adding a two-digit number & a multiple of 10 1.NBT.4 Quick image John A. Van de Walle, Elementary and Middle School Mathematics: Teaching Developmentally • Say the Ten Fact, p. 165

1.NBT.4 Standard Add within 100, including adding a two-digit number and a one-digit number, and adding a two-digit number and a multiple of 10, 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. Understand that in adding two-digit numbers, one adds tens and tens, ones and ones; and sometimes it is necessary to compose a ten.

Let’s count by tens starting with 3….. Grade 1 is students first encounter with the three linked components of the place value system. Use a hundreds chart. Use ten frame.

3 13 What do you see ? Kindergarten ……3 ones and 10 more ones 13 3 + 10 = 13

3 13 23 33 Can you count from any given number? 3, 13, 23, 33 Use drawings Count backwards by 10’s to show that the ones place will remain 3 33

3 + 10 + 10 + 10 = 33 Relate the strategy to a written method and explain the reasoning. Understand that in adding two digit numbers, one adds tens and tens, ones and ones; and sometimes it is necessary to compose a ten. Is 10+10+13=33?

10 20 + = 43 30 Understand place value is not the final goal on its own: the goal is to use place value understanding and properties of operations to add and subtract. Use models and drawings to = 43 What needs to be added to 33 to get to 43? Explain 33 + 10

Let’s count by tens starting with 24….. Being able to represent these additions with materials that show base ten structure Have a strong mental image and ability with simple versions of these additions 24+10=34 24+10+10=44 Count on Show how the ones place stays at 4 but the 10’s place increases each time you add 10

= 34 + Use base 10 blocks. Think of 10 as a unit and understanding that the digits of a two-digit number represent the number of complete tens in that number and the number of remaining ones. If we added 3 more sets of 10 what would we have now? Explain or draw your answer. 24 10

= 44 + 34 10 What was added to 34 to equal 44? What would come next if we added another group of 10? 34 10

= 54 + Will the 4 ever change if we are only adding groups of 10? Students can use models such as base ten blocks to initially solve addition problems, but should fully understand that this type of problem involves adding multiples of ten. 44 10

= 64 + Demonstrate understanding of adding tens and multiples of ten as only changing the tens digit using decomposition. Review if need be counting by just 10’s. A ten frame be used instead of base 10 blocks. Use a hundreds chart. 54 10

What is the pattern? Students gradually come to use sophisticated strategies (such as making ten) that depend on the properties of addition and subtraction. To extend students understanding of place value they should be given opportunities to count starting at any given number and add 10. Draw the pattern and use base ten blocks with a partner.

Now Try These 10 + 4 = 14 Have students write two addition equations in their notebooks: This one and an equation with a “friendly ten”

Now Try These 20 + 4 = 24 Have students write two addition equations in their notebooks: This one and an equation with a “friendly ten” Is 20+4 the same as 10+10+4

Now Try These 30 + 4 = 34 Have students write two addition equations in their notebooks: This one and an equation with a “friendly ten” What was added to 20+4=24 to get to 30+4=34 Higher level thinking student can solve missing addends 30+?= 34

Now Try These 40 + 4 = 44 Have students write two addition equations in their notebooks: This one and an equation with a “friendly ten”