Deprecated: Creation of dynamic property wpdb::$categories is deprecated in /var/www/twodee/blog/wp-includes/wp-db.php on line 668

Deprecated: Creation of dynamic property wpdb::$post2cat is deprecated in /var/www/twodee/blog/wp-includes/wp-db.php on line 668

Deprecated: Creation of dynamic property wpdb::$link2cat is deprecated in /var/www/twodee/blog/wp-includes/wp-db.php on line 668

Deprecated: Return type of WP_Theme::offsetExists($offset) should either be compatible with ArrayAccess::offsetExists(mixed $offset): bool, or the #[\ReturnTypeWillChange] attribute should be used to temporarily suppress the notice in /var/www/twodee/blog/wp-includes/class-wp-theme.php on line 554

Deprecated: Return type of WP_Theme::offsetGet($offset) should either be compatible with ArrayAccess::offsetGet(mixed $offset): mixed, or the #[\ReturnTypeWillChange] attribute should be used to temporarily suppress the notice in /var/www/twodee/blog/wp-includes/class-wp-theme.php on line 595

Deprecated: Return type of WP_Theme::offsetSet($offset, $value) should either be compatible with ArrayAccess::offsetSet(mixed $offset, mixed $value): void, or the #[\ReturnTypeWillChange] attribute should be used to temporarily suppress the notice in /var/www/twodee/blog/wp-includes/class-wp-theme.php on line 535

Deprecated: Return type of WP_Theme::offsetUnset($offset) should either be compatible with ArrayAccess::offsetUnset(mixed $offset): void, or the #[\ReturnTypeWillChange] attribute should be used to temporarily suppress the notice in /var/www/twodee/blog/wp-includes/class-wp-theme.php on line 544

Deprecated: Return type of WP_REST_Request::offsetExists($offset) should either be compatible with ArrayAccess::offsetExists(mixed $offset): bool, or the #[\ReturnTypeWillChange] attribute should be used to temporarily suppress the notice in /var/www/twodee/blog/wp-includes/rest-api/class-wp-rest-request.php on line 960

Deprecated: Return type of WP_REST_Request::offsetGet($offset) should either be compatible with ArrayAccess::offsetGet(mixed $offset): mixed, or the #[\ReturnTypeWillChange] attribute should be used to temporarily suppress the notice in /var/www/twodee/blog/wp-includes/rest-api/class-wp-rest-request.php on line 980

Deprecated: Return type of WP_REST_Request::offsetSet($offset, $value) should either be compatible with ArrayAccess::offsetSet(mixed $offset, mixed $value): void, or the #[\ReturnTypeWillChange] attribute should be used to temporarily suppress the notice in /var/www/twodee/blog/wp-includes/rest-api/class-wp-rest-request.php on line 992

Deprecated: Return type of WP_REST_Request::offsetUnset($offset) should either be compatible with ArrayAccess::offsetUnset(mixed $offset): void, or the #[\ReturnTypeWillChange] attribute should be used to temporarily suppress the notice in /var/www/twodee/blog/wp-includes/rest-api/class-wp-rest-request.php on line 1003

Deprecated: Return type of WP_Block_List::current() should either be compatible with Iterator::current(): mixed, or the #[\ReturnTypeWillChange] attribute should be used to temporarily suppress the notice in /var/www/twodee/blog/wp-includes/class-wp-block-list.php on line 151

Deprecated: Return type of WP_Block_List::next() should either be compatible with Iterator::next(): void, or the #[\ReturnTypeWillChange] attribute should be used to temporarily suppress the notice in /var/www/twodee/blog/wp-includes/class-wp-block-list.php on line 175

Deprecated: Return type of WP_Block_List::key() should either be compatible with Iterator::key(): mixed, or the #[\ReturnTypeWillChange] attribute should be used to temporarily suppress the notice in /var/www/twodee/blog/wp-includes/class-wp-block-list.php on line 164

Deprecated: Return type of WP_Block_List::valid() should either be compatible with Iterator::valid(): bool, or the #[\ReturnTypeWillChange] attribute should be used to temporarily suppress the notice in /var/www/twodee/blog/wp-includes/class-wp-block-list.php on line 186

