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Checking Your Work

Homework is a tricky subject in our house.  One family member is an elementary teacher, one family member is in kindergarten and one family member has chaperoned a field trip, helped on the weekends and attended elementary school many, many years ago.  You can imagine that a certain someone – ok, it’s the dad in our house – tends to get told what to do all to often when trying to help out with homework.

This week, as I was fixing dinner, Adam sat down to help out with the weekly math homework.  Things are pretty simple at this stage of the game.  We’ve seen lots of tracing numbers 1 through 5 and some matching numerals with dots or cubes.  This week’s homework asked the kids to extend a bug pattern.  Lots of cutting and pasting – right up kindergarten alley.  Since patterning didn’t seem to require too much nuanced discussion, I happily let Adam take over.

Math Practice 6

After assembling all of the materials and lots of cutting, they set about figuring out what bug came next in the pattern.  Then, the magic happened.  I heard Adam say, “Check it to make sure it sounds right.”  Ah, be-still my heart.  Without even knowing it, he was instilling in our barely 5 year old daughter, an overarching habit of mind – oh so important to mathematical proficiency.

Outlined in the Common Core State Standards of Mathematics are content standards (what the kids should know) and the practice standards (how kids should “behave” with math).  The content standards are what many think about and, unfortunately, the practice standards are often brushed aside.  This might be be due, in part, to their location in the standards document but it is also because the wording tends to be a bit complex.  Many teachers have been working on trying to understand the eight math practice standards and apply them at the level they teach.  While the ideas are big, and extremely important, at the earliest grades, these practice standards can look quite simple.

Math Practice 6, Attend to precision, emphasizes precise use of math language and vocabulary as well as accuracy.  This obviously looks different at different levels but with kindergarten, “Checking your work” can elicit this standard.  Every time you ask your child to check his/her work or praise him/her for doing it independently, you are reinforcing the idea that review supports precision.  If you think about it, you can apply this thinking to a variety of subject areas.  How many times did your teacher ask you to reread your writing looking for errors and opportunities to improve?

Just like everything you do with your very young children, establishing routines early can lead to habit.  Maybe I’ll let the novice take over more of the responsibilities with math homework!

You can learn more about the standards for mathematical practice from Dreambox.  If you want more in depth information you can get it from Think Math and Illustrative Mathematics.

The simplest math tool you never knew existed . . .

How are you feeling about your child’s knowledge of addition and subtraction facts?  Are you worried that he hasn’t memorized them yet. Worried that his teacher isn’t focusing on facts enough?  Well, if you’re older than 18, you probably learned math very differently than your child is learning math today.  Here are a couple of tidbits that differ greatly from math instruction in “our day” and math instruction today:

1. The Common Core State Standards for Mathematics specify that children should learn their addition and subtraction facts through strategy work, not from drill and practice.

2. The standards outline that, by the end of kindergarten, kids should “add and subtract fluently within 5” which means that they should be able to add or subtract any numbers up to 5 and get the correct answer with relative speed.  By the end of first grade kids should be able to do this within 10 and that not until the end of second grade should they “know all sums within 20 from memory.”

So how can you help your child with math homework if you don’t know how they’re supposed to learn their facts?  I’m just going to lay it out on the table – talk to your child’s teacher first if you’re not sure what to do or how to help.  Also, remember that your job is to help your child “figure it out” not to do the thinking for him.  Beyond all that, here’s an amazing tool you can create and use to help your child at home.

Ready for it?  It’s called a . . . Rekenrek.  If it’s easier, call it a number rack.  Literally translated it means arithmetic rack and it was created in the Netherlands.  It was invented a good time ago to help children understand the number system, develop number sense and improve computational fluency (learn addition and subtraction facts).

Rekenreks are easy to build.  All you need is 2 black pipe cleaners, 10 red pony beads, 10 white pony beads and a piece of foam board (a piece about 4 inches by 8 inches is plenty big).  Cut 2 slits on the short sides of the board, evenly spaced between each other and the edges of the board.  String 5 red and 5 white beads on each pipe cleaner and pull through the slits on the foam board.  It is important to make sure that the bead color lines up on both pipe cleaners.  When completed, all beads should be pushed to the right and the beads on the left should be red and the beads on the right should be white.  See the images below.

The simplest math tool you never knew existed . . .The simplest math tool you never knew existed . . .The simplest math tool you never knew existed . . .

 

These are easy to build and there is value in having your child build it (with guidance).  On a Rekenrek, each bead represents 1 so by building it himself, your child will see the embedded structure of 5 red and 5 white to make 10 and the overall structure of 10 and 10 to make a total of 20.

So here’s how the Rekenrek can help your child.  When working on facts, typically your child only sees the numeral (the symbol for the number).  Using the Rekenrek allows your child to see the quantity attached to each number.  Through practice your child will eventually come to just know these facts.  What’s more, your child is likely learning strategies for adding and subtracting.  For example, many children learn doubles  (4+4, 5+5) automatically.  Children can use this knowledge to solve near doubles.  Children recognize that in the problem 6+7, 7 can be split into a 6 and 1 to make the problem 6+6+1.  The problem with this strategy is that because children easily memorize doubles they don’t “think” about what the fact means.  So asking them to use the double to solve a close fact isn’t always intuitive.  Demonstrating this on the Rekenrek lets your child literally see the double plus 1.

