Math Mania Continues! This week, meet The Value Pak family! We struggled with this character to truly be able to create something that captured what I was thinking. The Value Pak family represents the strategy of partial sums in our Math Mights Addition Strategies 8-in-1 Flip Chart and visually is a representation of the place value strips that we use all the time (you can get them in our store!). We use them for everything from place value to addition and subtraction (the Why Before How book talks more about how to use this versatile manipulative). Place value is a fairly abstract concept for kids. When you have a number like 135 and you need to add 40 more, kids often have a hard time manipulating and seeing the different parts of the numbers. They don’t realize that the numeral 3 in the number 135 has the value of 30 because it just looks like it is a 3. Place value strips are manipulatives help kids decompose numbers by place value to see that 135 is really 100 + 30 + 5. The strips actually show the zeros associated with each quantity and because the zeros are hidden underneath each number, it allows children to understand the places. Typically, zero means none for kids, but the place value strips help them see that zero can actually hold a place and that, if we were to add 70 to 136, we couldn’t just squish the two place values together because they all represent their own place.
The Value Pak
The Value Pak was designed to remind kids of a family, or a pack, that would all represent their own value. When we started thinking of a character for this idea, we struggled with both a name for the character and what it would look like. I chuckle a little bit now thinking back to John (of Johnny ‘Toons) and Ken (our graphic designer) and I meeting in a library in Plymouth, MI to share ideas. We talked about a character that would fit together like a puzzle. Originally, we had these monster-like characters with really large noses and, if you got them close, they would use their noses to click together. As we started looking at the characters and what kids might think about them, we decided we needed John to come up with something else! What he brought instead was the idea to have the characters click together, not with a nose or a body part, but with interlocking sides when they came near each other. The Value Pak really does look like the manipulatives they’re patterned after. The place value strips (and discs) all have a certain color for each value – the 1s are white, the 10s are red, etc. – which is really helpful and consistent for kids as they start to understand place value. We chose a family because, in a family, everyone works together in a family unit, but each individual person within the family holds their own value. Whether that’s the mom or dad that’s working, or the children being responsible for taking care of certain things at home or school, they all have their own responsibilities. But when they’re together, they click together to form one whole group. For example, if you were to look at the number 26, and break it apart into individual units, it would be 20 and a 6. We don’t just use place value with whole numbers, though. We also sell place value strips in decimals, which has been pivotal for 4th and 5th graders who perhaps didn’t understand whole number place value and are now struggling with trying to grasp that same concept with decimal numbers. With Math Mights, when you flip to the advanced side of our 8-in-1 poster, you can use the same partial sums strategy of The Value Pak with the family that has decimals. They also are consistent in their colors, where the tenths are brown, the hundredths are green, and they all have their own value.
Understanding Place Value
We have identified place value as an area where students tend to be weak among our project schools. Kids don’t often have the number sense they need to be able to grasp place value and it is such an important concept. There are three questions I use when I’m helping kids understand place value:
- What is the digit? Digits in our place value system are the numbers we use – 0 through 9. Kids need to be fluid in being able to identify the digits within various numbers.
- Where does that number live? In that family (the number as a whole), where does that particular digit reside – hundreds? tens?
- What is the value? Finally, kids need to be able to articulate what value a number holds. When I’m looking at the number 125, what value does the 2 hold? It’s worth 20, or two 10s.
When we think of the strategy for The Value Pak using partial sums, you can be reminded of D.C. Partial sums is like D.C. where you decompose, but in this case, you’re only decomposing by place value. If I had 25 + 32, I would decompose (break apart) 25 into 20 and 5, and I would decompose 32 into 30 and 2. This way, the problem becomes simple because you can add your 10s and then add your 1s. You can use this same strategy of partial sums when adding decimals. Kids need to attend to place value and identify what they’re doing as decomposing. The way that they write it, they have to be careful that they’re keeping the value of the number while they’re doing the decimals to make sure they know if they’re in the tenths or hundredths because if they go beyond the number will go into the next place value (10 tenths = 1 whole or 10 hundredths = 1 tenth). While we were growing up, it was drilled into our heads that if we had to add two 2-digit numbers (or higher) together, you would ALWAYS start in the 1s column. And then you’d have to carry the one over to the next column and so forth. Partial sums lets kids know that they can really pick any part in the problem that you want to and start adding and it doesn’t have to be so isolated to one particular way. The place value strips will come back to make another appearance when we use them in the subtraction Math Mights 8-in-1 poster that is coming early summer 2018!
Variations and Terminology
We choose, in the poster, to use number bonding. I’m a fan of number bonding because it’s such concrete visual for kids to see numbers coming apart. Some schools and some programs use a different method, though, so you might show the partial sums strategy differently than we do on the poster. You might show place value in expanded form of the algorithm. Either way is correct. If kids want to write it out more abstractly, they’re welcome to do that. Students that don’t understand partial sums truly need to act it out with the place value strips where they literally are using manipulatives to exchange and add numbers to figure out the total so they can really understand what they’re doing. You don’t want them to just follow a procedure, but they’re able to explain why they’re doing what they’re doing. Many of our 2nd and 3rd graders love this strategy of partial sums! Remember that a lot of many of the Math Mights strategies are called different things. For partial sums, in your book, it might be called the distributive property, or it might be called expanded form, but to me, that is really taking the number and breaking it apart. The act of adding the numbers together is the part that we call partial sums, where you take the parts of the numbers and add them together separately. So, you might use expanded form or distributive property for place value, but then use partial sums when you’re ready for the act of adding the parts together. It’s important that kids know the different names, what your book actually calls it, and then what the state test might call it. The test probably won’t say “math mountains” or certain words that your math program might use, so kids almost need a thesaurus of different vocabulary words for how we might talk about these strategies so they’re prepared when they see it written differently.