Deprecated: Return type of WP_Block_List::rewind() should either be compatible with Iterator::rewind(): void, or the #[\ReturnTypeWillChange] attribute should be used to temporarily suppress the notice in /var/www/twodee/blog/wp-includes/class-wp-block-list.php on line 138

Deprecated: Return type of WP_Block_List::offsetExists($index) should either be compatible with ArrayAccess::offsetExists(mixed $offset): bool, or the #[\ReturnTypeWillChange] attribute should be used to temporarily suppress the notice in /var/www/twodee/blog/wp-includes/class-wp-block-list.php on line 75

Deprecated: Return type of WP_Block_List::offsetGet($index) should either be compatible with ArrayAccess::offsetGet(mixed $offset): mixed, or the #[\ReturnTypeWillChange] attribute should be used to temporarily suppress the notice in /var/www/twodee/blog/wp-includes/class-wp-block-list.php on line 89

Deprecated: Return type of WP_Block_List::offsetSet($index, $value) should either be compatible with ArrayAccess::offsetSet(mixed $offset, mixed $value): void, or the #[\ReturnTypeWillChange] attribute should be used to temporarily suppress the notice in /var/www/twodee/blog/wp-includes/class-wp-block-list.php on line 110

Deprecated: Return type of WP_Block_List::offsetUnset($index) should either be compatible with ArrayAccess::offsetUnset(mixed $offset): void, or the #[\ReturnTypeWillChange] attribute should be used to temporarily suppress the notice in /var/www/twodee/blog/wp-includes/class-wp-block-list.php on line 127

Deprecated: Return type of WP_Block_List::count() should either be compatible with Countable::count(): int, or the #[\ReturnTypeWillChange] attribute should be used to temporarily suppress the notice in /var/www/twodee/blog/wp-includes/class-wp-block-list.php on line 199

Deprecated: Creation of dynamic property Automattic\Jetpack\Connection\Manager::$error_handler is deprecated in /var/www/twodee/blog/wp-content/plugins/jetpack/vendor/automattic/jetpack-connection/src/class-manager.php on line 91

Deprecated: Creation of dynamic property WPCOM_REST_API_V2_Endpoint_Instagram_Gallery::$is_wpcom is deprecated in /var/www/twodee/blog/wp-content/plugins/jetpack/_inc/lib/core-api/wpcom-endpoints/class-wpcom-rest-api-v2-endpoint-instagram-gallery.php on line 23

Deprecated: Creation of dynamic property WPCOM_REST_API_V2_Endpoint_Mailchimp::$wpcom_is_wpcom_only_endpoint is deprecated in /var/www/twodee/blog/wp-content/plugins/jetpack/_inc/lib/core-api/wpcom-endpoints/class-wpcom-rest-api-v2-endpoint-mailchimp.php on line 17

Deprecated: Creation of dynamic property WPCOM_REST_API_V2_Endpoint_Tweetstorm_Gather::$wpcom_is_wpcom_only_endpoint is deprecated in /var/www/twodee/blog/wp-content/plugins/jetpack/_inc/lib/core-api/wpcom-endpoints/class-wpcom-rest-api-v2-endpoint-tweetstorm-gather.php on line 21

Deprecated: Creation of dynamic property WPCOM_REST_API_V2_Endpoint_Tweetstorm_Gather::$is_wpcom is deprecated in /var/www/twodee/blog/wp-content/plugins/jetpack/_inc/lib/core-api/wpcom-endpoints/class-wpcom-rest-api-v2-endpoint-tweetstorm-gather.php on line 22

Deprecated: Creation of dynamic property WPCOM_REST_API_V2_Endpoint_Gutenberg_Available_Extensions::$wpcom_is_site_specific_endpoint is deprecated in /var/www/twodee/blog/wp-content/plugins/jetpack/_inc/lib/core-api/wpcom-endpoints/gutenberg-available-extensions.php on line 20

Deprecated: Creation of dynamic property WPCOM_REST_API_V2_Endpoint_Memberships::$wpcom_is_wpcom_only_endpoint is deprecated in /var/www/twodee/blog/wp-content/plugins/jetpack/_inc/lib/core-api/wpcom-endpoints/memberships.php on line 23