 

The simplest math tool you never knew existed . . .

Work with Rekenreks support much more basic understanding of number as well.  Rekenreks help children subitize (recognize small quantities without counting) and work with composing and decomposing numbers.

The simplest math tool you never knew existed . . .

Below are links to 2 activity guides (meant for the classroom) you could use with your child to support understanding of numbers and operations.  They are free!

Using the Rekenrek as a Visual Model for Strategic Reasoning in Mathematics

From the Math Learning Center – an in-depth series of lessons that builds from most basic number sense skills to addition and subtraction activities.

Mathrack Activities and Directions

From Mathematically Minded – a brief description of activities as well as assembly instructions.

Bedtime Math

My principal has started sharing all the math related articles he finds with me.  On the one hand, it means I’ve got more reading to do.  On the other, I find out about awesome resources like . . . Bedtime Math!

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So the idea is this: everyone knows about the importance of reading a bedtime story.  Why not some bedtime math problems?  This nonprofit, working in partnership with the Overdeck Foundation, has developed bedtime math problems associated with a short story.  Each story has 3 levels of problems based on age and skill.

daily math problem

 

They’ve even got a book for sale that builds on the same ideas you find on the website.

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Upload the app for bedtime math on the go!

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Perhaps my favorite at bedtimemath.org is the Crazy 8s Club.  This club is designed to meet after school for about 8 weeks for varying grade levels/ages.  Anyone can lead the club and the materials are free.  What an amazing resource!

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Restaurant Math

I was never amazing at packing enticing activities for my little one while waiting at a restaurant.  I’d always remember, right as we handed our waitress the menus, that prepared moms packed a goodie bag to keep their children occupied.  Luckily, I learned how to make due with what we had.  As my daughter hit toddlerhood, we began playing games with the sugar and jelly packets often found at breakfast diners.  From this, restaurant math was born.

The idea of this activity is to support a child’s ability to subitize (seeing a quantity without having to count it).  This is a vital skill and kids are able to subitize small quantities from a very early age.

So the idea is this . . .

Select a few different sugar or jelly packets.  Quickly scatter them in groups for your child to see.  Initially, put out one or two items and ask, “How many?”  Your child will likely be able tell you without having to count.  Here’s the most important part.  After your child tells you how many, always follow up with, “How do you see it?”  This will seem silly with just 1 or 2 packets because it’s pretty obvious, even if you’re 3!  Even so, it’s ok for your child to learn to say, “I can just see it!”  When you start to increase the quantity, it helps your child develop a  verbal pathway to explain his/her thinking about the connection between quantity and adding.  So if you put out 5 packets, your child might say, “I see 3 and 2.” or “I see 4 and 1.”  The colors you use and the arrangement you use will impact what your child sees.  When you first start increasing the quantity, separate the items with a lot of space and by color.  This will help your child “see” the groups.  As your child gets stronger at subitizing, you can put the items in one group.  Think about dice patterns.  Here are some photos of what this might look like early on.

 

"How many?" "5!" "How did you see it?" "I see 2 purple and 2 red.  That's 4 and 1 orange is 5!"

“How many?”
“5!”
“How did you see it?”
“I see 2 purple and 2 red. That’s 4 and 1 orange is 5!”

 

"How many?" "Um, 6!" "How did you see it?" "I saw 2 blue and 1 pink.  That's 3.  And 3 yellow are 6!"

“How many?”
“Um, 6!”
“How did you see it?”
“I saw 2 blue and 1 pink. That’s 3. And 3 yellow are 6!”

Even though your child may be able to see the groups, don’t expect him/her to know the total without counting.  Early on, children will need to count to determine the total.  In the picture above, your child might say, “I see 2 blue and 1 pink, that’s 3.  There are 3 yellow!  So 1, 2, 3, 4 ,5, 6!”  As children become more familiar with the different groupings, he/she will begin to recognize how smaller groups are combined to create a larger total.

 

For more information on early subitizing, read the article, Beyond Counting by Ones, by Deann Huinker.  This article is full of activities you can do with your child.

What activities have you invented to keep your kiddo occupied?  I’d love to hear about it!

Counting by Twos

Counting by twos supports a variety of other mathematical tasks.  Counting by twos allows students to count more quickly.  More importantly counting by twos supports doubling, pairs and grouping for multiplication.  Here are some activities you can do to help your child learn to count by two numbers and understand what it means to count by two.
 
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  • Take turns counting.  You say “1”, your child says “2”, you say “3”, your child says “4”, etc. through 20.  Do the counting again but this time you whisper (your child still says the number out loud).  The third time you just mouth the number but your child still says the number out loud.  This will reinforce the counting by twos skills.
  • Think of a toy that is both small and interesting, that already belongs to your child.  Legos, blocks, cars, etc.  Play a game where you set out a pile and ask your child to figure out how many.  Your child should touch two and count two as he/she pushes them away from the pile.  Also, when he/she is done counting, ask if every item had a partner.  Ask if the group was even (each item had a partner) or odd (one item was left without a partner).  Take turns selecting and then counting piles.

