example, Player 1 selected a 9. Then, Player 2 will select a card that when combined with 9 will have a value of ten. The Ace, which represents the value of one, is selected to make a ten.
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Player 2 will use the two cards to record the answer with a drawing or an equation.
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Play continues until all combinations of 10 are made.

This is a quick and easy game that can be used to reinforce combinations to 10!

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Division Progression

Division Progression

The progression of division starts in 3rd grade…and it is crucial that students really develop a deep concrete understanding of division. If your 4th grade students are still relying on drawing pictures of equal groups with tally marks, they may not have that deep understanding necessary to progress to more efficient strategies, such as the area model.
3rd division area model
3rd division area model 2
Checkout the short video below about the progression of division, so that you can support your students in finding whole-number quotients…using strategies based on place value, the properties of operations, and/or the relationship between multiplication and division…illustrate and explain…using equations, rectangular arrays, and/or area models (MAFS.4.NBT.2.6). There sure is A LOT packed into that 4th grade standard, and this video will not only show you the foundational understanding they need, but it helps to unpack what students’ understanding of division should look like in 4th grade.
4th division area model division

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Kids Confused by Conversions? Kick the Quick Tricks!

Kids Confused by Conversions? Kick the Quick Tricks!

Teachers are often wary about teaching measurement conversions through problem solving…we revert to mnemonic devices, tricks and chants rather than encouraging students to use the same problem solving strategies we have been trying to instill in them all year.

Why is it that we suddenly think it is more valuable to have students practice drawing the “Gallon Man”, memorizing how “King Henry Died Drinking Chocolate Milk…”, or chanting “Larger to smaller means to Multiply” than to provide them with experiences and strategies to help them make sense of the units and their relationships?

On her website www.mathcoachscoarner.com, Donna Boucher suggests encouraging students to use a 4-step problem solving process to develop their concrete understanding of the relationship between the units while incorporating the use of a reference sheet.

The steps are:
1) Write down what you are trying to identify from the story problem.
2) Identify the useful conversion from the reference sheet.
3) Draw a model of the conversion from the reference sheet.
4) Draw a model to represent the values from the story problem.

ref sheet

Here is her example of the steps for the following story problem: “Sue needs two gallons of lemonade. The lemonade she wants to buy only comes in quart containers. How many quart containers will she need to buy?”
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Not only does this strategy help with making sense of story problems, it is also useful when students complete a 2-column conversion table. Read more at http://www.mathcoachscorner.com/2012/01/two-ways-to-approach-measurement-conversions/

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But my 4th graders can’t tell time!

But my 4th graders can’t tell time!


Elapsed time is incorporated into the 4th grade standard MAFS.4.MD.1.2: Use the four operations to solve word problems involving…intervals of time…and represent intervals of time using linear models. But what do you do when your students can’t tell time, let alone represent time on a number line? These 3rd grade blog posts have some great instructional strategies that you may find helpful when scaffolding instruction and trying to find the “time” to reteach telling time.

It’s That Time! Ideas on how to incorporate mini time tasks
time match
Relate a clock to a number line!
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Use a number line to determine elapsed time!
elapsed time number line

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The Progression of Multiplication

The Progression of Multiplication

By the end of 4th grade, students should be able to apply their understanding of place value and properties of operations to multiply a whole number of up to 4 digits by a one-digit whole number and multiply two two-digit numbers and then illustrate and explain their thinking using equations, arrays and/or area models (MAFS.4.NBT.2.5)….but we know that students access standards at varying levels, and it can sometimes be tricky to pinpoint where that is exactly. This video clip can provide you with some insight on where your students are at in the progression of multiplication, so that you can respond with instruction that builds foundational understanding they may be missing, or help students make connections so that they can move forward along the progression.

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Arrays, Area and Perimeter Game

Arrays, Area and Perimeter Game

Checkout this interactive game “Area Blocks” at http://www.mathplayground.com/area_blocks.html !

This game is a fun way for students to relate area and perimeter to the operations of multiplication and addition. Students either play against the computer or another player to create shapes of a given perimeter and area on a grid.

area blocks directions

area blocks image

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Taking a Step Back to Support Students with Area and Perimeter

Taking a Step Back to Support Students with Area and Perimeter

Are your 4th graders struggling with area and perimeter? It may be time to take a step back.

Ms. Park noticed that her 6th (yes, SIXTH) graders were struggling with the concepts of area and perimeter, too. Watch the clip below to see how she revisited the 3rd grade standards of area and perimeter of rectangles to solidify students’ conceptual understanding before she introduced the 6th grade standards. Could your 4th graders be struggling with applying the formulas for area and perimeter of rectangles for the same reasons?

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Putting the ‘Fun’ Back into Functions

Putting the ‘Fun’ Back into Functions

zoltar

Functions can be overwhelming with all of the f’s, x’s, and f(x)’s. But in reality, functions are quite easy to understand once you know how they work.

So what is a function? Well, a function can be described as a relation from a set of inputs to a set of possible outputs where each input is related to exactly one output. Think of a function as a fortune telling machine. If you fill out a card with your first name and birthday and then feed the card into the machine you will receive your fortune. It is important to note that in order for this to be a function, the same name and birthday combination will receive the same fortune as you. Think about it this way: If it were truly a fortune machine, why would you expect to get a different fortune if you did it 3 times in a row? You wouldn’t!

In math class, the information that you feed the machine is called the input or x. Your fortune is called the output or the function of x. The functional notation for this is f(x) although other variables can be used such as g(x) or h(x). As outputs are generated, a table can be used to visually display the values.

function table A function is the mathematical computation(s) in between the input and output. In this example, we need to determine what happened to the input to get the corresponding output. Each input was multiplied by 3. Therefore, the function is f(x)= 3x. A common error occurs when only the inputs or outputs are compared. While a pattern may be seen, it is important to make the connection between the input and output.

Want to have some fun? Check out this interactive function machine where you guess the function!

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