Deprecated: Creation of dynamic property WPCOM_REST_API_V2_Endpoint_Memberships::$wpcom_is_site_specific_endpoint is deprecated in /var/www/twodee/blog/wp-content/plugins/jetpack/_inc/lib/core-api/wpcom-endpoints/memberships.php on line 24

Deprecated: Creation of dynamic property WPCOM_REST_API_V2_Endpoint_Subscribers::$wpcom_is_wpcom_only_endpoint is deprecated in /var/www/twodee/blog/wp-content/plugins/jetpack/_inc/lib/core-api/wpcom-endpoints/subscribers.php on line 15

Deprecated: Creation of dynamic property Automattic\Jetpack\Sync\Queue::$random_int is deprecated in /var/www/twodee/blog/wp-content/plugins/jetpack/vendor/automattic/jetpack-sync/src/class-queue.php on line 38

Deprecated: Creation of dynamic property Automattic\Jetpack\Sync\Queue::$random_int is deprecated in /var/www/twodee/blog/wp-content/plugins/jetpack/vendor/automattic/jetpack-sync/src/class-queue.php on line 38

Deprecated: Creation of dynamic property WPCOM_Widget_Goodreads::$shelves is deprecated in /var/www/twodee/blog/wp-content/plugins/jetpack/modules/widgets/goodreads.php on line 33

Deprecated: DateTime::__construct(): Passing null to parameter #1 ($datetime) of type string is deprecated in /var/www/twodee/blog/wp-includes/script-loader.php on line 348

Deprecated: Creation of dynamic property Advanced_Editor_Tools::$toolbar_classic_block is deprecated in /var/www/twodee/blog/wp-content/plugins/tinymce-advanced/tinymce-advanced.php on line 347

Deprecated: Creation of dynamic property Advanced_Editor_Tools::$toolbar_block is deprecated in /var/www/twodee/blog/wp-content/plugins/tinymce-advanced/tinymce-advanced.php on line 349

Deprecated: Creation of dynamic property Advanced_Editor_Tools::$toolbar_block_side is deprecated in /var/www/twodee/blog/wp-content/plugins/tinymce-advanced/tinymce-advanced.php on line 350

Deprecated: Creation of dynamic property Advanced_Editor_Tools::$panels_block is deprecated in /var/www/twodee/blog/wp-content/plugins/tinymce-advanced/tinymce-advanced.php on line 351

Deprecated: Creation of dynamic property Advanced_Editor_Tools::$used_block_buttons is deprecated in /var/www/twodee/blog/wp-content/plugins/tinymce-advanced/tinymce-advanced.php on line 354

Deprecated: Creation of dynamic property WP_Block_Type::$plan_check is deprecated in /var/www/twodee/blog/wp-includes/class-wp-block-type.php on line 333

Deprecated: Creation of dynamic property WP_Block_Type::$plan_check is deprecated in /var/www/twodee/blog/wp-includes/class-wp-block-type.php on line 333

Deprecated: Creation of dynamic property WP_Block_Type::$plan_check is deprecated in /var/www/twodee/blog/wp-includes/class-wp-block-type.php on line 333

Deprecated: Creation of dynamic property WP_Block_Type::$plan_check is deprecated in /var/www/twodee/blog/wp-includes/class-wp-block-type.php on line 333

Deprecated: Creation of dynamic property WP_Block_Type::$plan_check is deprecated in /var/www/twodee/blog/wp-includes/class-wp-block-type.php on line 333

Deprecated: Creation of dynamic property WP_Block_Type::$plan_check is deprecated in /var/www/twodee/blog/wp-includes/class-wp-block-type.php on line 333

Deprecated: ltrim(): Passing null to parameter #1 ($string) of type string is deprecated in /var/www/twodee/blog/wp-includes/wp-db.php on line 3030

Deprecated: Creation of dynamic property WP_Term::$object_id is deprecated in /var/www/twodee/blog/wp-includes/class-wp-term.php on line 198

Deprecated: Creation of dynamic property WP_Term::$object_id is deprecated in /var/www/twodee/blog/wp-includes/class-wp-term.php on line 198

Deprecated: Creation of dynamic property WP_Term::$object_id is deprecated in /var/www/twodee/blog/wp-includes/class-wp-term.php on line 198

Deprecated: Creation of dynamic property WP_Term::$object_id is deprecated in /var/www/twodee/blog/wp-includes/class-wp-term.php on line 198

