Final answer:
Dienes blocks allow Foundation Phase learners to represent and solve the addition sum 176+245 by using physical blocks for hundreds, tens, and ones, teaching them to combine and exchange blocks to handle carrying over numbers.
Step-by-step explanation:
Foundation Phase learners can use Dienes blocks (also known as base-10 blocks) to visually represent the addition sum 176+245 by using physical blocks to denote hundreds, tens, and ones. For the number 176, learners would select 1 hundred block, 7 ten blocks, and 6 one blocks. For the number 245, they would need 2 hundred blocks, 4 ten blocks, and 5 one blocks. When these blocks are combined, the students need to group them according to their place value.
The students then begin by adding the ones: 6 one blocks plus 5 one blocks equals 11 one blocks. As 10 one blocks can be exchanged for 1 ten block, this leaves them with 1 one block and 1 extra ten block. Now, the tens are added: 7 ten blocks plus 4 ten blocks plus the extra ten block from the ones exchange equal 12 ten blocks. Again, since 10 ten blocks can be exchanged for 1 hundred block, 12 ten blocks are condensed into 1 hundred block and 2 ten blocks. Lastly, when adding the hundreds, the students combine the original 1 hundred block from 176 with the 2 hundred blocks from 245 and the extra hundred block from the tens exchange, totaling 4 hundred blocks.
Now all the place values are counted: 4 hundred blocks, 2 ten blocks, and 1 one block, which summed up gives the result 421. Through this activity, they understand how addition can lead to changes in place value and how to handle carrying over numbers to the next highest place value.