Penny Stacking

Penny StackingI still remember the giant tootsie roll piggy bank that held all of my pennies for college.  I’m pretty sure that those pennies didn’t pay for more than a semester’s worth of books but they did create some very fond memories of my childhood.  When I was a little girl, my dad was the best playmate I ever had.  Sometimes I think he had more fun playing than I did.  One thing we did was play with pennies.  Nope, I didn’t lack toys.  It was just something different to do.  Somehow he knew, without formal training, ways to incorporate math into play.  Here are a few penny ideas (with lots of credit to my dad):

  • Count them . . . So this is obvious!  But, since the value of a penny is 1 cent, it’s a perfect item to count.  Starting a penny collection is both interesting to kids and financially responsible!

Counting Pennies

  • Stack them in towers of 5 or 10 . . . This reinforces skip counting which is a vital skill to counting mixed sets of coins (down the road).  It also shows the difference (in height) between 5 and 10 and lends itself to the idea of 5 being half of 10.  Build two 5 towers and one 10 tower, then let your child explore what happens when the five towers are combined.  Compare with the height of the 10 tower.

Penny Towers

  • Build structures with them . . . Pyramids, mazes, designs, anything!  This activity helps kids see what can be done with circular objects and consider structure.  After building, count the pennies to see how many it took to build each structure.

Penny Building

  • Tell stories . . . Young children can solve simple word problems, especially about food and other things at their interest level.  Money is a bit trickier because it doesn’t mean to kids what it means to us.  If you use pennies to solve word problems, focus on the coin, not the value.  For example, say, “Lilly had 5 pennies.  Then she got 2 more.  How many pennies does she have now?” instead of, “Lilly has 5 cents.  Then she earned 2 more cents.  How much money does she have now?”  At early ages, coins are more about collecting the object than the financial value they hold for adults.
  • Pretend to “buy” things around the house . . . You can help your child develop the idea of using money to buy something.  They see you buy things all the time but what are you usually using to pay?  Even if it isn’t your credit/debit card, you’re probably not paying in coins!  But kids idea of money and what they will learn about money early in school revolves around coins.  Set up a store with things around the house.  You can even label items with their value (5 cents, 2 cents, etc.).  This would help them with recognizing numbers and connect the numeral to a quantity (the fancy word for that is cardinality).
  • Build a penny staircase . . . So this is similar to the idea of using pennies to build different structures.  The important thing about the staircase is the increase by 1 nature.  This visual shows kids clearly how our counting sequence refers to quantity (cardinality again) and how when we count forward, we are actually adding and when we count backwards, we are subtracting.

Penny Staircase

Can you think of other fabulous things to do with pennies?  Please leave a comment.  I’d love to hear your ideas!

Understanding Teen Numbers – Kindergarten/First Grade

This video shows a quick activity, families (or teachers) can do at home (or school) to support understanding of teen numbers.  I used what I had – buttons, paper, marker and a four year old.  This activity is more appropriate for kindergarten age students or first grade students still developing their sense of teen numbers.  It gets at the idea of ten being not only a group of ten ones, but that it could also be considered one ten, an important concept for children to grasp to understand place value. It moves from using concrete objects, to representing them on a ten frame and then using the number symbol for teen numbers. It also helps children see the “hidden” 10 in teen numbers, something not obvious since we say “teen” not “ten”.

Credit for the idea of this activity goes to Melissa Hedges and Beth Schefelker who facilitate the Numbers and Operations in Base Ten, K-2 module for the Brookhill Institute of Mathematics.  They are amazing teachers and mathematics leaders!

Here are a couple of items to note:

  • This activity requires that your child/student know how to count and read numbers to 20.
  • After counting, it is important to ask, “So how many?”  This indicates that your child/student understands an aspect of cardinality that the last number you say represents to total collection.  If your child needs to recount the collection each time, this task might be too advanced.  Working on basic counting and one-to-one correspondence would be more appropriate.
  • If your child is an older kindergartener, a good question to ask about the group of 10 ones would be, “What else could we call this group?”  The idea is to help your child think flexibly about 10 as a set or group.  Ten can be considered 10 ones (that can be broken apart when regrouping in double digit subtraction) or ten can be 1 ten that can be thought of as a clump or group (so that 2 can represent 20 in the numeral 25).
  • The steps of this activity are important.  Children/students move from working with concrete objects (i.e. buttons) to representations (ten frames – adding a step where students match a ten frame to their button ten frame would be good) and then to the symbolic (using the numerals to represent the teen numbers).  For children/students who have worked with or have understanding of number bonds, number trees or equations, ask the child to represent the activity with one of these abstract concepts as a concluding step.

The handmade ten frames are available for free as (nicer) PDFs on  Teachers Pay Teachers.  The place value cards are available there too but I had list them at a cost (too many pages).  I’ve added a new page for downloads so you can find the place value cards right here for free!

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