Deprecated: Creation of dynamic property WP_Term::$object_id is deprecated in /var/www/twodee/blog/wp-includes/class-wp-term.php on line 198

Deprecated: Creation of dynamic property WP_Term::$object_id is deprecated in /var/www/twodee/blog/wp-includes/class-wp-term.php on line 198

Deprecated: Creation of dynamic property WP_Term::$object_id is deprecated in /var/www/twodee/blog/wp-includes/class-wp-term.php on line 198

Deprecated: Creation of dynamic property WP_Term::$object_id is deprecated in /var/www/twodee/blog/wp-includes/class-wp-term.php on line 198

Deprecated: Creation of dynamic property WP_Term::$cat_ID is deprecated in /var/www/twodee/blog/wp-includes/category.php on line 378

Deprecated: Creation of dynamic property WP_Term::$category_count is deprecated in /var/www/twodee/blog/wp-includes/category.php on line 379

Deprecated: Creation of dynamic property WP_Term::$category_description is deprecated in /var/www/twodee/blog/wp-includes/category.php on line 380

Deprecated: Creation of dynamic property WP_Term::$cat_name is deprecated in /var/www/twodee/blog/wp-includes/category.php on line 381

Deprecated: Creation of dynamic property WP_Term::$category_nicename is deprecated in /var/www/twodee/blog/wp-includes/category.php on line 382

Deprecated: Creation of dynamic property WP_Term::$category_parent is deprecated in /var/www/twodee/blog/wp-includes/category.php on line 383

Deprecated: Creation of dynamic property WP_Term::$cat_ID is deprecated in /var/www/twodee/blog/wp-includes/category.php on line 378

Deprecated: Creation of dynamic property WP_Term::$category_count is deprecated in /var/www/twodee/blog/wp-includes/category.php on line 379

Deprecated: Creation of dynamic property WP_Term::$category_description is deprecated in /var/www/twodee/blog/wp-includes/category.php on line 380

Deprecated: Creation of dynamic property WP_Term::$cat_name is deprecated in /var/www/twodee/blog/wp-includes/category.php on line 381

Deprecated: Creation of dynamic property WP_Term::$category_nicename is deprecated in /var/www/twodee/blog/wp-includes/category.php on line 382

Deprecated: Creation of dynamic property WP_Term::$category_parent is deprecated in /var/www/twodee/blog/wp-includes/category.php on line 383

Deprecated: Creation of dynamic property WP_Term::$cat_ID is deprecated in /var/www/twodee/blog/wp-includes/category.php on line 378

Deprecated: Creation of dynamic property WP_Term::$category_count is deprecated in /var/www/twodee/blog/wp-includes/category.php on line 379

Deprecated: Creation of dynamic property WP_Term::$category_description is deprecated in /var/www/twodee/blog/wp-includes/category.php on line 380

Deprecated: Creation of dynamic property WP_Term::$cat_name is deprecated in /var/www/twodee/blog/wp-includes/category.php on line 381

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Deprecated: Creation of dynamic property WP_Term::$category_parent is deprecated in /var/www/twodee/blog/wp-includes/category.php on line 383
» math

teaching machines

Seven Digit Study

My son and I are on our way to school. It’s just the two of us. These drives should be a great opportunity for some genuine father-son talk, but it rarely happens. My mind is usually anxious about the day ahead, the traffic around us, and the hazards of winter. Even when we do talk, […]

Apathetic Numbers

My son is 11, and he likes to think about numbers. In this time of working and learning from home, I’ve had him reading Isaac Asimov’s Realm of Numbers. The other day my son stumbled upon this numerical curiosity: $$3 \times 1.5 = 3 + 1.5$$ How fascinating that the numbers don’t care whether they […]

The Law of Doubled Digit Transposition Over Multiplication

My son is learning long division at school. He was intimidated by it, so we started practicing for just a few minutes every day after school. The format is simple: I generate two numbers, a big dividend and a small divisor, and he divides them. One day I wanted the quotient to be 99 because […]

Five through Fifteen

On our walks home from school, my 8-year-old son has been telling me of a math problem that he has not been able to solve. Yesterday, after a week of not finding a solution, he wrote down the problem on paper for us to investigate together. Here is the task in my own words: Distribute […]